Science, Faculty of
Earth, Ocean and Atmospheric Sciences, Department of
DSpace
UBCV
Calderwood, Arthur Robertson
Doctor of Philosophy - PhD
University of British Columbia
Numerical mineral physics modeling is used in seven studies to constrain the composition and dynamics of the Earth's mantle. First, using updated, published experimental data, I evaluate two competing mineralogical models for the composition of the mantle by calculating and comparing one dimensional profiles of density (ρ) and bulk sound velocity (V[sub Φ]) against seismologically inferred profiles. I find that the mineralogy of a uniform bulk composition provides an excellent fit to the seismic properties of the whole mantle along a self-consistent adiabatic geotherm which lacks any thermal boundary layers internal to the mantle. In contrast, the mineralogy of a chemically layered bulk composition results in predicted profiles which cannot satisfy the observations. Second, to further test the predicted properties of the uniform composition, pyrolite model, the mineral physics calculations are extended to predict one dimensional profiles of shear (V[sub S]) and compression (V[sub P]) velocity across the upper mantle and transition zone. Previous studies that modeled V[sub S] and V[sub P] suffered from having to estimate many of the necessary temperature and pressure derivatives required in the calculations and hence, the results were ambiguous. Fortuitously, many of these critical material properties (μ, (მμ/მT)[sub P,] (მμ/მP)[sub T],) are now experimentally measured and this study incorporates the latest results. I find that the predicted profiles of V[sub S] and V[sub P] are in excellent agreement in terms of both velocity gradient and absolute velocity with the latest, high-resolution regional seismic profiles. The predicted mineral physics profiles also give a mutually consistent estimate of the olivine content of the mantle from the velocity jumps at the 410 km seismic discontinuity. Lastly, the predicted V[sub S] and V[sub P] normalincidence reflectivity of the 410 km, 520 km and 660 km discontinuities matches a number of independent seismic estimates. Third, I estimate a high temperature value for [მμ/მT)[sup Mg-Pv][sub p] of Mg-perovskite via constrained adiabatic decompression of the lower mantle PREM seismic properties. A simplified pyrolite lower mantle mineralogy of magnesiowustite and Mg-Fe perovskite is used to provide apriori constraints for some of the unknown high temperature decompressed properties thereby restricting the possible parameter space for the decompressed hot shear modulus (μ[sub O]). This property is used to constrain the value of [მμ/მT)[sup Mg-Pv][sub p] when the room temperature properties are corrected up to the decompressed, but hot lower mantle elastic properties. Fourth, adopting this estimate of [მμ/მT)[sup Mg-Pv][sub p],and estimating ([მμ/მT)[sup Ca-Pv][sub p]) via a high temperature thermodynamic approximation, I then iteratively adjust the unmeasured pressure derivative, [მμ/მP)[sup Mg-Pv][sub T] , under the first order assumption [მμ/მP)[sup Mg-Pv][sub T]= [მμ/მP)[sup Ca-Pv][sub T] , until predicted one dimensional profiles of V[sub S] and V[sub P] for a pyrolite mineralogy match the seismic profiles across the lower mantle. I justify "tuning" the predicted profiles to the observed ones on the basis of the results of chapter two where it was demonstrated with ρ and V[sub Φ] profiles that a pyrolite mineralogy could match the lower mantle properties along a self-consistent adiabatic geotherm. Because the selfconsistent adiabatic geotherm and all of the thermoelastic properties used earlier in calculating ρ and V[sub Φ] are also used to model shear and compression velocity, the predicted V[sub S] and V[sub P] profiles must also agree with the observed profiles. Fifth, I incorporate the recent experimental (Sinelnikov et al., 1998) and theoretical (Karki et al., 1997) values for Mgperovskite and compare these with the inferences deduced in the previous chapters. While the estimated temperature derivatives compare favorably with the with the recent experimental values, I find that to satisfy both the experimental and theoretical pressure dependence, Mg-perovskite must be fit by a 4th order, rather than 3rd order, Birch-Murnaghan equation of state. Sixth, I utilize the pyrolite V[sub S] and V[sub P] profiles to evaluate the ratio of relative V[sub S] and V[sub P] velocity heterogeneity in the mantle via the parameter (მlnV[sub S]/ მlnV[sub P]) . I find that the predicted profile of (მlnV[sub S]/ მlnV[sub P])[sub p] for the pyrolite mantle is within error of the various seismic estimates, and hence, there is no discrepancy between the tomographic models and a melt-free, uniform bulk composition mantle. Seventh, I estimate new extremal bounds for the lateral temperature anomalies in the mantle using the pyrolite mineral physics model of V[sub S] and V[sub P]. I find that the inferred magnitude of the lateral temperature anomalies are significantly reduced compared to previous inferences with δT now ranging from ~ 100 °K at 660 km to ~ ± 480 °K at the top of the D" layer. I conclude that away from chemical and thermal boundary layers, the lateral seismic anomalies resolved in tomographic studies are largely thermal in origin and consequently, the dominant force driving mantle convection is indeed thermal buoyancy.
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Mineral Physics constraints on the Chemical Composition Temperature of the Earth's mantle By Arthur Robertson Calderwood B. Sc. Hon. (Geological Sciences) University of British Columbia M.Phil. (Geology and Geophysics) Yale University A THESIS SUBMITTED IN PARTIAL F U L F I L L M E N T OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE F A C U L T Y OF G R A D U A T E STUDIES E A R T H A N D O C E A N SCIENCES - G E O L O G Y We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH C O L U M B I A 1999 © Arthur Robertson Calderwood, 1999 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of / f e s S ^ / fhv)? tVsx&W £*G/J&&CS The University of British Columbia Vancouver, Canada DE-6 (2/88) Abstract Numerical mineral physics modeling is used in seven studies to constrain the composition and dynamics of the Earth's mantle. First, using updated, published experimental data, I evaluate two competing mineralogical models for the composition of the mantle by calculating and comparing one dimensional profiles of density (p) and bulk sound velocity (T 0) against seismologically inferred profiles. I find that the mineralogy of a uniform bulk composition provides an excellent fit to the seismic properties of the whole mantle along a self-consistent adiabatic geotherm which lacks any thermal boundary layers internal to the mantle. In contrast, the mineralogy of a chemically layered bulk composition results in predicted profiles which cannot satisfy the observations. Second, to further test the predicted properties of the uniform composition, pyrolite model, the mineral physics calculations are extended to predict one dimensional profiles of shear (V$) and compression (Vp) velocity across the upper mantle and transition zone. Previous studies that modeled Vg and Vp suffered from having to estimate many of the necessary temperature and pressure derivatives required in the calculations and hence, the results were ambiguous. Fortuitously, many of these critical material properties (p, (d[i/dT)p, (d\x/dP)T,) are now experimentally measured and this study incorporates the latest results. I find that the predicted profiles of V$ and Vp are in excellent agreement in terms of both velocity gradient and absolute velocity with the latest, high-resolution regional seismic profiles. The predicted mineral physics profiles also give a mutually consistent estimate of the olivine content of the mantle from the velocity jumps at the 410 km seismic discontinuity. Lastly, the predicted V$ and Vp normal-incidence reflectivity of the 410 km, 520 km and 660 km discontinuities matches a number of i i independent seismic estimates. Third, I estimate a high temperature value for [d\\./dT) 8 v of Mg-perovskite via constrained adiabatic decompression of the lower mantle P R E M seismic properties. A simplified pyrolite lower mantle mineralogy of magnesiowustite and Mg-Fe perovskite is used to provide apriori constraints for some of the unknown high temperature decompressed properties thereby restricting the possible parameter space for the decompressed hot shear modulus (u.0). This property is used to constrain the value of (du./3r)^ g P v when the room temperature properties are corrected up to the decompressed, but hot lower mantle elastic properties. Fourth, adopting this estimate of {d^i/dT)^8 Pv,and estimating (<3u,/9r)^a Pv via a high temperature thermodynamic approximation, I then iteratively adjust the unmeasured pressure derivative, ( 5 p / 5 P ) ^ g P v , under the first order assumption ( 9 p / 3 P ) ^ g P v = (du./dP)^ a P v , until predicted one dimensional profiles of Vg and Vp for a pyrolite mineralogy match the seismic profiles across the lower mantle. I justify "tuning" the predicted profiles to the observed ones on the basis of the results of chapter two where it was demonstrated with p and V0 profiles that a pyrolite mineralogy could match the lower mantle properties along a self-consistent adiabatic geotherm. Because the self-consistent adiabatic geotherm and all of the thermoelastic properties used earlier in calculating p and V® are also used to model shear and compression velocity, the predicted V$ and Vp profiles must also agree with the observed profiles. Fifth, I incorporate the recent experimental (Sinelnikov et al., 1998) and theoretical (Karki et al., 1997) values for Mg-perovskite and compare these with the inferences deduced in the previous chapters. While the estimated temperature derivatives compare favorably with the with the recent experimental i i i values, I find that to satisfy both the experimental and theoretical pressure dependence, Mg-perovskite must be fit by a 4 t h order, rather than 3 r d order, Birch-Murnaghan equation of state. Sixth, I utilize the pyrolite Vs and Vp profiles to evaluate the ratio of relative V$ and Vp velocity heterogeneity in the mantle via the parameter (d\nVs/dlnVP) . I find that the predicted profile of (dlnVs/d\nVP)p for the pyrolite mantle is within error of the various seismic estimates, and hence, there is no discrepancy between the tomographic models and a melt-free, uniform bulk composition mantle. Seventh, I estimate new extremal bounds for the lateral temperature anomalies in the mantle using the pyrolite mineral physics model of V$ and Vp. I find that the inferred magnitude of the lateral temperature anomalies are significantly reduced compared to previous inferences with 87 now ranging from « ± 100 °K at 660 km to « ± 480 °K at the top of the D" layer. I conclude that away from chemical and thermal boundary layers, the lateral seismic anomalies resolved in tomographic studies are largely thermal in origin and consequently, the dominant force driving mantle convection is indeed thermal buoyancy. iv Table of Contents Abstract i i Table of Contents v List of Figures xi List of Tables xlii i Dedication xlvii Acknowledgments xlix 1. Introduction 1 1.1 Background 1 1.2 Isotopic structure of the Mantle 8 1.3 Subduction zone structure 10 1.4 Bulk Mantle Composition 13 1.5 Presentation 15 1.6 References 20 2. Mineral Physics constraints on the Chemical composition and Temperature of 41 the Earth's mantle from Density and Bulk Sound velocity profiles. 2.1 Abstract 42 2.2 Introduction 44 2.3 Previous work 51 2.4 Methods 53 2.5 Mineralogical models 53 2.6 Equation of state 59 2.7 Elasticity data set 59 2.8 Olivine phases 60 2.9 Orthopyroxene phases 61 2.10 Majorite phases 63 2.11 Lower Mantle phases 65 2.12 Steps in Calculating p, and V® 72 2.13 Self-Consistent Adiabatic Geotherm 78 2.14 Results 82 2.15 Adiabatic Geotherm 82 2.16 Upper Mantle Density 83 2.17 Lower Mantle Density 86 2.18 Upper Mantle Bulk Sound 88 Velocity v 2.19 Lower Mantle Bulk Sound Velocity 91 2.20 Discussion 94 2.21 Thermal Boundaries at Chemical boundaries 95 2.22 Independent Constraints on Mantle Geotherms and 98 chemistry 2.23 Can a Chemically Distinct Lower Mantle be seismically 104 invisible? 2.24 Implications of the Next Generation of Reference 106 Seismic Models 2.25 Conclusions 109 2.26 References 115 2.27 Appendix 146 3. Mineral Physics constraints on the Chemical Composition of the Earth's 220 mantle from V s and V P velocity profiles; a test of the Pyrolite model. 3.1 Abstract ~ 221 3.2 Introduction 223 3.3 Methodology 236 3.4 Thermoelastic database 236 3.5 Fe effect on P-olivine phase 247 3.6 Majorite phases 247 3.7 Orthopyroxene 251 3.8 Perovskites 252 3.9 Temperature and Pressure derivatives 254 3.10 Mineralogically plausible values for (9 \x/d-P)T and 263 3.11 Equation of State: steps in calculating Vs and Vp 267 3.12 High Pressure Parameterization; density and bulk 267 modulus 3.13 High Pressure Parameterization; shear modulus 271 3.14 Shear modulus; non-linear extrapolations 272 in pressure 3.15 Self-consistent Adiabatic Geotherm 273 3.16 Aggregate properties 276 3.17 Results 277 3.18 A Mutually consistent olivine content from the 410 km 284 ( ; \ olivine d[i/8Tj 3.19 Reflection Properties of Mantle discontinuities 293 3.20 Vs reflectivity; ScS reflection coefficients 294 3.21 Vp reflectivity 300 3.22 Discussion 305 3.23 Conclusions 311 3.24 References 314 vi 3.25 Appendix 334 4. Constrained Adiabatic Decompression of a Pyrolite Lower Mantle and 394 constraints on {d u,/d Tj^ for Mg-perovskite from \xn and Poisson's ratio (a). 4.1 Abstract 395 4.2 Introduction 397 4.3 Methods 409 4.4 4th order finite strain equations 409 4.5 Constrained Decompression 414 4.6 Mineralogical Model: simplified pyrolite model 417 4.7 Correction from room temperature to Tp 422 4.8 Results 423 4.9 Discussion 428 4.10 Conclusions 436 4.11 References 439 5. Mineral Physics constraints on the Chemical Composition of the Earth's lower 453 mantle from Vs and VP velocity profiles; a test of the Pyrolite model. 5.1 Abstract ~ 454 5.2 Introduction 456 5.3 Methodology 462 5.4 Experimental Data base 463 5.5 magnesiowustite (Mg 0 8 6 Fe 0 ! 4 )0 465 5.6 Ca-perovskite shear modulus 466 5.7 Mg-perovskite 468 5.8 Temperature and Pressure derivatives of the shear 489 modulus 5.9 Mineralogical Plausible estimates of (d\i/dT\, 497 5.10 Equation of State 501 5.11 High Pressure Parameterization; density 502 and bulk modulus 5.12 High Pressure Parameterization; Shear 5 06 Modulus 5.13 Self-Consistent Adiabatic Geotherm 507 5.14 Aggregate properties 510 5.15 Results . 5 1 1 5.16 Discussion 512 5.17 Conclusions 515 5.18 References 519 6. Lower Mantle Kyand VP profiles revisited: The effects of experimental values of 549 (Sp/Sr)^ and (d\x/dP)T for Mg-perovskite. 6.1 Abstract 550 vii 6.2 Introduction 5 51 6.3 Experimental values for Mg-perovskite (d p/5 T)p 553 and (d[i/8P)p 6.4 Theoretical predictions of Ks(P) and p(P) for Mg- 554 perovskite: (d\i/dP)p and (d2 \i/dP2)p 6.5 Magnesiowiistite (Mg 0 8 6 Fe 0 1 4 )0 557 6.6 Results 558 6.7 Conclusions 559 6.8 References 561 7. Mineral Physics estimates of the ratio of Relative Vs and VP velocity 570 heterogeneity \\d\nVjd \nVP} in the mantle. 7.1 Abstract 571 7.2 Introduction 573 7.3 Previous Seismic estimates of (d lnVs /8 XnVp ) p 577 7.4 Upper mantle (d XnVs /8 XnVP ) p from the ratio of PP-P 578 and SS-S differential travel time residuals. 7.5 Upper mantle (dlnVs /8XnVP )p from Global S and P 580 station corrections. 7.6 (5 XnVs /8 \nVP ) p at the top of the Lower Mantle from 588 the Caribbean anomaly 7.7 Lower mantle (d XnVs /d XnVP ) p from the ratio of ScS-S 591 and PcP-P differential time residuals (&tPcP_P /§tScS_s) and the ratio of absolute S and P travel time residuals. 7.8 Ratio of RMS velocity amplitudes of S and P-wave 596 tomographic models 7.9 Stochastic inversion of ISC P and S traveltimes 616 7.10 Lower Mantle average from free oscillation seismology 621 7.11 (dXnVj8 XnVP}pintheD" region fromPlU>(ab-dt) 6 4 2 differential travel times? 7.12 Summary of Seismic estimates of (d ln^ /dXnVp ) p 646 7.13 Previous estimates of (d XnVs /8 XnVP ) p from Mineral Physics. 652 7.14 Theoretical Mineral Physics estimates; molecular 653 dynamics simulations 7.15 (a In Vs /8XnVP)p: hydrous Partial Melts in the Lower 659 Mantle? 7.16 The effects of Anelasticity 670 7.17 (a XnVs/8 XnVP)p from experimental mineral physics 675 7.18 Summary of Mineral physics estimates 677 viii 7.19 Methodology 678 7.20 Results and Discussion 680 7.21 Conclusions 692 7.22 References 696 8. A Thermal Origin for Seismic Anomalies from Mineral Physics modeling of a 783 Pyrolite mantle and Seismic Tomography. 8.1 Abstract 784 8.2 Introduction 786 8.3 Previous Work 787 8.4 Lava eruption temperatures 788 8.5 Oceanic heat flow and bathymetry 788 8.6 The genesis of M O R B magmas; decompression melting 800 of mid-ocean ridge basalts. 8.7 Estimates on Lateral Temperature Anomalies in the 819 Transition zone from ScS Reverberations. 8.8 Global Mapping of transition zone discontinuity 829 topography by SS precursors. 8.9 S-to-P wave conversions and discontinuity topography 840 near subduction zones 8.10 Spreading Ridges and Mantle Plumes 851 8.11 Lower Mantle Thermal anomalies 854 8.12 Methodology 871 8.13 Results and Discussion 875 8.14 Conclusions 878 8.15 References 883 9. Summary and Future Research 990 9.1 Abstract 991 9.2 Introduction and Summary of chapters 992 9.3 Caveats and non-uniqueness 998 9.4. Reference 1005 9.5 Future work: Introduction 1014 9.6. References 1016 9.7 Future work: Direct seismic tests of the predicted profiles. 1017 9.8 Future work: Stacked SS precursor phases and transition zone density and velocity 1018 structure 9.9 Preliminary Conclusions 1020 9.10 References 1021 ix 9.11 Future work: Forward models of Normal mode Free Oscillation frequencies for 1024 the pyrolite mineral physics density profile. 9.12 Preliminary Conclusions 1027 9.13 References 1028 9.14 Future work: Implications for the 3 r d generation of joint S- and P-wave 1032 tomographic models. 9.15 References 1035 9.16 Future work: Other Chemically layered models 1037 9.17 Preliminary Conclusions 1040 9.18 References 1043 x List of Figures Figure 1.1 Radial profiles of density, shear, bulk sound, and compression velocity 32 from the global seismic reference model akl35 (Kennett et al., 1995). Figure 1.2 Illustration of a compositionally layered mantle structure (after 33 Gasparik, 1997). Figure 1.3 Interpretation of an isochemical mantle with whole mantle convective 34 flow. Figure 1.4 Calculated phase buoyancy parameter for a pyrolite mantle as a 35 function of the Clapeyron slope. Also plotted are values from numerical convection studies (right facing arrows). Figure 1.5 Comparison between the pyrolite mineral physics geotherm and the 36 geotherms of Jeanloz & Richter (1979) for whole and layered mantle convection. Figure 1.6 Trade-off curves for selected within slab earthquakes showing slab 37 penetration depth as a function of the scaling factor which converts temperature to velocity. Figure 1.7 Variance reduction between predicted and observed travel time 38 residuals as a function of slab penetration depth (after Fischer et al. 1991). Figure 1.8 A vertical cross-section through the Japan Trench, Western Pacific 39 showing P-wave velocity anomalies. Blue coloured material may be interpreted as reflecting the cold subducting oceanic lithosphere of the Pacific plate which extends from the surface to base of the mantle. C M B is the core-mantle boundary. Figure from van der Hilst et al. (1977). Figure 1.9 A schematic cross-section illustrating thermally-coupled convective 40 downwellings in a compositionally layered mantle. Figure after Anderson (1981b). Figure 2.1 P R E M (Dziewonski, and Anderson, 1981) and akl35 (Kennett, et a l , 168 1995) bulk sound velocity versus depth. Note the significant differences at 220 and =410 km depths between the two seismic models. x i Figure 2.2 PPvEM (Dziewonski, and Anderson, 1981) and akl35 (Kennett, et al., 169 1995) density versus depth. Figure 2.3 The 1700 °K pyrolite isentrope of Ita and Stixrude (1993). Note the 170 offset between the predicted temperature at the top of the lower mantle determined from the upper mantle isentrope and the best fit lower mantle pyrolite isentrope. Figure 2.4 Comparison of the predicted bulk sound velocity profile for the 171 pyrolite and piclogite compositions with the seismic profile from P R E M . Figure redrawn from Ita and Stixrude (1993). Figure 2.5 Comparison of the predicted density profile for the pyrolite and 172 piclogite compositions with the seismic profile from P R E M . Figure redrawn from Ita and Stixrude (1993). Figure 2.6 Volume percentage of the mantle minerals present in the pyrolite 173 model as a function of depth. Figure redrawn from Ita and Stixrude (1992). Figure 2.7 Mineral phase relations proposed by Anderson (1979). Note the 174 inferred stable stratification sketched in the center column of peridotite, eclogite, and garnetite. Figure 2.8 Schematic plate tectonic cycle for a the chemically stratified upper 175 mantle of Anderson (1979). Figure 2.9 Schematic illustration of the convective flow in a chemically stratified 176 upper mantle (Anderson, 1983). The locations of descending convective flow in the lower mantle is inferred to be thermally linked to the location of cold convective downwelling in the upper mantle. Figure 2.10 Volume percentage of the mantle minerals present in the piclogite 177 model as a function of depth. Figure redrawn from Ita and Stixrude (1992) . Figure 2.11 Composite figure of density and bulk sound velocity calculated along a 178 2000 °K adiabat for a pure olivine composition using a Birch-Murnaghan finite strain equation of state (solid line) and the Universal equation of state (dashed line). Figure redrawn from Ita and Stixrude (1993) . Figure 2.12 Inferred linear relationship of molar volume for P-olivine as a function 179 of Mg content. xu Figure 2.13 Inferred linear relationship of density for P-olivine as a function of Mg 180 content. Figure 2.14 Estimated isothermal bulk modulus for the iron bearing P-olivine 181 studied by Fei etal. (1992) for [dKrJdP^ =4.3. This estimate rests on the assumption that the Zha et al. (1996) pressure derivative, determined for a pure Mg end-member, is also applicable to this composition. Figure 2.15 Inferred linear relationship of the isothermal bulk modulus for P- 182 olivine as a function of Mg content. Figure 2.16 Inferred linear relationship of molar volume for y-olivine as a function 183 of Mg content. Figure 2.17 Inferred linear relationship of density for y-olivine as a function of Mg 184 content. Figure 2.18 Inferred linear relationship of the isothermal bulk modulus for y-olivine 185 as a function of Mg content. Figure 2.19 Inferred linear relationship of unit cell volume for Majorite as a 186 function of Fe content. Figure 2.20 Inferred linear relationship of the adiabatic bulk modulus for Majorite 187 as a function of Fe content. Figure 2.21 Inferred linear relationship of the molar volume for Ca bearing 188 Majorite as a function of Ca content. Figure 2.22 Inferred linear relationship of density for Ca bearing Majorite as a 189 function of Ca content. Figure 2.23 Inferred linear relationship of isothermal bulk moduli for Ca bearing 190 Majorite as a function of Ca content. Figure 2.24 Iron partitioning between silicate perovskite and magnesiowustite. 191 Figure 2.25 Enlargement of iron partitioning between silicate perovskite and 192 magnesiowustite. Figure 2.26 Theoretical stability field of silicate perovskite at 3500 °K across the 193 lower mantle. Figure redrawn from Stixrude and Bukowinski (1992). xiii Figure 2.27 Theoretical temperature-depth phase boundaries for the structural 194 polymorphs of silicate perovskite as determined by Stixrude and Cohen (1993). Figure 2.28 Theoretical temperature-depth phase boundary for the orthorhombic to 195 tetragonal structural polymorph of silicate perovskite as determined by Warren and Ackland (1996). Also plotted is the theoretical phase boundary for the structural transition in Ca-perovskite (Stixrude et al., 1996). Figure 2.29 The calculated pyrolite adiabatic geotherm for the upper mantle, 196 transition zone, and the upper part of the lower mantle. Figure 2.30 The calculated pyrolite adiabatic geotherm for the whole mantle 197 compared to the initial upper and lower mantle geotherms that were used in the calculations. Figure 2.31 Predicted bulk density of pyrolite and piclogite as a function of depth 198 across the upper mantle and transition zone. The mean and standard deviation of the seismic densities are represented by the dot-dash and triple dot-dash lines, respectively. P R E M and akl35 density profiles are also plotted. Figure 2.32 Predicted bulk density of pyrolite as a function of depth compared to 199 the global reference models akl35-Q and akl35-F density profiles (Montagner and Kennett, 1996) and the high resolution regional models AU3 and PA5 (Gaherty and Jordan, 1995; Gaherty et a l , 1996). Figure 2.33 Predicted bulk density of pyrolite and piclogite as a function of depth 200 across the lower mantle. Figure 2.34 Percentage difference of the predicted pyrolite density profile from 201 P R E M or akl35 density profiles. Figure 2.35 Percentage difference of the predicted pyrolite density profile from 202 akl35-Q or ak!35-F density profiles. Figure 2.36 The predicted density profiles for the lower mantle mineral phases. 203 Figure 2.37 Predicted bulk sound velocity for pyrolite and piclogite as a function of 204 depth. The mean and standard deviation of the seismic densities are represented by the dot-dash and triple dot-dash lines, respectively. PREM and akl35 bulk sound velocity profiles are also plotted. xiv Figure 2.38 Upper mantle S- and P- wave velocity profiles from proposed global 205 reference models MD89ps, and iasp89 (Kennett, 1991). Figure 2.39 Predicted bulk sound velocity for pyrolite as a function of depth 206 compared to AU3 (Gaherty and Jordan, 1995) and PA5 (Gaherty et al., 1996). Figure 2.40 Predicted bulk sound velocity for pyrolite and piclogite as a function of 207 depth across the lower mantle. Figure 2.41 Percentage difference of the predicted pyrolite bulk sound velocity 208 profile from the akl35 profile. Figure 2.42 Percentage difference of the predicted pyrolite bulk sound velocity 209 profile from the akl35-Q and akl35-F profiles. Figure 2.43 The predicted bulk sound velocity profiles for the lower mantle mineral 210 phases. Figure 2.44 Predicted bulk density of pyrolite and piclogite as a function of depth 211 across the lower mantle for a Mg-Fe-Al bearing perovskite pyrolite assemblage. Figure 2.45 Percentage difference of the predicted Mg-Fe-Al bearing perovskite 212 pyrolite density profile from the akl35 density profiles. Figure 2.46 Predicted bulk sound velocity of pyrolite and piclogite as a function of 213 depth across the lower mantle for a Mg-Fe-Al bearing perovskite pyrolite assemblage. Figure 2.47 Percentage difference of the predicted Mg-Fe-Al bearing perovskite 214 pyrolite bulk sound velocity profile from the akl35 density profiles. Figure 2.48 Pyrolite geotherm compared to the whole mantle and enforced layered 215 mantle geotherms calculated from 3D numerical simulations of mantle convection (Glatzmaier and Schubert, 1993). Figure 2.49 Mineral physics pyrolite geotherm from this study compared with the 216 pyrolite geotherm calculated by Saxena (1996). Figure 2.50 Enlargement of the upper mantle and transition zone temperature 217 structure comparing the Pyrolite geotherm calculated in this study to that determined by Saxena (1996). Figure 2.51 Oceanic crustal thickness versus mantle temperature for half spreading 218 xv rates of 1 cm/yr and 5 cm/yr. The axes are normalized to the intersection point of the curves where 7 km thick oceanic crust is produced from decompression melting of a mantle with a potential temperature of 1317°C. Figure redrawn from Su et al., (1994). Figure 2.52a Theoretical iasp91 travel times superimposed on the times for test 219 events (dots). Figure redrawn from Kennett and Engdahl (1991). Figure 2.52b Composite figure of the residual travel times predicted for the iasp91 219 model and the smoothed empirical traveltimes for 18 seismic phases. Figure from Kennett et al., (1995). Figure 3.1 Volume percentage of the mantle minerals present in the pyrolite 351 model as a function of depth. Figure redrawn from Ita and Stixrude (1992). Figure 3.2. Inferred linear relationship of the shear modulus for P-olivine as a 352 function of Fe content. Figure 3.3 Inferred linear relationship of unit cell volume for Majorite as a 353 function of Fe content. Figure 3.4 Inferred linear relationship of the adiabatic bulk modulus for Majorite 354 as a function of Fe content. Figure 3.5 Inferred linear relationship of the shear modulus for Majorite as a 355 function of Fe content. Figure 3.6 Inferred linear relationship of the molar volume for Ca bearing 356 Majorite as a function of Ca content. Figure 3.7 Inferred linear relationship of density for Ca bearing Majorite as a 357 function of Ca content. Figure 3.8 Inferred linear relationship of isothermal bulk moduli for Ca bearing 358 Majorite as a function of Ca content. Figure 3.9 Plot of (d \i/d f)p versus (5 p /d P)T for measured compounds with 359 the previous inferred values for P-olivine and the recently reported experimental values. Abbreviations are; DA89, Duffy and Anderson (1989); DLA88, Anderson (1988); 187, Irifune (1987); W86, Weidner (1986); BW87, Bina and Wood (1987). xvi Figure 3.10 plot of (d p/5 f)p versus [d p/5 P) for measured compounds with 360 the previous inferred values for y-olivine. Abbreviations are; DA89, Duffy and Anderson (1989); DLA88, Anderson (1988); 187, Irifune (1987); W86, Weidner (1986); BW87, Bina and Wood (1987). Figure 3.11 Fourth order fit to the experimental shear moduli as a function of 361 pressure (Abramson et al., 1997). Figure 3.12 The adopted pyrolite adiabatic geotherm for the upper mantle, 362 transition zone, and the upper part of the lower mantle. Figure 3.13 The adopted bulk density of pyrolite as a function of depth compared 363 to the global reference models akl35-Q and akl35-F density profiles (Montagner and Kennett, 1996) and the high resolution regional models AU3 and PA5 (Gaherty and Jordan, 1995; Gaherty et al., 1996). Figure 3.14 The predicted shear wave velocity profiles for the individual minerals 364 which comprise the Pyrolite composition. Also shown is the V R H average profile for Pyrolite composition together with the akl35 profile. Figure 3.15 The predicted bulk shear wave velocity profile of pyrolite as a function 365 of depth. The mean (dot-dot-dash), standard deviation (dot), and maximum deviation (dash) of the published seismic velocities as calculated by Ita (1992) are also plotted. Figure 3.16 The predicted compression wave velocity profiles for the individual 366 minerals which comprise the Pyrolite composition. Also shown is the V R H average profile for Pyrolite composition together with the akl35 profile. Figure 3.17 The predicted bulk compression wave velocity profile of pyrolite as a 367 function of depth. The mean (dot-dot-dash), standard deviation (dot), and maximum deviation (dash) of the published seismic velocities as calculated by Ita (1992) are also plotted. Figure 3.18 The predicted bulk S-wave velocity profile of pyrolite as a function of 368 depth compared to the proposed global reference seismic models iasp89 (Kennett, 1991), MD89ps (Kennett, 1991), iasp91 (Kennett and Engdahl, 1991), akl35 (Kennett et al., 1995), akl35-F (Montagner and Kennett, 1996), and the seismic mean of Ita (1992). Figure 3.19 The predicted bulk P-wave velocity profile of pyrolite as a function of 369 depth compared to the proposed global reference seismic models xvn iasp89 (Kennett, 1991), MD89ps (Kennett, 1991), iasp91 (Kennett and Engdahl, 1991), akl35 (Kennett et al., 1995), akl35-F (Montagner and Kennett, 1996), and the seismic mean of Ita (1992). Figure 3.20 The predicted bulk S-wave velocity profile as a function of depth 370 compared to the high resolution regional seismic models A U3 (Gaherty and Jordan, 1995) and PA5 (Gaherty et al., 1996). Figure 3.21 The predicted bulk P-wave velocity profile as a function of depth 371 compared to the high resolution regional seismic models AU3 (Gaherty and Jordan, 1995) and PA5 (Gaherty et al., 1996). Figure 3.22 Comparison of seismic S-wave velocity gradients through the 372 transition zone (410 - 660 km depth) to the predicted Pyrolite velocity gradient. Note the good agreement between the Pyrolite model and the purely oceanic, high resolution regional seismic model PA5 (Gaherty et a l , 1996). Both PA5 and AU3 (Gaherty & Jordan, 1995) are the only seismic models which explicitly include a 520 km seismic discontinuity and allow the velocity gradients above and below to differ; all the remaining models treat the transition zone as homogenous. Figure 3.23 Comparison of seismic P-wave velocity gradients through the 373 transition zone (410 - 660 km depth) to the predicted Pyrolite velocity gradient. Again there is good agreement between the oceanic, high resolution, regional seismic model PA5 and the mineral physics model. Only PA5 and the mixed oceanic-continental AU3 seismic models include a 520 km seismic discontinuity and allow the velocity gradients above and below to vary independently; all the remaining models assume that the transition zone is homogeneous. Figure 3.24 Predicted olivine content (volume percent) from the 410 km seismic 374 discontinuity jumps in density, bulk sound velocity, S-wave, and P-wave velocity (after Bina, 1993). Horizontal lines indicate the expected olivine content for the pyrolite (Ringwood, 1975, 1991; Irifune, 1987) and piclogite compositional models (Bass and Anderson, 1984; Anderson and Bass, 1984; Anderson and Bass, 1986; Duffy and Anderson, 1989). Figure 3.25 Predicted olivine content (volume percent) from the 410 km seismic 375 discontinuity jumps in density, bulk sound velocity, S-wave, and P-wave velocity using pyrolite mineral physics model together with the akl35, iasp91,AU3, PA5, PREM or CREMO seismic models. Figure 3.26 The predicted pyrolite P-wave velocity profile compared to the high 376 xviii resolution, oceanic regional seismic models PA5 (Gaherty et al, 1996) and the original akl35 model (Kennett et al., 1995) and the modified version discussed in the text which results in consistent estimates for the olivine content across the 410 km discontinuity. Figure 3.27 Predicted olivine content (volume percent) from the 410 km seismic 377 discontinuity jumps in density, bulk sound velocity, S-wave, and P-wave velocity using the modified akl35 and iasp91 seismic models where the P-wave velocity directly above the 410 km discontinuity was decreased such that the predicted olivine content was self-consistent. Note that by only adjusting the P-wave jump of the seismic model, both the P and bulk sound velocity predictions are affected (but the S-wave prediction remains unaltered). Figure 3.28 Comparison of the predicted density and Vp velocity profiles to that 378 calculated by Lees et al. (1983). Figure 3.29 Schematic ray paths for the ScS family of reverberations. The top three 379 diagrams represent topside reflections from the 650 km discontinuity that constructively interfere to produce an observable arrival. The bottom three diagrams are similar, but represent underside reflections off the 650 km discontinuity. Figure from Revenaugh and Jordan (1989). Figure 3.30 Smoothed density, S- and P-wave velocity profiles as a function of 380 depth. Figure 3.31 Smoothed S- and P-wave velocity profiles as a function of depth 381 compared to profiles from global reference seismic models. Figure 3.32 Smoothed density and S-wave velocity profiles as a function of depth 382 compared to PA5, a high resolution regional model for old («120 Ma) Pacific oceanic upper mantle (Gaherty et al., 1996). Also shown is the transition zone S-wave model SSFIT1 of Shearer (1996). Figure 3.33 Predicted normal-incidence shear wave reflectivity as a function of 383 depth for an adopted transition width of 4 km. Also shown are the inferred seismic estimates from Revenaugh and Jordan (1991) and Revenaugh and Sipkin (1994a). Figure 3.34 Predicted normal-incidence shear wave reflectivity as a function of 384 depth for an adopted transition width of 10 km. Note the effect of increasing the transition width is to increase the predicted S-wave reflectivity. xix Figure 3.35 Predicted P-wave velocity profile as a function of depth. Also shown 385 for comparison are velocity profiles inferred from seismic data (Vidale et al., 1995; Neele, 1996; Estabrook and Kind, 1996; Gaherty et al., 1996). Figure 3.36 Schematic ray paths for the SS waves and the underside precursors 386 SA]0S and SmS. There exist equivalent P-wave ray paths. Figure from Shearer (1996). Figure 3.37 (Note figure caption on page 387) Predicted and observed stacked and 388 normalized travel times as a function of epicentral distance (Estabrook and Kind, 1996). The top panel (A) is the observed stack of 20,000 digital seismograms normalized to the PP phase, the thick, horizontal solid red-blue-red tricolour band located at 0 second time. The end points for the expected trace of the P660P precursor phase are marked by the solid black triangles (see also bottom panel (C)). The middle panel (B) illustrates the calculated stacked and normalized travel times as a function of epicentral distance when seismic events are traced through the iasp91 global reference seismic model. Note that iasp91 predicts an observable P660P precursor phase, which is not seen in the compilation of seismic observations in panel A . Figure 3.38 P-wave velocity models EK1 (solid line) and iasp91 (dotted line). 389 Figure from Estabrook and Kind (1996). See also figure 2.29 where EK1 is plotted against the smoothed pyrolite mineral physics model. Figure 3.39 A comparison of the upper mantle, shear wave velocity profile for the 390 oceanic regional model pac91 (Kennett, 1992), PA5 (Gaherty et al., 1996), iasp91 (Kennett et al., 1991), the forerunner of pac91, and the smoothed pyrolite mineral physics model. Figure 3.40 Predicted normal-incidence P-wave reflectivity for the pyrolite mineral 391 physics model versus that of EK1 (Estabrook and Kind, 1996), and iasp91 (Kennett and Engdahl, 1991). Figure 3.41 Schematic ray paths for the P'660P' and PP' waves through the Earth 392 together with a schematic waveform illustrating the different amplitudes of the two phases. Figure from Lees et al., (1983). Figure 3.42 Predicted 660 km P-wave reflection coefficient as a function of 393 wavelength of incident Vp for the pyrolite mineral physics model, EK1, akl35, and PREM compared to the range of calculated 660 Vp reflection coefficients discussed by Lees et al. (1983). Note that Lees et al. suspected that the reported seismic values were overestimated and xx hence adopted a value of « 0.05 rather than the range of 0.07-0.13. Figure 4.1 Theoretical F-f equations of state for Mg-perovskite. The solid lines 444 were calculated from molecular dynamic data complete to zero pressure where as the 3rd and 4th order finite strain fits were based on a least squares fit to data above 20 GPa and extrapolated to zero pressure. Note that increasing temperature increases the discrepancy between the extrapolated and actual curves. Figure re-drawn from Bukowinski and W o l f (1990). Figure 4.2 Theoretical F-f equation of state fits to the P R E M lower mantle. Figure 445 re-drawn from Bukowinski and W o l f (1990). Figure 4.3 Constrained 4th order equation of state fit to the lower mantle part of 446 P R E M showing normalized pressure G^, and moduli G^, and G a as a function of depth. Figure 4.4 Decompressed shear modulus (u.) versus decompressed adiabatic bulk 447 modulus (Ks). Figure 4.5 Decompressed Poisson's ratio (a) versus decompressed Seismic 448 parameter (O). Figure 4.6 Trade off curves between (d\i/dT)p and (d\i/8P)T for M g 449 perovskite in pyrolite, chondrite and pure perovskite lower mantle compositions. Figure 4.7 Calculated Poisson's ratio as a function of iron content for a pyrolite 450 composition. Also plotted is the calculated Poisson's ratio determined from constrained adiabatic decompression of the lower mantle P R E M seismic properties. Figure 4.8 Trade off curves between (dKs/dT)p and (dKs/dP)T for M g 451 perovskite in pyrolite, chondrite and pure perovskite lower mantle compositions. Also plotted are recent inferred values for (d Ks/d p based on converted experimental estimates of (d KT/d T) . Figure 4.9 Trade off curves between (d\i/dT)p and (d\x/dP)T for . M g 4 5 2 perovskite in pyrolite, chondrite and pure perovskite lower mantle compositions. Also plotted are the inferred values for [d\i/dT)p adopted by Duffy and Anderson (1989) and Zhao and Anderson (1994) and that calculated in this study. xx i Figure 5.1 Volume percentage of the mantle minerals present in the pyrolite 528 model as a function of depth. Figure redrawn from Ita and Stixrude (1992). Figure 5.2 Volume percentage of the mantle minerals present in the piclogite 529 model as a function of depth. Figure redrawn from Ita and Stixrude (1992). Figure 5.3 (5 p/5 7")^ versus iron content in Magnesiowiistite. 530 Figure 5.4 Theoretical Expansivity of Mg-perovskite as a function of temperature 531 and Gruneisen parameter. Figure redrawn from Anderson and Masuda (1994). Figure 5.5 Theoretical Expansivity of Mg-perovskite as a function of temperature 532 compared to experimental data. Figure Wang et al., (1994). Figure 5.6 Theoretical Coefficient of thermal expansion of Mg-perovskite as a 533 function of temperature and Gruneisen parameter. Figure redrawn from Anderson and Masuda (1994). Figure 5.7 Experimentally constrained Coefficient of thermal expansion of Mg- 534 perovskite as a function of temperature. Figure 5.8 Experimentally constrained Coefficient of thermal expansion of Mg- 535 perovskite as a function of temperature. Also shown are the recent results of Gillet et al., (1996) as a function of pressure. Figure 5.9 Coefficient of thermal expansion of Mg-perovskite as a function of 536 pressure. Figure redrawn from Zhao and Anderson (1994). Figure 5.10 Shear modulus as a function of temperature. 537 Figure 5.11 Inferred coefficient of thermal expansion of Mg-perovskite for Duffy 538 and Anderson (1989) and Zhao and Anderson (1994). Figure 5.12 Inferred behavior of [d\x/8T)p for Mg-perovskite as a function of 539 temperature for Duffy and Anderson (1989), Zhao and Anderson (1994) and this study. Figure 5.13 Plot of (d p/9 T)p versus [d \x/d P)T for measured compounds with 540 the inferred values for Mg-perovskite from Duffy and Anderson xxii (1989), Zhao and Anderson (1994) and this study. Also shown is the recent estimate of (3u./3P) 7 , from molecular dynamic computer simulations (Patel et al., (1996). Figure 5.14 The adopted pyrolite adiabatic geotherm for the upper mantle, 541 transition zone, and the upper part of the lower mantle. This geotherm is calculated self-consistently from the mineral physics parameters used in calculating whole mantle profiles of density and bulk sound velocity. Figure 5.15 Pyrolite geotherm compared to the whole mantle and enforced layered 542 mantle geotherms calculated from 3D numerical simulations of mantle convection (Glatzmaier and Schubert, 1993). The adopted piclogite lower mantle geotherm used in this study is also shown. Figure 5.16 Comparison of the predicted bulk V$ and Vp velocity profiles of 543 pyrolite as a function of depth in the lower mantle to the global reference seismic models akl35 (Kennett et al., 1995), akl35-F (Montagner and Kennett, 1996). Figure 5.17 Comparison of the predicted bulk Vs velocity profiles of pyrolite as a 544 function of depth in the lower mantle to the global reference seismic models akl35 (Kennett et al., 1995), akl35-F (Montagner and Kennett, 1996). Figure 5.18 Comparison of the predicted bulk Vp velocity profiles of pyrolite as a 545 function of depth in the lower mantle to the global reference seismic models akl35 (Kennett et al., 1995), akl35-F (Montagner and Kennett, 1996). Figure 5.19 Percentage difference of the predicted pyrolite Vg velocity profile from 546 the akl35 and ak!35-F profiles. Figure 5.20 Percentage difference of the predicted pyrolite Vp velocity profile from 547 the akl35 and akl35-F profiles. Figure 5.21 Comparison of the predicted bulk Vs and Vp velocity profiles of 548 piclogite as a function of depth in the lower mantle to the global reference seismic models akl35 (Kennett et a l , 1995), akl35-F (Montagner and Kennett, 1996). Figure 6.1 Comparison between the molecular dynamics prediction of the 563 pressure variation of the isotropic adiabatic bulk and shear moduli of Mg-perovskite and a 3rd order EOS prediction with the pressure xxiii derivatives of Sinelnikov et al. (1998). Figure 6.2 Comparison between molecular dynamics predictions of Karki et al. 564 (1997b) and a 4th order EOS prediction. Figure 6.3 Comparison between the high temperature and pressure prediction of 565 Mg-perovskite using a 4th order EOS and the lower mantle pyrolite adiabat and the zero temperature molecular dynamics prediction of Karki etal. (1997b). Figure 6.4 Comparison of predicted pressure variation of the adiabatic bulk and 566 shear moduli at room temperature and along the pyrolite lower mantle geotherm. Also shown are the molecular dynamic predictions of Karki et al. (1997a) and the experimental predictions of Chopelas (1996). Figure 6.5 Comparison of the predicted bulk VS and VP velocity profiles of 567 pyrolite as a function of depth in the lower mantle to the global reference seismic models akl35 (Kennett et al., 1995), akl35-F (Montagner and Kennett, 1996). Figure 6.6 Percentage difference of the predicted pyrolite VS velocity profile from 568 the akl35 profile for the 3rd order EOS with estimated parameters and the 4th order EOS with measured parameters. Figure 6.7 Percentage difference of the predicted pyrolite VP velocity profile from 569 the akl35 profiles using the 3rd order EOS with estimated parameters versus the 4th order EOS with measured values. Figure 7.1 Summary figure illustrating the discrepancy between seismic estimates 713 and room pressure experimental values. Figure 7.2 Schematic diagram illustrating the SS and S raypaths through the 714 Earth's mantle. Figure 7.3 Plot of SS-S travel time residuals versus PP-P travel time residuals 715 averaged by tectonic province (after Woodward and Masters, 1991a). Figure 7.4 Schematic diagram illustrating the effect of cooling and thickening 716 oceanic lithosphere with respect to the reflected bounce point. Figure 7.5 Plot of SS-S and PP-P travel time residuals as a function of seafloor 717 age at the SS or PP bounce point (after Woodward and Masters, 1991a). xxiv Figure 7.6 Comparison of the long-period, oceanic upper mantle estimate derived 718 from Woodward and Masters (1991a) SS-S and PP-P residuals as a function of age with the lower mantle estimate of Dziewonski and Woodhouse (1987). Figure 7.7 Summary of upper mantle estimates from continental station 719 corrections. Also plotted is the "oceanic" estimate derived from Woodward and Masters (1991a). Figure 7.8 Summary of the preferred upper mantle estimates. A l l of these 720 estimates are based on comparing self-consistent S and P-wave observations to derive the upper mantle average (dlnVs/d\nVP)p value. Figure 7.9 (left) Maximum variation of the S and P-wave travel time residuals as a 721 function of turning depth in the lower mantle beneath the Caribbean, (right) The related (dlnVs /dlnVp)p values for the two depth intervals. Figure 7.10 Schematic diagram illustrating raypaths for the core reflected ScS 722 phase relative to surface reflected SS phase. ScS-S differential travel time residuals are primarily sensitive to lowermost velocity structure, while SS-S differential residuals reflect the velocity heterogeneity below the surface bounce point. Figure 7.11 Schematic diagram illustrating raypaths for S-waves bottoming in the 723 lower mantle. Boxes schematically represent the depth bins adopted by Bolton (1996) for plotting the co-located, cap-averaged S- versus P-wave travel time residuals. Figure 7.12 Scatter plots for the 4 depth bins in the lower mantle where Bolton 724 (1996) compared co-located, cap-averaged S- and P-wave travel time residuals. Figure 7.13 The scaling factor (dlnVs/dlnVp)p plotted as vertical bars over the 4 725 depth intervals considered by Bolton (1996). Also shown are the preferred upper mantle mean value and the lower mantle inference from the Caribbean anomaly. Note that when the anomalous values in the lowermost bin are not considered, the new estimate decreases substantially, and agrees with the earlier Pulver & Masters (1990) inference. Figure 7.14 Scatter plot of S- and P-wave residuals for those cap-averages which 726 xxv contain at least 25 observations in each cap (the plots in figure 7.12 contain points which have a minimum cut off of 5 observations per cap). Figure 7.15 Scatter plot of S- and P-wave residuals showing hypothetical 727 correlation lines for a constant value o f ^ l n f ^ / d l n 1^),, = 1.70 throughout the mantle (in red) compared to the least squares regression lines determined by Bolton (1996; blue). Figure 7.16 The rms amplitude of selected P-wave tomographic models discussed 728 in the text. Figure 7.17 The rms amplitude of selected S-wave tomographic models discussed 729 in the text. Figure 7.18 Profiles of the ratio of rms velocity for recent Vs global tomographic 730 models (Ritzwoller and Lavely, 1995) where L02.56 is the Vp tomographic model. Note the expanded scale. Figure 7.19 The depth profile of the ratio of rms amplitudes of Vs tomographic 731 models to the Vp tomographic model L02.56 but for only even degree 2 terms of the spherical harmonic expansion for which the tomographic models are parameterized laterally (after figure 23 a of Ritzwoller and Lavely, 1995). Figure 7.20 Correlation of joint S- to P-wave tomographic models across the lower 732 mantle (Robertson and Woodhouse, 1995). Also plotted are common mantle phase boundaries and the depth intervals where the tomographic models are likely to be unreliable. Figure 7.21 Distribution of S-wave summary rays as a function of bottoming depth 733 (Robertson and Woodhouse, 1996). Also shown are two regions in the lower mantle where they admit the resultant ratio of S to P scaling factor is unreliable. Figure 7.22 Ratio of S- to P-wave rms velocity amplitudes from joint lower mantle 734 tomographic models JLM4S6 and JLM4P6 (Robertson and Woodhouse, 1995). To assess the potential effect of damping during the inversion, the data set was filtered to included only S- and P-wave data that are common to the same seismogram. Figure 7.23 Ratio of S- to P-wave heterogeneity from explicitly solving for the 735 (dlnVs/dlnVp)p profile by inverting both P and S data sets for a xxvi single Vp tomographic model and the associated proportionality profile that maximizes the fit of a scaled-Vs model to the S data. Also shown are the profiles based on the ratio of rms velocity amplitudes. Figure 7.24 Correlation of joint S- and P-wave tomographic models WE1997 736 (Vasco and Johnson, 1998) and S16B30 to P16B30 (Bolton, 1996). Also shown is the correlation between the lower mantle joint models of Robertson & Woodhouse (1995). Figure 7.25 Model S16B30 of Masters et ah (1996) showing the relative S-wave 737 velocity perturbations at 12 depths through the mantle. Figure from Bolton (1996). Figure 7.26 Model P16B30 of Bolton (1996) showing the relative P-wave velocity 738 perturbations at 12 depths through the mantle. Figure from Bolton (1996). Figure 7.27 Radial profiles of the rms velocity amplitudes from the joint, whole 739 mantle S- and P-wave tomographic models of Bolton (1996) and Vasco and Johnson (1998). Note the discrepancy between the relative S- and P-wave amplitudes in the lowermost mantle. Figure 7.28 Profiles of the rms-derived (d\nVs/dlnVr)p factor for the two whole 740 mantle, joint tomographic models are compared to independent estimates. Note that the joint lower mantle models of Robertson and Woodhouse (1995) result in a large peak in the middle of the lower mantle, a feature absent in both whole mantle models. Figure 7.29 A comparison of the rms-ratio profiles to the 4 global, depth estimates 741 of Bolton (1996) that are based only on the ratio of absolute S- to P-wave residuals. Figure 7.30 A comparison of the rms-ratio derived profiles to those calculated 742 assuming 100% spatial correlation between the S- and P-wave velocity anomalies in the joint, whole mantle tomographic models. Figure 7.31 (left) The profile of slowness derived from a statistical analysis of the 743 ISC P-wave data (after Gudmundsson et al. 1990). (right) The associated profile of the correlation half width. Figure 7.32 (left) the profile of rms slowness perturbations in the mantle derived 744 from a statistical analysis of the ISC S-wave arrival times, (right) The associated profile of the correlation half width for the perturbations. xxvii Figure 7.33 The statistical inference of Davies et al. (1992) based on the variance 745 of ISC S- and P-wave arrival times, is compared against the profiles discussed in the text. Figure 7.34 The variance reduction obtained in comparing predicted to observed 746 free-oscillation structure coefficients for various combinations of the density-to-Vp and shear velocity-to-Vp scaling factors (after Giardini etal., 1988). Figure 7.35 The probability distribution of the S- to P-wave scaling factor in the 747 lower mantle (assuming a constant value applies across the lower mantle) derived by free-oscillation observations (after L i et a l , 1991). Figure 7.36 Summary of free-oscillation estimates where a constant lower mantle 748 value was assumed. Note that the most recent estimates (e.g. L i et al., 1991b; Ritzwoller and Lavely, 1995) favour relatively low values of 1.81-2.00. Figure 7.37 A comparison of the depth-dependent profiles of Ishii and Tromp 749 (1997; 1998) against the preferred lower mantle mean value of L i et al. (1991b). The 1997 profile of Ishii & Tromp is not reliable. Figure 7.38 Comparison of the depth-dependent profile of Ishii and Tromp (1998) 750 to the rms-ratio derived profiles determined from the whole mantle, joint S- and P-wave tomographic models. Their preliminary 1997 profile is also plotted and led them to argue in favour of the profiles which assume a 100% spatial correlation between the S- and P-wave anomalies. In marked contrast, their 1998 profile strongly agrees with the rms-ratio derived profiles. Figure 7.39 Schematic diagram illustrating raypaths for the core reflected PcP 751 phase and core penetrating PKP phases. Figure 7.40 Variance reduction in the lowermost mantle for various values of the 752 (dlnVs /d\nVp)p scaling factor and shear wave tomographic models (after Song and Helmberger, 1997). The yellow band represents likely values based on this work. Figure 7.41 Summary of the preferred seismic estimates reviewed in the text. 753 Figure 7.42 The radial profile of the shear to adiabatic bulk moduli ratio from the 754 seismic reference model P R E M and the Pyrolite mineral physics model. xxviii Figure 7.43 Profiles of theoretical estimates of the periclase Anderson-Gruneisen 755 parameter as a function of pressure (after Agnon and Bukowinski, 1990) . Figure 7.44 Profiles of the isothermal (dlnVs/d\nVP)T (after Parker and Wall, 756 1991) . Note that these profiles are not directly comparable to the adiabatic value, which is of interest here. Figure 7.45 Profiles of periclase T as a function of pressure and temperature (after 757 Isaak etal., 1992). Figure 7.46 Profiles of the theoretical scaling factor for periclase (Isaak et al., 758 1992) compared to some of the seismic estimates reviewed in the text. Figure 7.47 Comparison of the predicted melt-bearing S- to P-wave scaling factor 759 to some of the seismic estimates discussed in the text. Figure 7.48 Comparison of the melt-bearing scaling factor to the seismic estimates 760 which assumed a perfect 100% spatial correlation between the S- and P-wave velocity anomalies (Robertson and Woodhouse, 1996a; Bolton, 1996). Figure 7.49 Comparison of the melt-bearing scaling factor with the rms-ratio 761 derived profiles of Robertson and Woodhouse (1996a) and other seismic profiles discussed in the text. Figure 7.50 Comparison between predicted lower mantle melt-free and melt- 762 bearing scaling factors as calculated by Duffy and Ahrens (1992). Also shown is the Dziewonski and Woodhouse (1987) lower mantle estimate. Figure 7.51 Comparison of theoretical melt-free and melt-bearing profiles (Duffy 763 and Ahrens, 1992) to the preferred seismic profiles discussed in the text. Note the very good agreement between the melt-free profile and the rms-ratio derived profiles. Figure 7.52 Radial profiles of the shear wave quality factor Qs taken from seismic 764 studies. Note the high values in the lower mantle relative to the shallow most 100-200 km. The low values at shallow depths are interpreted to reflect the presence of partial melt. If correct, then the high values in the lower mantle argue against the presence of partial melt in this region. Figure 7.53 A comparison of velocity and density profiles from the recent seismic 765 xxix reference model SP6 (Morelli and Dziewonski, 1993) with the P R E M model (Dziewonski and Anderson (1981). Also shown is the free-oscillation derived profiles advocated by Kumagai et al. (1992). Figure 7.54 The density to velocity scaling factor profiles estimated by Karato 766 (1993). The mid-mantle peaks directly reflect the use of the QM1 shear attenuation profile. Figure 7.55 A comparison of the predicted S- to P-wave scaling factor derived from 767 the density to velocity profiles of Karato (1993) to the preferred seismic profiles discussed in the text. Figure 7.56 Profiles of elastic logarithmic shear and compression velocity 768 temperature derivatives (after Karato, 1993). Figure 7.57 A comparison of the elastic and anelastic profiles derived from Karato 769 (1993) with the melt-free profile of Duffy and Ahrens (1992b) and the preferred seismic profiles discussed in the text. Figure 7.58 A comparison of the experimental inference of Zaug et al. (1993) with 770 the upper mantle seismic estimates discussed in the text. Figure 7.59 A comparison of the elastic and anelastic profiles derived from Karato 771 (1993) with the melt-free profile of Duffy and Ahrens (1992b) and the preferred seismic profiles discussed in the text. Figure 7.60 A comparison of the calculated S- and P-wave velocity profiles for a 772 uniform Pyrolite mantle with the reference seismic profiles of akl35 (Kennett et al., 1995). Figure 7.61 The upper and lower mantle adiabatic geotherms for the Pyrolite 773 mineral physics model. Re-running the mineral physics model involves only adjusting the two anchor temperature values at 100 and 661 km depth. Figure 7.62 The predicted Pyrolite anharmonic scaling factor. 774 Figure 7.63 A comparison of the predicted Pyrolite anharmonic scaling factor with 775 the preferred seismic estimates which are discussed in the text. Figure 7.64 A comparison of the predicted Pyrolite anharmonic scaling factor with 776 the mineral physics estimates discussed in the text. Figure 7.65 A comparison of the predicted Pyrolite anharmonic scaling factor with 777 the lower mantle seismic inferences of Robertson and Woodhouse xxx (1995; 1996a). Figure 7.66 Profile of the predicted Pyrolite coefficient of thermal expansion. The 778 cusp in the profile between 420 and 490 km is likely to be an artifact of the adopted mineral assemblage. Figure 7.67 Predicted profile of the dimensionless parameter, T for a Pyrolite 779 mantle. Figure 7.68 The predicted Pyrolite profile of the Anderson-Gruneisen parameter 780 compared with the inferences from Anderson (1987). Figure 7.69 A comparison of the required lower mantle profile of T to satisfy the 781 calculated (Sln^ /SlnF, , ) , , profile assuming a 100% spatial correlation between S- and P-wave anomalies in joint, whole mantle tomographic models of Bolton (1996) and the predicted T profile for the pyrolite mantle. Figure 7.70 A comparison between the required 5 S profile to satisfy the calculated 782 (dlnVs/d\nVP)p profile assuming a perfect 100% spatial correlation between the S- and P-wave velocity anomalies (Bolton, 1996) and the predicted Pyrolite profile. Figure 8.1 Top; Predicted heat flow as a function of age for the cooling half-space 905 model (HS), the original constant thickness plate model of Parsons and Sclater (1977; PS77), and the recent version of it GDH1 (Stein and Stein, 1992). Bottom; predicted subsidence as a function of age for the three thermal models for oceanic lithosphere. Also plotted is the observed bathymetry for the Argentine basin and the Gulf of Mexico. Figure 8.2 A comparison of conductive oceanic geotherms for the cooling 906 halfspace model (HS), the original constant plate model of Parsons and Sclater (1977; PS77), and the recent constant plate model of Stein and Stein (1992; GDH1). Also plotted is the Pyrolite mineral physics adiabatic geotherm and a representative geotherm for an Archean stable continent. Figure 8.3 Partial melt zone beneath a mid-ocean ridge predicted from passive 907 upwelling of mantle in response to the negative pressure head associated with rifting. Figure 8.4 Subsidence as a function of age for North Atlantic margin of the North 908 American Plate. Using the parameters of Marty and Cazenave (1989), who noted the bathymetry fit the half-space model to ages of 160-170 xxxi Ma. The observed bathymetry is displaced above the predicted HS model due the shallow ridge crest depth - when this reduced (see orange curve), the bathymetry as a function of age now fits the HS model very well. Figure 8.5 Depth versus heat flux predictions for the cooling half-space model, 909 the constant thickness plate model of Parsons and Sclater (1977; PS77) and Stein and Stein (1992; GDH1). Also shown is the Gulf of Mexico (after Nagihara et al. 1996). Figure 8.6 Top; Seismic structure used to forward model average phase velocities 910 in the Pacific plate as a function of age. Bottom; Age versus average Love wave phase velocities for the Pacific plate. The smooth curves represent predicted phase velocities while the triangles represent observations (after Zhang and Tanimoto, 1991). Figure 8.7 Predicted plate thickness from Love wave phase velocity modeling of 911 Tanimoto and Zhang (1990). Also shown is the predicted plate thickness for the cooling half- space model using equation 4-124 of Turcotte and Schubert (1982; p. 164) for the 1020 C and 1145 C isotherms. Figure 8.8 Schematic diagram illustrating the SS and S raypaths through the 912 Earth's mantle. Figure 8.9 Observed S-wave travel time residuals versus SS-S residuals. The lack 913 of a correlation implies that the observed signal is not due to lower mantle shear structure "seen" by the S-leg (after Woodward and Masters, 1991) Figure 8.10 Observed SS-wave travel time residuals versus SS-S residuals. The 914 good correlation supports the interpretation that signal is reflecting seismic structure at the SS bounce point (after Woodward and Masters, 1991) Figure 8.11 Schematic diagram illustrating the effect of cooling and thickening 915 oceanic lithosphere with respect to the reflected bounce point of SS raypaths. Figure 8.12 Plot of SS-S (top) and PP-P (bottom) travel time residuals as a function 916 of seafloor age at the SS or PP bounce point (after Woodward and Masters, 1991a). Figure 8.13 Relationship between mantle potential temperature (left) and the three 917 xxxii ways in which melting may be triggered within the mantle (right). Figure 8.14 Melt paths in the partial melt zone for different mantle potential 918 temperatures. The decrease in temperature with melting reflects the latent heat of fusion. Thus, lava eruption temperatures can not be directly extrapolated to depth to infer the mantle temperature. Figure 8.15 Global compilation of the thickness distribution of normal and fracture 919 zone ocean crust thickness (after Brown and White, 1994) Figure 8.16 Predicted melt thickness (ocean crust thickness) as a function of mantle 920 potential temperature (after McKenzie and Bickle, 1988). Figure 8.17 (top) Comparison of observed ocean crustal thickness (dots) as a 921 function of full spreading rate at the mid-ocean ridge versus predicted oceanic crustal thickness as a function of mantle potential temperature (after Brown and White, 1994). Figure 8.18 (bottom) Comparison of observed ocean crustal thickness (dots) as a 921 function of REE inversions against predicted ocean crustal thickness as a function of both mantle potential temperature and full spreading rate (after Brown and White, 1994). Figure 8.19 Global correlation of Na O (wt%) versus FeO (wt%). The correlation 922 may be interpreted to reflect the effects of increasing mantle potential temperature after Langmuir et al.* 1992. Figure 8.20 Global correlation of Na 2 0 (wt%) versus axial ridge depth (after 923 Langmuir et al., 1992) Figure 8.21 Global correlation of crustal thickness versus Na 2 0 (wt%) from 924 Langmuir et al., 1992. Note the large difference between the predicted effects of perturbations in mantle potential temperature and mantle chemistry on crustal thickness. Figure 8.22 Correlation of Na_0 (wt%) as a function of full spreading rate (after 925 Brown and White, 1994). Note the large variation for the Australian-Antarctic discordance (Klein et al., 1991). Figure 823 Inferred mantle potential temperature along the equatorial Mid-Atlantic 926 ridge (after Schilling et al., 1995). Note that the geochemistry is consistent with perturbations of 50 C around a mean mantle potential temperature of 1330 C. Figure 8.24 The effects of compositional buoyancy on predicted oceanic crustal 927 xxxiii thickness as a function of spreading rate (after West et a l , 1994). Predictions which do not include compositional buoyancy are blue lines, while models which include this are red lines. Note that the largest effect occurs only for slow spreading rates. Figure 8.25 Compilation of lateral temperature anomalies inferred through melt 928 chemistry and/or ocean crustal thickness plotted around the pyrolite mineral physics adiabat. Note that the estimates of Klein and Langmuir (1987) and Langmuir et al. (1992), if true would imply that temperature perturbations beneath mid-ocean ridges exceed the observed temperature of hotspots. Figure 8.26 Inferred temperature anomalies along the North-Atlantic spreading 929 ridge from joint inversion of shear wave travel time residuals and geoid and depth anomalies (after Sheehan and Solomon, 1991). If the temperature perturbations are restricted to shallow depths, the magnitude of the inferred anomalies increases. Figure 8.27 Expected maximum temperature contrast between a mid-ocean ridge 930 and old (>100 Ma) oceanic and Archean continental lithosphere at roughly 40-50 km depth. For oceanic lithosphere, the temperature estimate is insensitive to the adopted thermal model (e.g. GDH1 or cooling halfspace). Figure 8.28 Bathymetry along the south-east Indian ridge (after Kuo, 1993). A A D 931 is the Australian-Antarctic Discordance. Figure 8.29 Compilation of estimated lateral temperature anomalies beneath the 932 Australian-Antarctic Discordance. Note the large difference between the magnitude of the temperature anomalies when the depth extent of the anomalies is increased from 100 km to 300 km. Figure 8.30 Plot of Na 2 0 (wt%) for ocean crust basalts dredged along the SE Indian 933 Ridge (data from Klien et al., 1991. Figure 8.31 Comparison of calculated mantle potential temperatures from the Na O 934 (wt%) data of Klien et al (1992) using the Niu and Batiza (1991) parameterization. Figure 8.32 Calculated mantle potential temperatures along the SE Indian Ridge 935 superimposed over the inferred temperature anomalies of Kuo (1993). Figure 8.33 Plot of along axis mantle potential temperature for the East Pacific 936 Rise (after Niu and Batiza, 1991). xxxiv Figure 8.34 Summary of preferred lateral temperature anomalies beneath the mid- 937 ocean ridge system as estimated by geochemistry and geophysical techniques. These are plotted around the Pyrolite mineral physics geotherm. Figure 8.35 The effect of varying temperature within the transition zone (410 to 938 660 km depth). Because of the opposing Clapeyron slopes of the 410 and 660 km olivine phase boundaries, the transition zone will thin or thicken in response to hotter or colder temperatures. Figure 8.36 Schematic raypaths for ScS shear waves (after Revenaugh and Jordan, 939 1991a). Figure 8.37 Representative SH polarized seismogram (time is in minutes after the 940 earthquake rupture. Right traces are portions of the seismogram between the ScSn and sScSn wave groups (after Revenaugh and Jordan, 1989) Figure 8.38 Calculated lateral temperature anomalies in the transition zone based 941 on converting the mean transition zone travel time anomaly. The lateral temperature anomalies were then added to the Pyrolite mineral physics geotherm to obtain absolute temperatures. Figure 8.39 Calculated transition zone temperatures derived from the apparent 942 depth of the 410, 520, and 660 km seismic discontinuities tabulated by Revenaugh and Sipkin (1994). Figure 8.40 Calculated lateral temperature anomalies at the 410 and 660 km 943 seismic discontinuities by converting the apparent depths of Revenaugh and Jordan (1991) into temperature. Figure 8.41 Schematic raypaths for SS and 410 and 660 km SS precursor seismic 944 phases Figure 8.42 Global plots of the SS bounce points (After Flanagan and Shearer, 945 1998) Figure 8.43 Smooth maps of topography of the 410, 520, 660 km and the transition 946 zone thickness obtained by applying spherical splines to the cap average data (from Flanagan and Shearer, 1998). Contour intervals are 6 km. xxxv Figure 8.44 Individual cap average depths of the 410 and 660 km seismic 947 discontinuities as a function of the standard error (data from Flanagan, personal communication). Also shown are the mean depths and the mean upwards and downwards deflections. Figure 8.45 Calculated temperature anomalies corresponding to the individual cap 948 average depths of the 410, 520, and 660 km seismic discontinuities. Figure 8.46 Calculated temperature anomalies corresponding to the mean upwards 949 and downwards deflections from the Flanagan and Shearer (1998) data set. Also shown are temperatures calculated from the mean deflections calculated by Vasco et al. (1995). Figure 8.47 Correlation of the 410 versus 660 km seismic discontinuity depths. The 950 lack of a trend implies that the vertical extent of the temperature anomalies does not extend across the full width of the transition zone. Figure 8.48 A comparison between the calculated temperature anomalies inferred 951 from the mean deflections of the 410 and 660 km seismic discontinuities (Flanagan and Shearer, 1998; Vasco et al. (1995)) versus the calculated temperatures from a 2D axisymmetric convection simulation (Solheim and Peltier, 1994b). Figure 8.49 Location of the Kuril-Kamchatka subduction zone (after Fischer et al. 952 1988). Figure 8.50 Plot showing the flow lines of the subducted slab over the fixed 953 interval of 580-730 km depth. The slab thickening is parameterized the width after thickening divided by the initial width (after Fischer et al., 1988). Figure 8.51 Predicted isotherms for the Kuril slab calculated by a finite difference 954 thermal model which incorporates variable divergent flow and cross strike thickening (after Fischer et al., 1988). Contour interval is 200 C. Figure 8.52 Predicted temperature structure for the Tonga slab (after Marone and 955 Liu, 1998) calculated by a finite difference model. The contour interval is 200 C. Figure 8.53 Schematic raypaths for S-to-P converted phases and pP surface 956 underside reflections (after Shearer, 1992). Figure 8.54 Schematic raypaths for the S-to-P converted phases at the deflected 957 660 km seismic discontinuity. Raypaths are superimposed on the xxxvi predicted temperature structure for the Tonga slab. Figure 8.55 Top; Slab earthquakes (red triangles) outlining the Japan slab above the 958 estimated depth of the 660 km discontinuity (blue circles. Bottom; enlargement of corrected depths for upper mantle heterogeneity (after Shearer and Masters, 1992). Figure 8.56 Inferred temperatures at the 410 and 660 km seismic discontinuities 959 based on converting the seismic depths of the 410 and 660 discontinuities to equivalent temperatures on the olivine phase boundaries. Figure 8.57 Alternative interpretation of the temperatures at the 410 km 960 discontinuity assuming that the depths of Vidale and Benz (1992) correspond to the depth of the kinetically hindered alpha to beta olivine phase boundary (roughly 1000 K isotherm). Figure 8.58 Alternative interpretations of the 410 km seismic discontinuity 961 assuming that it is deflected due to kinetic hindering of the conversion (top) or its equilibrium position. Figure 8.59 Estimated temperatures reflecting S-to-P conversions from a depressed 962 660 km seismic discontinuity adjacent to the Tonga subduction zone (Richards and Wicks, 1990). Figure 8.60 Residuum phase diagram (modified after Ita & Stixrude, 1992) which 963 shows the sub-660 km phase boundaries which may explain the second set of S-to-P conversions observed by Richards and Wicks (1990). Figure 8.61 Schematic plot of ray paths of S-to-P converted phases directed 964 towards Japan and California (after Niu and Kawakatsu, 1995). Figure 8.62 Depths of the 660 seismic discontinuity as inferred by the depths of S- 965 to-P converted depths. Red circles represent data to Japan array, blue circles represent US array data. After Niu and Kawakatsu (1995). Figure 8.63 Estimated temperature reflecting S-to-P conversion depths from the 966 660 km seismic discontinuity for the Niu and Kawakatsu (1995) depths. Figure 8.64 Location of Izu-Bonin Subduction earthquakes recorded at the 967 Warramunga array used by Wicks and Richards (1993). Figure 8.65 Cross section A - A ' across the Izu-Bonin subduction zone showing the 968 xxxvii ISC earthquakes which define the subducting slab and the S-to-P conversion depths from the 660 km discontinuity (after Wicks and Richards, 1993). Figure 8.66 Cross section B-B' across the Izu-Bonin subduction zone showing the 969 S-to-P conversion depths for the 660 km discontinuity (after Wicks and Richards, 1993). Figure 8.67 Estimated temperature of the S-to-P conversion depths from the 660 970 km discontinuity Figure 8.68 Smoothed contour maps of the 410 (top) and 660 (bottom) km 971 discontinuity at the Izu-Bonin subduction zone (after Collier and Helffrich, 1997). Figure 8.69 Depth of the 410 and 660 km discontinuities from the maps of Collier 972 and Helffrich (1997) along the lines of Wicks and Richards (1993) cross section B-B'. Figure 8.70 Depths of the 410 and 660 km discontinuities from the maps of Collier 973 and Helffrich (1997) plotted along the cross section A - A ' of Wicks and Richards (1993). Figure 8.71 Estimated temperatures for the 410 and 660 km discontinuity depths of 974 Collier and Helffrich (1997). Note that the map of 410 km topography indicates that here the boundary is in equilibrium. Figure 8.72 Plume geotherm calculated with the equations of Griffiths and 975 Campbell (1991) with a C M B temperature anomaly of 1500 K . Also shown as a box is the calculated width of the transition zone beneath the Iceland plume from differential travel times for S-to-P conversions from both the 410 and 660 km discontinuities. Figure 8.73 Possible interpretation of the "920" km seismic discontinuity as the 976 conversion of garnet dominated ocean crust on the top of subducting oceanic lithosphere. Figure 8.74 Comparison of the isothermal dimensionless density to velocity scaling 977 factor for MgO, A1 2 0 3 (Chopelas, 1992) and Y A G garnet (Reichmann, 1993). After Zhang and Chopelas (1994). Figure 8.75 Calculated extremal temperature perturbations across the lower mantle 978 estimated from seismic tomographic models of shear wave perturbations. After Cadek et al., 1994. xxxviii Figure 8.76 Absolute temperature perturbations across the lower mantle where the 979 relative estimates of Cadek et al. (1994) have been added to the Pyrolite mineral physics adiabatic geotherm. Also shown at 660 km depth are the temperatures corresponding to the mean up and downwards deflections of the 660 discontinuity (Flanagan and Shearer, 1998; Vasco etal., 1995). Figure 8.77 Radial profiles of the shear wave quality factor Qs taken from seismic 980 studies. Note the high values in the lower mantle relative to the shallow most 100-200 km. The low values at shallow depths are interpreted to reflect the presence of partial melt. If correct, then the high values in the lower mantle suggest that the mantle temperatures are well below the solidus. Figure 8.78 Estimated plume temperatures through the Pacific Superplume below 981 the central Pacific (after Yuen et al. 1993). The large magnitude of the anomalies led Yuen et al. (1993) to reject a purely thermal origin for the seismic anomalies, and instead, appeal to both thermal and chemical anomalies. Figure 8.79 Correlation of cold thermal anomalies in seismic tomographic 982 SH8WM13 (Woodward et al., 1993) with the surface distribution of subducting regions for the past 180 m.y (Richards and Engebretson (1992). Figure after Cadek et al. (1994). Figure 8.80 Schematic illustration of the convective flow in a chemically stratified 983 mantle (adapted after Anderson, 1983). Schematic isotherms of convection are illustrated where subducting slabs trigger thermally linked cold convective down welling in the lower mantle. Figure 8.81 Cold thermal anomalies at the core-mantle boundary (CMB) for the 984 SH8WM13 (Woodward et al., 1993) tomographic model. The contour intervals of temperature are in intervals of 200 K as calculated by Yuen et al. (1994). Figure after Yuen et al. (1994). Figure 8.82 Cold thermal anomalies at the core-mantle boundary (CMB) for the 985 SH8WM13 (Woodward et al., 1993) tomographic model. The heavy shaded area encloses the area of paleo-subduction zones in the last 180 m.y. based on the plate reconstructions of Richards and Engebretson (1992) expanded to spherical harmonic order 8. Figure after Yuen et al. (1994). Figure 8.83 The rms amplitude of SH8WM13 and S16B30 shear wave 986 tomographic models discussed in the text. xxxix Figure 8.84 Corrected relative extremal temperature perturbations across the lower 987 mantle. Figure 8.85 Corrected absolute extremal temperature perturbations across the lower 988 mantle. Also shown are the calculated temperature anomalies from the mean upwards and downwards deflections of the 410 and 660 km discontinuities of Vasco et al., 1995. Figure 8.86 Calculated temperature perturbations across the whole mantle for the 989 rms velocity anomalies from the S-wave tomographic model S16B30 (Masters et al., 1996). Figure 9.1 Schematic representation of a chemically layered model (top), such as 1008 the piclogite compositional model, and a chemically uniform model of the mantle such as the pyrolite model (bottom). Figure 9.2 Pyrolite geotherm compared to the whole mantle and "enforced" 1009 convectively layered mantle geotherm calculated from 3D simulations of mantle convection (Glatzmaier and Schubert, 1993). The adopted piclogite lower mantle geotherm used in this thesis is also shown. Figure 9.3 Predicted density and bulk sound velocity profiles of pyrolite and 1010 piclogite as a function of depth across the lower mantle. The piclogite assemblage is calculated along the hotter geotherm estimate from the results of mantle convection simulations (see figure 9.2) Figure 9.4 Comparison of the predicted radial Vs and Vp velocity profiles for the 1011 piclogite and pyrolite compositional models to the lower mantle portions of the global reference seismic models akl 35 (Kennett et al., 1995), akl35-F (Montagner and Kennett, 1996). Figure 9.5 A comparison of the predicted pyrolite purely elastic scaling factor 1012 with the preferred seismic estimates discussed in chapter 7. Figure 9.6 Corrected absolute extremal temperature perturbations across the lower 1013 mantle. Also shown are the calculated temperature anomalies from the mean upwards and downwards deflections of the 410 and 660 km seismic discontinuities (derived from the discontinuity topography of Vasco et al., 1995). Also plotted for comparison are an independently calculated plume and subducting slab geotherms. Figure 9.7 A comparison of the shear wave velocity model SSFIT1 (Shearer, 1022 1996), the starting model iasp91 (Kennett and Engdahl, 1991) and the xl predicted pyrolite mineral physics profile. Figure 9.8 A comparison between a predicted synthetic SS precursor waveform 1023 data stack and the observed oceanic data stack of Shearer (1996). The full details of generating SS precursor waveforms from an upper mantle velocity model is described in Shearer (1996) and was used here except that the density profile for the predicted trace uses both the pyrolite S-wave velocity and density profiles, in contrast to SSFIT1, where the density profile was simply a scaled version of the iasp91 velocity model. This plot, generated by Peter Shearer, uses an earlier version of the pyrolite model described in chapter 3. Although the amplitudes of both the 410 and 660 precursors are slightly overestimated, note the good fit to the 520 km discontinuity and the trough that precedes the 660 peak. Shearer (1996) demonstrated that this trough reflects the steep velocity gradient immediately underlying the 660 discontinuity and modified the iasp91 S-wave velocity profile to better fit the data stack by reducing the width of this zone from 760 to 727 km depth. In the pyrolite mineral physics model this steep gradient zone extends to 730 km depth. Figure 9.9 Comparison of the P R E M density profile against 50 successful density 1029 models (Kennett, 1998) which satisfy Earth mass, moment of inertia, and observed normal mode frequencies. Also shown is the predicted pyrolite density model. Figure 9.10 A comparison between the density perturbation to P R E M (Kennett, 1030 1998) when the P R E M lower mantle density profile is adjusted to satisfy mass, moment of inertia, and a recent set of observed frequencies for particular normal modes. Also shown is the difference between pyrolite and P R E M density profiles. Figure 9.11 A comparison of the spherical models of Kumagai et al. (1992) with 1031 respect to the P R E M and SP6 models. Kumagai et al., (1992) held the velocity and density structure above a 200 km thick D" region fixed, while the structure in D" was varied. Figure 9.12 Illustration of a recent compositionally layered mantle structure where 1046 the chemical layer lies deep in the lower mantle (after Hager et al., 1998). xii List of Tables Table 2.1 Estimates of pyrolite and piclogite mineralogy under low pressure 57 conditions. Table 2.2 Summary of thermal coefficient data used in calculations. 143 Table 2.3 Summary of elastic data for all phases used in calculations. 144 Table 2.A1 Comparison of Forsterite thermoelastic data (V0, K$, Kj, 146 (d KT/d P)T, [dKT/dT)p, y, bp) used in this study with recent experimental results. Table 2.A2 Comparison of Fayalite thermoelastic data (V0, K$, Kj, (d KT/d P)T, 1 4 8 [d KT/df)p, y, 87) used in this study with recent experimental results. Table 2.A3 Comparison of Mg P-olivine thermoelastic data (V0, Kg, Kj, 149 (dKT/dP)T, {dKT/dT)p, y, 87) used in this study with recent experimental results. Table 2.A4 Comparison of Fe P-olivine thermoelastic data (V0, Ks, Kj, 151 [d KT/d P)T, (d KT/dT) p , y, 5j) used in this study with recent experimental results. Table 2.A5 Comparison of Mg y-olivine thermoelastic data (V0, Kg, Kj1, 152 (3 KT/dP)T, {dKj/df) , y, 87) used in this study with recent experimental results. Table 2.A6 Comparison of Fe y-olivine thermoelastic data (V0, Ks, Kf, 153 (3 KT/8 P) (3 Kj/df) , y, 87) used in this study with recent experimental results. Table 2.A7 Comparison of natural orthopyroxene thermoelastic data (V0, Ks, Kj, 154 (5 KT/d P) , [d KT/dT)p, y, 87) used in this study with recent experimental results. Table 2.A8 Comparison of diopside thermoelastic data (V0, Ks, Kj, (dKT/dP)T, 1 5 6 (3 Kj/df) p , y, 87) used in this study with recent experimental results. ) xiii Table 2.A9 Comparison of Hedenbergite thermoelastic data (V0, Kg, Kj, 157 (9 KT/d P)T, (d KT/dT)p, y, bf) used in this study with recent experimental results. Table 2.A10 Comparison of pyrope garnet thermoelastic data (V0, Kg, Kf, 158 (9 KT/d P)T, (9 KT/df) y, bf) used in this study with recent experimental results. Table 2 . A l l Comparison of almandine garnet thermoelastic data (V0, Kg, Kj, 159 (9 KT/9 P)T, (9 KT/dT) y, of) used in this study with recent experimental results. Table 2.A12 Comparison of grossular garnet thermoelastic data (V0, Kg, Kf, 160 [dKT/dP)T, (9KT/dT) , y, 87) used in this study with recent experimental results. Table 2.A13 Comparison of Mg-Majorite thermoelastic data (V0, Ks, Kj, 161 (9 KT/dP)T, (9 KT /df) , y, 87) used in this study with recent experimental results. Table 2.A14 Comparison of Fe-Majorite thermoelastic data (V0, Kg, Kp, 162 (9 KT/d P)T, (9 KT/df) y, of) used in this study with recent experimental results. Table 2.A15 Comparison of Ca-Majorite thermoelastic data (V0, Ks, Kj, 163 (9 KT/d P)T, (9 KT/df)p, y, 87) used in this study with recent experimental results. Table 2.A16 Comparison of Mg-perovskite thermoelastic data (V0, K$, Kj, 164 (9 KTjd P)T, [dKT/df)p, y, of) used in this study with recent experimental results. Table 2.A17 Comparison of Ca-perovskite thermoelastic data (V0, Kg, Kj, 166 (9 KT /d P)T, [dKTldf)p, y, bf) used in this study with recent experimental results. Table 2.A18 Comparison of Magnesiowustite thermoelastic data (V0, Kg, Kj, 167 (9 KT /d P)T, [dKT/d f) , y, bf) used in this study with recent experimental results. xlii i Table 3.1 Summary of elastic data (V0, Kp, (d KT/d T) p , (d KT/d P) T , 8 7., y) 2 3 7 for all phases used in calculations. These values in this table were used in modeling predicted depth profiles of F 0 and p and remain unchanged when used in modeling Vs and Vp depth profiles. Table 3.2 Summary of constants for the coefficient of thermal expansion used in 239 calculations. Table 3.3 Summary of shear moduli elastic data (p, [d[i/dT)p, ( 3 p / 3 P ) r ) 241 for all phases used in calculations. Table 3.4 Summary of the elastic data used by Duffy and Anderson (1989) in 245 modeling Vs and Vp depth profiles across the upper mantle, transition zone, and the top of the lower mantle. Entries in bold are based on experimental measurements that have undergone subsequent revision since their study, entries in shaded boxes are estimated using the {DLA} formalism of Anderson (1988). Table 3.5 Summary of the elastic data used in this study in modeling V$ and Vp 246 depth profiles across the upper mantle, transition zone, and the top of the lower mantle. Entries of {d\i/dT)p and ( 3 p / 9 P ) r in shaded boxes are estimated using the high temperature thermodynamic approximation of Isaak (1992), while entries of 8p in shaded boxes are estimated using the approximation 8 r = [l/(a -rvr)J(d KT/d T)p. The single p in a shaded boxes is estimated using Mg- perovskite systematics as discussed in the text. Italic entries are estimated on experimental values for similar minerals (e.g. the estimated value for Fe-majorite (d\i/dT}p based on the experimentally measured value of Mg-majorite (d n/d T)p). Comparison of majorite elastic data from Duffy and Anderson (1989) 248 and this study. A Summary of the temperature and pressure derivatives of the bulk 257 and shear moduli for the Mg-olivine phases from recent studies that have modeled upper mantle and transition zone Vs and Vp velocity profiles. Table 3.8 Predicted olivine content from the velocity and density increases at the 265 410 km seismic discontinuity. Table 3.6 Table 3.7 Table 3.9 Coefficients of the constants used in the polynomial fits which 286 xliv "smooth" the predicted Vs and Vp velocity profiles. Table 3.10 Seismological estimates for the parameter increases across the 410 km 286 seismic discontinuity. The top row is the representative inference utilized by Bina(1993). Table 3.11 Predicted olivine content from the velocity and density increases at the 291 410 km seismic discontinuity. Table 3.12 Coefficients of the constants used in the polynomial fits to the 297 predicted F^and Vp velocity profiles. Table 3.A1 Comparison of Forsterite Ks, Kj, u, (dKT/dP)T, (d\i/dP)T, 3 3 4 (8KT/8T)p, [d\i/dT)p data used in this study with recent experimental results. Table 3.A2 Comparison of Fayalite Ks, Kp, \i, (dKT/dP)T, (d\j./dP)T, 3 3 5 [8KT/8T)p, (d\i/dT) data used in this study with recent experimental results. Table 3.A3 Comparison of Mg-p-olivine Ks, Kj, \i, (d KT/dP)T, (d \i/dP)T, 3 3 6 [d KT/dT) , (d\i/8T) data used in this study with recent experimental results. Table 3.A4 Comparison of Fe-P-olivine Ks, Kj, p, (8KT/8P)T, (d\i/dP)T, 3 3 7 (d KT/df) , [d\i/dT)p data used in this study with recent experimental results. Table 3.A5 Comparison of Mg-y-olivine Ks, Kj, \i, (dKT/8P)T, (d\i/dP)T, 3 3 8 {p'KTldt) , {8\i/8T)p data used in this study with recent experimental results. Table 3.A6 Comparison of Fe-y-olivine Ks, Kp, u, (8KT/8P)T, (d\i/dP)T, 3 3 9 [8KT/8T)p, [d\x/8T)p data used in this study with recent experimental results. Table 3.A7 Comparison of orthopyroxene Ks, Kj, \i, (d KT/8P)T, (8 \i/dP)T, 3 4 1 [d KT/dT) , [d\ildT) data used in this study with recent experimental results. xiv Table 3.A8 Comparison of Diopside Ks, Kj, P, (dKT/dP)T, (d\i/dP)T, 3 4 2 (dKT/dT)p, {d\i/dT^p data used in this study with recent experimental results. Table 3.A9 Comparison of Hedenbergite Ks, Kj, p, (dKT/8P)T, (d\i/dP)T, 3 4 3 (9 KT/dT)p, (d\i/dT}p data used in this study with recent experimental results. Table 3.A10 Comparison of Pyrope garnet Ks, Kj, p, (dKT/dP)T, (d\i/dP)T, 3 4 4 (9 KT/dT}p, (d[i/dT)p data used in this study with recent experimental results. Table 3.A11 Comparison of Almandine garnet Ks, Kj, p, (dKT/8P)T, 34$ (d[i/8P)T, (dKT/8T)p, (d\i/dT)p data used in this study with recent experimental results. Table 3.A12 Comparison of Grossular garnet Ks, Kj, \i, (d KT/dP)T, (d n/dP)T, 3 4 6 [dKT/dT)p, [d[i/dT)p data used in this study with recent experimental results. Table 3.A13 Comparison of Mg-Majorite Ks, Kj, \i, (dKT/8P)T, (d[i/dP)T, 3 4 7 (9 KT/dT)p, (d[i/dT)p data used in this study with recent experimental results. Table 3.A14 Comparison of Fe-Majorite Ks, Kf, \i, (8KT/8P)T, (d\i/8P)T, 3 4 9 [d KT/dT) , (d\ildf)p data used in this study with recent experimental results. Table 3.A15 Comparison of Ca-Majorite Ks, Kj, \n, (dKT/dP)T, (d\i/dP)T, 3 5 0 {d KT/dT)p, [d[i/dT)p data used in this study with recent experimental results. Table 4.1 Tabulated values for measures properties Mg-perovskite, periclase, 421 and wustite. Table 4.2 Values for the coefficient of thermal expansion used in the 422 calculations. xlvi Table 4.3 Table 4.4 Table 5.1 Table 5.2 Table 5.3 Table 5.4 Table 5.5 Table 5.6 Table 6.1 Table 6.2 Table 7.1 Table 7.2 Decompressed parameters from a constrained 4th order equation of 425 state fit to the P R E M lower mantle. Also shown are the value estimated by Bukowinski and Wolf (1990) and Jeanloz and Knittle (1986). Expected shear moduli temperature derivatives for the listed {DLA} 435 parameter {p}P. Summary of elastic data used previously in modeling p and 464 Constants in the polynomial expressions for the coefficient of thermal 464 expansion. Comparison of thermoelastic data used in some recent studies. Note 479 the change in room temperature value for the coefficient of thermal expansion. Comparison of thermoelastic parameters for Mg-perovskite. 488 Table 7.3 Shear moduli and associated temperature and pressure derivatives for 495 the lower mantle phases used in this study. Shaded entries are estimated values as described in the text. Summary of calculated {DLA} parameters for the elastic parameters 499 estimated in this and previous studies for Ca- and Mg-perovskite. Summary of shear moduli properties for Mg-perovskite from 554 Sinelnikov et al. (1998). Comparison of thermoelastic parameters for Mg-perovskite using a 4 t h 557 order Birch-Murnaghan EOS compared to the values used in the previous chapters (which utilized a 3 r d order Birch-Murnaghan EOS). High temperature experimental values for compounds relevant to 574 geophysics (Anderson and Isaak (1995). Summary of upper mantle estimates (d\nVs/8lnVp)p derived from 584 station corrections with an adopted upper mantle and transition zone mean ratio (Vs/Vp) = 0.5472 calculated from the akl35 seismic reference model (Kennett et al., 1995). Original values for the scaling factors adopted in construction of the 636 tomographic models evaluated by Ritzwoller and Lavely (1995). xlvii Dedication I would like to dedicate this thesis to my original PhD advisor at U B C , the late Professor Richard L . Armstrong, who died of liver cancer in the fall of 1991. His honesty, integrity, and generosity remain an inspiration to me. I sorely miss his council and deeply regret that I cannot share my thoughts and discoveries with someone so special. Although we never discussed the research projects that comprise this thesis, nor the isotopic modeling studies which have spun off from them, I am sure he would have approved, as some of these projects validate his once controversial hypothesis that virtually all of the continental crust was formed very early in Earth's history in a "Continental Big Bang". xlviii Acknowledgments M y sincere thanks to Professors Bruce Buffett and Michael Bostock in the Division of Geophysics, Earth and Ocean Sciences, who listened to, and ultimately, read some of my research projects. Professor Bruce Buffett effectively became my defacto thesis advisor in the closing months of this thesis and never once complained to me about having a geology graduate student imposed on him, especially one whose thesis topic was on subjects outside his expertise. Both Bruce and Michael never objected to my sudden appearance at their office doors when I would show them new figures unrelated to their research. I must have tested the patience of both of them with my abrupt interruptions and it is a measure of both men that neither told me to "get lost" when I burst in. I very gratefully acknowledge the early interest and advice of Professor Joann M . Stock, California Institute of Technology. I had hoped to pursue research on past global plate motions with her but the lack of financial support at the University of British Columbia led me to pursue research topics that are outside her interests (but are within my financial grasp). Nevertheless, I hope that the results and implications of the projects herein measure up to her high standards of excellence. Now that I have plumbed the depths of the mantle, it may be time to return to the surface of the Earth. It is a pleasure to acknowledge the friendship, encouragement, and advice of Professor Jerry Mitrovica, Dept. of Physics, University of Toronto. I greatly appreciate the kindness and generosity extended to me at numerous scientific conferences and eagerly look forward to the collaborative work with him and his former graduate student Dr. Russ Pysklywec. xlix The completion of this thesis could not be possible without the financial assistance provided via the following sources: a summer contract in 1992 as a Senior Field Assistant to Dr. Peter van der Heyden, Research Scientist, Geological Survey of Canada-Cordilleran Division; in the winter of 1992-93 as an Winter Works Program office assistant to Dr. Peter van der Heyden and Dr. Steve Gordy, Research Scientists, Geological Survey of Canada-Cordilleran Division; in the summer of 1993 as a tree planter with Apex Reforestation; also in the summer of 1993 as an office assistant to Mr. Max Holtby, Chief Geologist, Silver Standard Resources Inc., Vancouver; in the summer of 1994 a summer contract as a Senior Field Assistant with Mr. Jim Logan, Project Geologist, B C Ministry of Mines and Petroleum Resources; and from 1993 to present as a part-time medical office assistant/security guard with the Seymour Medical Clinic, Vancouver/Ms. Shirley Fine, Office Manager, Seymour Medical Clinic, kindly allowed me the flexibility in scheduling my hours such that I had the opportunity to attend scientific conferences while employed by the Clinic. In addition, the Doctors at SMC kindly offered me extra hours and duties many times over the past years to augment my regular pay. I am deeply grateful to these people and institutions, since without the funds generated from these temporary jobs, I would have been financially driven out of the PhD program at U B C shortly after the death of my original thesis supervisor Professor R.L. Armstrong. Lastly, it is a pleasure to acknowledge the kindness and encouragement of my mum during the long sojourn through graduate school - while her eyes would often glaze over when listening to the latest discovery on mantle composition, her constant support and encouragement to complete my sentence at U B C was greatly appreciated. Finally, she can say those special words "my son the Doctor " 1 Chapter 1, page 1 1. Introduction 1.1 Background Seismology has determined that the Earth's mantle may be conveniently parameterized in terms of simple, one dimensional profiles of density (p), shear (Vs) and compression (Vp) velocity (see figure 1.1). This figure, constructed from the akl35 seismic global reference model (Kennett et al., 1995) illustrates these properties together with a profile of the bulk sound velocity (V®), calculated via the relationship (Anderson, 1989; p. 83): v = .Iv2 -±V2 Inspection of these profiles reveals that superimposed on these smoothly increasing profiles are abrupt jumps in density and velocity, which exist globally within the earth's mantle, albeit with some regional variance in the precise depth and magnitude of the jumps. Global mean depths to these abrupt jumps, termed "seismic discontinuities", are 418, 520, 660 km depth (Shearer, 1996; Flanagan and Shearer, 1998; note that the akl35 reference model does not incorporate the 520 km discontinuity). These seismic discontinuities, and related high gradient zones (660 to and 730 km depth), have provided a convenient way for seismologists to divide up the mantle into the shallow upper mantle (extending from the surface down to 418 km depth), the transition zone (extending from 418 to 730 km depth), and the lower mantle (extending from 730 to 2891 km, the base of the mantle). While one of the earliest global seismic reference models, P R E M (Dziewonski and Anderson, 1981) also included a shallower 210 km discontinuity, subsequent seismic studies have failed to demonstrate that this represents a truly global feature, and subsequent global seismic reference models (e.g. Chapter 1, page 2 CPvEMO (Montagner and Anderson, 1989), iasp91 (Kennett and Engdahl, 1991), SP6 (Morelli and Dziewonski, 1993), ak!35 (Kennett et al., 1995), ak!35-F, and akl35-Q (Montagner and Kennett, 1996)) do not include this feature. In addition to these relatively shallow seismic discontinuities, very recent seismological studies have suggested that a single, very deep discontinuity, located roughly 290 km above the core-mantle boundary, may also exist (see reviews of this region by Loper and Lay, 1995; Lay et al., in press). However, this thesis will not focus on the interpretation of this basal mantle seismic discontinuity. The correct interpretation of the shallow seismic discontinuities (418, 520, and 660) is of great interest in the Earth Sciences. If any one of these seismic discontinuities represents a chemical boundary, perhaps fortuitously superimposed upon a phase boundary, then convection within the mantle would likely be restricted to flow within the separate mantle layers with little mass flux across the chemical boundary (e.g. Richter and Johnson, 1974, Richter and McKenzie, 1981). A schematic illustration of such a layered mantle, taken from Gasparik (1997) is shown in figure 1.2. Theoretical and tank experiments indicate that a chemical density jump of as little as 1% in a constant viscosity fluid may lead to convective isolation with separate, layered convection (Richter and McKenzie, 1981). Alternatively, i f the seismic discontinuities represent the effects of phase changes within an isochemical mantle, then it is likely that whole mantle convection would occur with complete mass exchange between the upper and lower mantle (e.g. O'Connell, 1977). Such a convective regime is shown in figure 1.3. Chapter 1, page 3 While some recent numerical simulations of mantle convection indicate the negative Clapeyron slope of the 660 km y-olivine breakdown reaction might hinder flow across this phase change (e.g. Solheim and Peltier, 1994a, b; Tackley et a l , 1993; 1994) it is uncertain i f this effect is a real feature of the Earth. The ability of the 660 km y-olivine to Mg-perovskite and magnesiowustite phase transition to cause partial layering within a convection model depends upon a number of input parameters that must be specified apriori. Specifically, Tackley et al. (1994) point out that most studies which have incorporated the effects of transition zone phase changes have simply stressed the magnitude of the Clapeyron slope as the critical parameter controlling the propensity towards partial layering within the numerical convection model. They note this is incorrect since the anomalous buoyancy forces associated with vertical deflection of the phase boundary is actually a function of a number of parameters which may be expressed as a nondimensional number, referred to as the phase buoyancy parameter, P (Schubert and Turcotte, 1971; Christensen and Yuen, 1985), which represents the ratio of buoyancy due to phase boundary deflection to the buoyancy due to thermal effects (integrated over a column): deflection — r phase ' Pg Flher„ia, =pgaATh, ^deflection Y Clap P = Fthermal « P ' g " where Fdefleclion is the anomalous density due to the deflection of the phase boundary, ^thermalls anomalous density due to latent heat effects, y c l a p is the Clapeyron slope of the phase transition, Ap is the change in density across the phase change, p is the local mean Chapter 1, page 4 density at the phase transition boundary, g is the acceleration due to gravity, a is the local mean coefficient of thermal expansion at the phase transition boundary, Ar is a temperature scale usually taken as the superadiabatic temperature change across the full convection layer, and h is the scale height, taken as the depth of the convecting layer. Note that while AT enters into the formulation of both FdefleCfion and PV/zerma/' it cancels out of the expression for the phase buoyancy parameter, P. Inspection of the various terms in the phase buoyancy parameter reveals that the change in density, local mean density, and local mean thermal expansion are as important in as the Clapeyron slope in defining the magnitude of the phase buoyancy parameter, and thus, all of these properties affect the phase change in aiding or retarding flow across it (Tackley et al., 1994; Christensen, 1995). In contrast to Ap, p, a , and y , both h and g may be considered well known since it is convention to adopt h = the full depth of the mantle (2890 km) and adopt a typical value for the acceleration due to gravity (g = 9.8 m/sec2). Therefore, the phase buoyancy parameter, Pm is useful because it encapsulates a number of different material properties, which together, control the "strength" of the endothermic 660 km phase transition to induce partially layered convection (because the 418, and 520 km phase transitions within the olivine system have positive Clapeyron slopes, these reactions act to promote, rather than hinder, convective flow). Consequently, comparing Pm determined from the adopted values used in the numerical convection community, against P 6 6 0 derived from the pyrolite mineral physics model, described in detail in the following chapters, permits one to assess the validity of the input parameters upon which the numerical convection models depend. Chapter 1, page 5 Figure 1.4 plots the calculated 660 phase buoyancy parameter for a pyrolite mantle as a function of the Clapeyron slope of the y-olivine phase transition. Recent thermodynamic optimization of all of the experimental studies find that for pure y-Mg-olivine, the Clapeyron slope lies between -1.9 to -2.1 MPa/K (Bina and Helffrich, 1994). These authors note that their recommended value represents an upper bound since the effects of iron were not accounted for since iron is expected to reduce the Clapeyron slope (y-olivine is expected to contain 10-12 mol% iron; Ita and Stixrude, 1992). Furthermore, this value is applicable for a pure olivine mineralogy, whereas the mantle likely contains 62 vol% olivine for the pyrolite mineralogy (or 42 vol% for the piclogite mineralogy). Consequently, one way to account for the finite amount of olivine is to reduce the recommended value of Bina and Helffrich (1994) by multiplying it by a factor of 0.62 (or 0.42), where the exact number depends upon the olivine content in the assumed bulk composition, to reduce the value of the pure olivine Clapeyron slope to that effectively seen by a polyphase mantle (see Weidner and Wang, 1998). Lastly, as I will show in the following chapters, the calculated density jump at 660 km depth for a pyrolite mantle is considerably less than that of the seismic reference model P R E M , the source for the Ap, and p values adopted within the numerical convection community. Similar to the effect of decreasing the magnitude of the Clapeyron slope, reducing the values of both Ap, and p decreases the value of the 660 phase buoyancy parameter. The effect of reducing the magnitude of the Clapeyron slope to reflect the volume percent of olivine within a pyrolite mantle combined with the pyrolite density jump has a significant effect on the calculated 660 phase buoyancy parameter. Compare the curve Chapter 1, page 6 labeled "Pyrolite mantle" to that calculated using the P R E M density jump and the full value of the Clapeyron slope (equivalent to assuming the mantle is composed of pure olivine). This curve is labeled "100% olivine mantle P R E M density" and it should be noted that this curve represents input parameters commonly adopted with the numerical convection community -for example Tackley et al., (1994) present the results from one numerical run (case 4) where Yciap = -3.0 MPa/K and the density jump = PREM. Together with their remaining adopted parameters, this gives a 660 phase buoyancy parameter of -0.10 which is plotted, together with other P66Q values calculated from other published convection models, as left pointing arrows which are offset from the y-axis (to determine the adopted Clapeyron slope for a particular convection study, trace horizontally across from the appropriate arrow until intersecting the line of the calculated 660 phase buoyancy parameter for a 100%) olivine mantle and a P R E M density jump). It is interesting to note that case 4 of Tackley et al. (1994) exhibited virtually no partial layering due to the 660 km phase change, yet it is clear from figure 1.4 that the adopted input parameters have resulted in a 660 phase buoyancy parameter (P 6 6 0 = -1.0) which is roughly 38 times greater than that for a uniform pyrolite bulk composition (P660 = - 0.026). Another way of interpreting the P660 value is to note that a value of w-1.0 is equivalent to adopting an effective Clapeyron slope of about -8.0 MPa/K, assuming that all of the remaining parameters are taken from the pyrolite mineral physics model. Further note that for a piclogite mineralogy, both the density jump and the volume percent of olivine is significantly smaller than the pyrolite mantle, and hence, the discrepancy between the P 6 6 0 values from the numerical convection community and the P660 value inferred from mineral physics would widen. Chapter 1, page 7 Because increasing the negative magnitude of the Clapeyron slope significantly increases the propensity to layering, the use of a 660 km Clapeyron slope of-8.0 MPa/K, instead of 0.62 x (-2.0 MPa/K), should result in significant partial layering. Thus, it is evident from figure 1.4 that none of the published convection models have actually been run at "Earth-like" values, inspite of claims to the contrary. A complete discussion of the individual convection studies which are plotted in this figure will be presented elsewhere, but it is clear from this figure that partial mantle layering, as currently proposed by the numerical convection community may simply be a numerical artifact reflecting the use of incorrect input parameters, rather than an actual feature of the present day Earth's mantle. Consequently, I will focus below only on the end-member convection states of either whole mantle flow corresponding to a uniform bulk composition, or layered mantle flow reflecting changes in bulk composition. These two different convective regimes, layered, or whole mantle convection, result in significantly different predictions concerning the thermal and chemical evolution of the Earth. For whole mantle convection with a uniform bulk composition, the mantle geotherm (the variation of temperature with depth), is expected to be very nearly adiabatic within the bulk of the mantle away from either surface or basal thermal boundary layers. Furthermore, i f the whole mantle is of uniform composition, and ignoring the relatively small effects of latent heat associated with phase changes, the upper mantle, transition zone, and lower mantle geotherms must lie along the same adiabat (Richter and Jeanloz, 1979; Olson et al. 1990). In contrast, in a convectively layered mantle, a large thermal boundary must coincide with the chemical boundary such that the lower of the two convectively isolated layers is significantly hotter than the shallower layer (Jeanloz and Richter, 1979; Schubert and Spohn, 1991; Chapter 1, page 8 Richter and McKenzie, 1981; Spohn and Schubert, 1982; Kenyon and Turcotte, 1983; Davies, 1983; Jeanloz and Morris, 1986; Glatzmaier and Schubert, 1993). A n example of geotherms constructed for a uniform and chemically layered mantle, taken from Jeanloz and Richter (1979), are shown in figure 1.5 and compared against the pyrolite mineral physics adiabat, described in chapter 2. The increased temperature in the lower convective layer reflects the fact that advected heat within this layer must be transferred to the overlying, convectively isolated layer via thermal conduction across the chemical boundary. Because thermal conduction is a far less efficient way to transfer heat than convection, the thermal boundary layer at the chemical boundary results in a large temperature jump being developed across this interface (e.g. Richter and Jeanloz, 1979; Olson, 1981; Jeanloz and Morris, 1986; Glatzmaier and Schubert, 1993). 1.2 Isotopic Structure of the Mantle Convective isolation within a layered mantle provides a relatively straightforward, but non-unique, explanation of the isotopic heterogeneity observed at the Earth's surface. Within the classic isotopically layered model of the mantle, the volume of the shallow upper mantle and transition zone is interpreted as an isotopically depleted reservoir, termed " D M M " for depleted-MORB-Mantle (see Hart and Zindler, 1989), which supplies the global mid-ocean ridge spreading system. D M M is viewed as the complimentary reservoir to the isotopically enriched continental crust with early mass-balance isotopic studies concluding that the mass of the continental crust would result in a volume of depleted mantle in good agreement with Chapter 1, page 9 the volume of the combined upper mantle and transition zone (e.g. DePaolo and Wasserburg, 1976a; b; 1979; DePaolo, 1980; 1981; O'Nions et al., 1979. Jacobsen and Wasserburg, 1979; 1981; Allegre, 1982; Allegre et al., 1983a; 1983b; Allegre and Turcotte, 1985; Turcotte and Kellogg, 1986; O'Nions, 1987; Galer et a l , 1989). In contrast, the volume of the lower mantle (below 660 km depth), is interpreted as a more primitive, essentially undifferentiated, and rarely sampled isotopic reservoir which supplies primordial rare gas components and trace amounts of primitive material to hot spots (e.g. Allegre et al., 1996). However, this simple isotopic view of the mantle is not unique and whole mantle models have been proposed which appear to satisfy the isotopic observations (e.g. Davies, 1984; 1990; Loper, 1985; Silver et al,, 1988; Davies and Richards, 1992), albeit it should be noted that these particular models are based largely on geodynamic, rather than isotopic arguments. However, a major drawback of isotopic mass balance modeling studies is that isotopic values contain no information on where within the mantle the particular isotopic reservoir exists. In other words, the isotopic signature of a rock or mineral sample contains no information about the physical conditions (temperature or pressure), or location of the reservoir within the mantle (see for example Kellogg, 1992). Thus, while isotopic models may constrain the volume of the depleted mantle, they can state nothing on where within the mantle such a reservoir lies. For example, while most workers within the isotopic community adopt an isotopically layered mantle with a shallow depleted reservoir overlying a undepleted lower mantle, Anderson (1981a; 1982; 1995) has proposed an isotopic model where an undepleted reservoir exists within the upper mantle (less than 418 km depth), but overlies a depleted reservoir comprising the volume of the transition zone. This depleted reservoir which is envisioned to feed mid-ocean ridges, in turn, overlies a convectively-isolated lower Chapter 1, page 10 mantle. While this interpretation of the mantle is in conflict with surface observations where mid-ocean ridges have migrated across pre-existing hotspots (e.g. Richards, 1991), this particular isotopic model does not strictly conflict with information extracted during isotopic analysis of a rock sample. A n independent argument against the classic isotopically layered mantle of a depleted upper mantle (shallower than 660 km depth) overlying an undepleted lower mantle reservoir arises from concerns over heat flow. Schubert and Spohn (1981) and Spohn and Schubert (1982) calculate that two-layer mantle convection thermally insulates the lower mantle such that removal of heat from the lower mantle is significantly less efficient than whole mantle convection. They determine that the if two-layer convection exists within the Earth, the lower mantle cannot have an undepleted concentration of radiogenic heat producing elements because the volumetric heat production due to radioactive decay within the basal, convectively isolated layer must be less than 8-12% of the total average mantle heat production. Thermal evolution calculations using parameterized two-layer mantle convection models (Spohn and Schubert, 1982) support this conclusion. This flaw of the classic isotopically layered mantle models, which are still being proposed today (see Jacobsen, 1988a, b; Allegre et al., 1996), has not yet been addressed by the isotopic community. 1.3 Subduction zone structure Many various lines of evidence bear on the style of convection within the Earth, but none other than seismology have the potential to directly image present day convection (see reviews on mantle tomography by Lay, 1987; Masters, 1991; and Ritzwoller and Lavely, Chapter 1, page 11 1995). One of the most pertinent (and controversial) questions is whether subducting oceanic lithosphere extends into the lower mantle (see Lay, 1994a; b; Kincaid, 1995). Essentially two methods have been used to address this question. One technique, termed residual sphere analysis involves a comparison between a predicted pattern of seismic anomalies and seismic observations. A thermal model of subducting oceanic lithosphere relevant to the particular locality is first constructed and then converted, through the use of constant temperature derivative of velocity ((dV,,/dT)p ) which scales temperature into P-wave velocity anomalies. Ray tracing through this model is then performed and the results compared to seismic observations recorded at existing permanent stations around the world (Jordan, 1977; Creager and Jordan, 1984; 1986; Fischer et al., 1988; Zhou and Anderson, 1989; Jordan et al., 1989; Zhou et a l , 1990; Boyd and Creager, 1990; Fischer et a l , 1991; Ding and Grand, 1994). While most workers interpret the comparison between the pattern of predicted and observed travel time residuals as being consistent with extensions of fast slab velocity anomalies to depths in excess of 1000 km, it is admitted that the penetration depth of the slab trades off directly with the magnitude of the velocity anomaly of the subducting lithosphere. Because the magnitude of the slab velocity anomaly is linearly related to the adopted value for the scaling factor, (d Vp /d T)p , this parameter, which is unmeasured at the high temperature and pressure conditions of the deep mantle, is of paramount importance. For the values inferred by Creager and Jordan (1984; 1986) and Fischer et al., 1988; 1990), the predicted slab velocity anomalies is weak, and hence a deep extension into the lower mantle is required to generate the match between predicted and observed travel time residual. Alternatively, Anderson (1987) argues that the unique mineralogy within the cold subducting Chapter 1, page 12 oceanic lithosphere will result in an effective (d Vp/8T)p which is much greater than that adopted by Jordan and co-workers. Consequently, he asserts that the magnitude of the slab velocity anomaly is much larger, with the result that slabs may be restricted to only the upper mantle and transition zone yet still produce travel time residuals consistent with observations (see also Zhou et al., 1990). The trade-off between the apparent slab penetration depth and (dVp/dT)p is illustrated in figure 1.6, after Fischer et al. (1991). The plotted curves represent the effect of varying the adopted value of (dVp/dT)p on the inferred slab penetration depth for travel time residuals calculated for selected within slab earthquakes. On the basis of the maximum variance reduction between predicted and observed residuals (see figure 1.7), Fischer et al. (1991) argue for a preferred value of -0.5 m/sec K and a minimum slab penetration depth of just over 1000 km. Nevertheless, resolving between deep or shallow penetration of slabs into the mantle via residual sphere analysis requires an independent and robust estimation of (d Vp/dT)p . The second approach to answering the question of whether subducting slabs penetrate into the lower mantle uses huge data sets of teleseismic and regional travel time arrivals in large-scale seismic tomographic inversions for regional mantle structure (Zhou and Clayton, 1990; Zhou, 1990; 1996; Grand, 1987; 1994; Grand et a l , 1997; Ding and Grand, 1994; van der Hilst et a l , 1991; 1993; 1997; van der Hilst, 1995; Widiyantoro and van der Hilst, 1996; 1997). While the early studies of this decade gave somewhat "fuzzy" tomographic images which were open to several different interpretations, the S-wave images of Grand and co-workers, and the independent P-wave images of van der Hilst and co-workers have become progressively sharper and converged on essentially the same present day picture of large Chapter 1, page 13 scale mantle structure. These S- and P-wave tomographic models clearly show continuous sheets of fast seismic velocity anomalies, coincident with the surface projections of present day subducting lithosphere at the Japan, Indonesian, Tonga, Kermadec, and North and Central American trenches, which extend well into the lower mantle, and in some cases, to the core-mantle boundary. Figure 1.8 shows a vertical section through the Japan trench from the P-wave tomographic model of van der Hilst et al. (1997). Faster and slower velocities relative to the radial reference akl35 P-wave velocity model are coloured blue and red, respectively. Thin lines at constant depth represent the location of the 410 and 660 km seismic discontinuities, while small dots in the upper mantle give the location of selected within-slab earthquakes. The simplest interpretation of these tomographic images is that the aseismic, fast seismic anomalies within the lower mantle represent subducting oceanic lithosphere and hence, indicate significant mass transfer is presently occurring between the upper and lower mantle (Kerr, 1997; Masters, 1997). However, it is recognized and acknowledged within the tomographic community (see van der Hilst et al., 1993) that it is not possible using tomographic images alone, to determine whether or not the fast seismic anomalies represent compositional or thermally induced variations in velocity. For example, Anderson (1981b) and Wen and Anderson (1995) assert that the apparent aseismic slab extensions into the lower mantle instead represent induced convective downwellings in a thermally-coupled, but compositionally, and hence, convectively layered mantle system. A cartoon illustrating this effect, reproduced from Anderson (1981b), is shown in figure 1.9. Therefore correctly interpreting the regional tomographic images of mantle subduction zone structure requires that the inherent ambiguity in interpreting the fast and Chapter 1, page 14 slow velocity anomalies as either thermal or chemically driven velocity anomalies be resolved. This requires independent evidence that the whole mantle is indeed isochemical, and in addition, a way in which to determine if the velocity anomalies recovered by tomography are indeed consistent with a thermal origin. 1.4 Bulk Mantle composition One of the main goals of mineral physics is to determine the bulk composition of the mantle by comparing predicted properties of candidate compositional models to seismological observables. A pioneering study was made by Birch (1952) who argued that the high seismic velocity gradients within the transition zone reflected the combined effects of successive phase changes. Many subsequent mineral physics studies have followed with the intent of constraining mantle composition by comparing the density and elastic properties (radial profiles of bulk modulus, shear, compression, and, or bulk sound velocity) of high pressure minerals to these properties extracted from seismic data (e.g. Birch, 1961; 1964; Press, 1968; Anderson, 1967; 1968; 1976, 1977; Davies, 1974. Davies and Dziewonski, 1975; Butler and Anderson, 1978; Anderson and Jordan, 1970; Anderson et al., 1971; Wang, 1970; Burdick and Anderson, 1975; Watt et al., 1975; Liu, 1977; 1979a; b; Watt and O'Connell, 1978; Jeanloz and Thompson, 1983; Lees et al., 1983; Jackson, 1983; Anderson and Bass, 1984; 1986; Bass and Anderson, 1984; Liu and Bassett, 1986; Bina and Wood, 1987; Weidner, 1985; 1986; Weidner and Ito, 1987; Jeanloz and Knittle, 1986; 1989; Duffy and Anderson, 1989; Chopelas and Boehler, 1989; 1992; Bina and Silver, 1990; Bukowinski and Wolf, 1990; Stixrude et a l , 1992; Ita and Stixrude, 1992; 1993; Bina and Helffrich, Chapter 1, page 15 1992; Agee, 1993; Bina, 1993; Zhao and Anderson, 1994; Anderson et al., 1995; Jackson, 1998; Irifune and Isshiki, 1998; Vacher et al., 1998). However, the petrological complexity of the mantle, particularly the transition zone, coupled with the lack of experimentally measured properties for many of the key properties, such as temperature and pressure derivatives of the bulk and shear moduli, which are necessary to extrapolate the mineralogical data to the high temperature and pressure conditions of the mantle, resulted in a lack of consensus. Thus, Anderson and co-workers have, in general, concluded that the upper mantle and transition zone is chemically, and hence, convectively layered with seismic discontinuities marking changes in bulk composition. In a recent study, Wen and Anderson (1995) appear to have conceded that the transition zone seismic discontinuities reflect phase changes, but now retreat deeper within the lower mantle and advocate the existence of a "seismically invisible" chemical boundary at roughly 1200 km depth. Alternatively, Jeanloz and co-workers (see Jeanloz, 1989; 1991 for recent summaries) have concluded that while the upper mantle and transition zone seismic properties are best satisfied by a uniform composition, the 660 km seismic discontinuity is both a chemical and phase boundary which convectively isolates the lower mantle from the overlying transition zone. In contrast, many of the other studies noted above, conclude that the seismic properties of the whole mantle are satisfied by a uniform bulk composition. As noted by Duffy and Anderson (1989), the rapid increase in both the number of experimental mineral physics laboratories around the world and the expanding temperature and pressure capabilities of the experimental apparatus has resulted in a rapidly growing data base of thermoelastic properties. This experimental data base means that rather than being forced to rely on guesses for many of the required elastic properties, predicted properties for Chapter 1, page 16 candidate bulk composition models can now be made which are based largely on measured parameters. 1.5 Presentation Theoretical mineral physics is used in six studies to constrain the composition and dynamics of the Earth's mantle. In chapter 2, using updated, published experimental data, I evaluate two competing mineralogical models for the composition of the mantle using calculated one dimensional profiles of density (p) and bulk sound velocity (V^) as discriminants to measure the success of these two models in satisfying the seismologically inferred profiles. Unlike recent studies I find that the mineralogy of a uniform bulk composition provides an excellent fit to the seismic properties of the whole mantle along a self-consistent adiabatic geotherm which lacks any thermal boundary layers internal to the mantle. In contrast, the mineralogy of a chemically layered bulk composition results in predicted profiles which cannot satisfy the observations. In chapter 3, to further test the predicted properties of the uniform bulk composition model, known as the pyrolite model, the mineral physics calculations are extended to predict one dimensional profiles of shear (Vs) and compression (Vp) velocity across the upper mantle and transition zone. Previous studies that modeled Vs and Vp suffered from having to estimate many of the necessary temperature and pressure derivatives required in the calculations and hence, the results were ambiguous. Fortuitously, many of these critical material properties (p, (d[i/dT)F, (d\i/dP)T,) are now being experimentally measured and this study incorporates the latest results. I find that the predicted profiles of V$ and Vp are in Chapter 1, page 17 excellent agreement in terms of both velocity gradient and absolute velocity with the latest, high-resolution regional seismic profiles. The predicted mineral physics profiles also give a mutually consistent estimate of the olivine content of the mantle from the velocity jumps at the 410 km seismic discontinuity. Lastly, the predicted Vs and Vp normal-incidence reflectivity of the 410 km, 520 km and 660 km discontinuities matches a number of independent seismic estimates. In chapter four, I estimate a high temperature value for [d\i/dT^s P v of Mg-perovskite via constrained adiabatic decompression of the lower mantle P R E M seismic properties. A simplified pyrolite lower mantle mineralogy of Magnesiowtistite and Mg-Fe perovskite is used to provide apriori constraints for some of the unknown high temperature decompressed properties thereby restricting the possible parameter space for the decompressed shear modulus (p0). This property is used to constrain the value of [d[i/8T)pg Pv when the room temperature properties are corrected up to the decompressed, but hot lower mantle elastic properties. Adopting this new estimate of (d\i/dT)pg Pvand estimating (dp/dr)^3 Pvvia a high temperature thermodynamic approximation, in chapter five I then iteratively adjust the pressure derivative, [d[i/8P)pg P v , under the first order assumption [d\i/dP)pg P v = (dn/dP)^" Pv, until predicted one dimensional profiles of Vs and Vp for a pyrolite mineralogy match the seismic profiles across the lower mantle. The resulting value of [d\i/dP)ps Pvis in good agreement with that predicted by a recent molecular dynamics study, giving us confidence that the resultant velocity profiles are permissible. I justify Chapter 1, page 18 "tuning" the predicted profiles to the observed ones on the basis of the results of study one where it was demonstrated using p and V® profiles that a pyrolite mineralogy could match the lower mantle properties along a self-consistent adiabatic geotherm. Because the self-consistent adiabatic geotherm and all of the thermoelastic properties used earlier in calculating p and are also used to model shear and compression velocity, the predicted Vs and Vp profiles must also agree with the observed profiles. In chapter six, I incorporate the very recent experimental (Sinelnikov et al., 1998) and theoretical (Karki et a l , 1997) values for Mg-perovskite and compare these with the inferences deduced in the previous chapters. While the estimated temperature derivatives compare favorably with the with the recent experimental values, I find that to satisfy both the experimental and theoretical pressure dependence, Mg-perovskite must be fit by a 4 t h order, rather than 3 r d order, Birch-Murnaghan equation of state. This modification, not surprisingly, results in an improved fit to density, V0, Vs, and Vp across the lower mantle. In chapter seven, I utilize the pyrolite mineral physics model of V$ and Vp to evaluate the ratio of relative Vs and Vp velocity heterogeneity in the mantle via the parameter (dmVs/dlnVp)p. Prior estimates of [dlnVs/d\nVP)p deduced from seismic tomography were interpreted as requiring either large scale chemical heterogeneities or widespread partial melt within the mantle. Neither scenario agrees with our mineral physics results where a melt-free and uniform pyrolite mantle matches the seismic profiles. I find that the predicted profile of (d\nVs/dmVp)p for the pyrolite mantle is within error of the various seismic estimates, and hence, there is no discrepancy between the tomographic models and a melt-free, uniform bulk composition mantle. Chapter 1, page 19 In chapter eight, I estimate new extremal bounds for the lateral temperature anomalies in the mantle using the pyrolite mineral physics model of V$ and Vp. Previous studies had concluded that extremely large temperature anomalies, 87* exist in the lower mantle on the order of +2500°K to -2000°K (Yuen et al., 1993; 1994; Cadek et al., 1994). The extreme magnitude of these temperature anomalies lead these researchers to reject a thermal origin for the seismic anomalies (8 Kg) and instead, to invoke chemical anomalies in the lower mantle, implying that chemical, rather than thermal, buoyancy is largely driving lower mantle convection. I correct the above temperature inferences by calculating an adiabatic, bulk temperature derivative for shear velocity, (d Vs/d T) for the pyrolite mantle by re-running the mineral physics model « 100 K hotter and colder than the reference geotherm and approximating (dVjdT),, as the mean of the difference between the hot (or cold) numerical runs and the-reference model. I find that the inferred magnitude of the lateral temperature anomalies are significantly reduced with ST now ranging from « ± 100 °K at 660 km to « ± 480 °K at the top of the D" layer. I conclude that away from chemical and thermal boundary layers, the lateral seismic anomalies resolved in tomographic studies are largely thermal in origin and consequently, the dominant force driving mantle convection is indeed thermal buoyancy. 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Chapter 1, page 32 4.00 8.00 12.00 d e n s i t y ( g / c m 3 ) // v e l o c i t y ( k m / s e c ) Figure 1.1. Radial profiles of density, shear, bulk sound, and compression velocity from the global seismic reference model akl35 (Kennett et al., 1995). Chapter 1, page 34 WMande .grf Figure 1.3. Interpretation of an isochemical mantle with whole mantle convective flow. Chapter 1, page 35 ^-0 .45 o ^-0 .50 - 4 0 - 3 8 - 3 6 - 3 4 - 3 2 - 3 0 - 2 8 - 2 6 - 2 4 - 2 2 - 2 0 - 1 8 - 1 6 - 1 4 - 1 2 - 1 0 - 8 - 6 - 4 - 2 0 6 6 0 k m C l a p e y r o n S l o p e ( M P a / K ) Figure 1.4. Calculated phase buoyancy parameter for a pyrolite mantle as a function of the Clapeyron slope. Also plotted are values from numerical convection studies (right facing arrows). 0 100 200 300 400 500 Chapter 1, page 36 ^ R J 1 1 1 1 1 1 1 1 I 1 I 1 I •_-— \\^1700K@400km \ V — ^2000 A bbU km *-2500K@ 660 km-Z — \% — 800 P 900 1000 1100 ^ 1 2 0 0 j § 1300 w 1 4 0 0 1500 g'tOoF-Q 1700 1800 1900 2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 n co T J CD 1600 1800 2000 2200 2400 2600 2800 3000 3200 T e m p e r a t u r e ( K ) Figure 1.5. Comparison between the pyrolite mineral physics geotherm and the geotherms of Jeanloz & Richter (1979) for whole and layered mantle convection. Chapter 1, page 37 1 I ' I ' I ' I ' I ' I ' I ' I 1300 E-1400 -2.0 -1.8 -1.6 -1.4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 (dVP/8T)p Figure 1.6. Trade-off curves for selected within slab earthquakes showing slab penetration depth as a function of the scaling factor which converts temperature to velocity. Chapter 1, page 38 1400 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 V a r i a n c e R e d u c t i o n Figure 1.7. Variance reduction between predicted and observed travel time residuals as a function of slab penetration depth (after Fischer et al. 1991). In this case, Fischer et al. (1991) allowed the value of (BVplcR) to vary to maximize variance reduction. Chapter 1, page 39 Central Japan T r e n c h c Figure 1.8. A vertical cross-section through the Japan Trench, Western Pacific showing P-wave velocity anomalies. Blue coloured material may be interpreted as reflecting the cold subducting oceanic lithosphere of the Pacific plate which extends from the surface to the base of the mantle. CMB is the core-mantle boundary. Figure from van der Hilst et al., (1997). Chapter 1, page 40 OO I Figure 1.9 Schematic illustration of the convective flow in a chemically stratified upper mantle (Anderson, 1983). In this lower figure isotherms of convection are illustrated with the locations of descending flow in the lower mantle is thermally linked to the location of cold convective downwelling in the upper mantle and transition zone. Chapter 2, page Chapter 2 Mineral Physics constraints on the Chemical composition and Temperature of the Earth's mantle from Density and Bulk Sound velocity profiles. Chapter 2, page 42 2.1 Abstract Recent studies that compare predicted profiles of density and bulk sound velocity to seismological models conclude that the lower mantle is chemically distinct from the upper mantle. However, this conclusion is critically dependent on the thermoelastic data adopted for the perovskite phases. I calculate, using third-order Birch-Murnaghan finite strain theory, density and bulk sound velocity profiles for a pyrolite and piclogite bulk composition throughout the mantle along adiabatic geotherms for which the temperature gradient is calculated from the Gruneisen parameter and adiabatic bulk modulus. I calculate the temperature jumps due to the a -> (3, (3 -> y, and y ->• Pv + Mw phase changes using the molar volumes at the respective temperature and pressure of the phase change. Thus, the resultant density, bulk sound velocity and mantle adiabats are internally consistent. I adopt the mineralogy as a function of depth from Ita & Stixrude (1992), but utilize the most up to date mineral physics data for the various minerals. For the lower mantle I utilize the data of Funamori et al. (1996) for Mg-perovskite and Wang et al., (1996) for Ca-perovskite. The predicted profiles are compared to density and bulk sound velocity profiles that are constructed from averaging published regional models. Because some of these regional models are old and thus, have low resolution, I also compare the predicted profiles against two new regional models that describe the average mantle velocity structure beneath old continents (Gaherty and Jordan, 1995) and oceans (Gaherty et al., 1996). Lastly, I compare the predicted profiles against new global reference seismic models akl35 (Kennett et al., 1995), and akl35-Q and akl35-F (Montagner and Kennett, 1996). The adiabatic geotherm initiates at 1680 °K at 100 km depth and extrapolates to a surface potential temperature of 1608 °K (1335 °C), a value consistent with independent estimates (1330-1350 °C) derived from M O R B decompression melt studies. In the upper mantle, the pyrolite model matches the average bulk sound velocity and density to within an average percent misfit of « 1%, whereas piclogite fails to match either property in the region of the 410 km seismic discontinuity. Surprisingly, the new global reference seismic model akl35 and its subsequent refinements differ systematically from both the predicted V® profile and the profiles of the high resolution regional studies in the upper mantle. The cause of this discrepancy is unclear, but likely represents a defect in the global model. I conclude that throughout the upper mantle and transition zone a pyrolite composition provides the best fit to the seismic properties. In the lower mantle, the pyrolite model is able to match density to within an average percent misfit of «< 0.5% and bulk sound velocity to « <0.5% on a geotherm concordant to that predicted from the upper mantle. This result is in contrast to previous studies which found that lower mantle adiabats that gave the best fit to seismic observations were 250 U K colder than that predicted from the upper mantle. To test i f the piclogite composition can satisfy the seismic properties of the lower mantle, but with a pyrolite upper mantle, I model the piclogite properties in the lower mantle along a "hot" geotherm that is increased by 1500 °K over that predicted at the base of the upper mantle to simulate the affects of a thermal boundary layer at the 660 km discontinuity. This temperature jump is based on the offset between geotherms calculated for whole mantle and layered convection from 3D numerical Chapter 2, page 43 convection simulations of mantle convection (Glatzmaier and Schubert, 1993). For such an adopted geotherm, the predicted p and V® profiles for a piclogite model grossly misfit the seismic observations and can be rejected with confidence. Therefore, I conclude that a pyrolite uniform bulk composition provides an excellent match to the seismic density and bulk sound velocity profiles throughout the mantle along a concordant adiabatic geotherm. In contrast, the piclogite model fails to satisfy observations in the transition zone and in the lower mantle when its properties are predicted along an appropriate geotherm. I conclude there is no thermal or compositional break between the upper and lower mantle and, therefore, the Earth is presently in a state of whole mantle convection. Chapter 2, page 44 2.2 Introduction The exercise of constraining the temperature and bulk composition of the mantle has a long history (e.g. Birch, 1952) where by comparisons have been made between the elastic properties of a mixture of mantle minerals and observed seismic profiles. Rare rock samples provide direct chemical data from depths as great as « 250 km, but below this depth, the bulk chemical composition, and the associated petrology of the mantle must be inferred on the basis of comparisons between elastic properties derived from one dimensional seismic profiles and laboratory-based elastic data. While thermodynamic calculations (e.g. Stixrude and Bukowinski, 1990) and phase equilibria experiments (e.g. Irifune, 1987; 1994; O'Neill and Jeanloz, 1990) provide a guideline for the likely stable phases and their composition at mantle temperature and pressure conditions, the final test of any proposed geochemical model for the constitution of the mantle is when an equation of state is used to extrapolate laboratory elastic data for the mineral assemblage up to the extreme conditions of the mantle where it is then tested against observed seismic velocities and density. This chapter reports and interprets mineral physics calculations for two competing composition models of the Earth's mantle, pyrolite and piclogite, using third-order Birch-Murnaghan finite strain theory (e.g. Bina and Helffrich, 1992). Both density (p) and bulk sound velocity (V^) are calculated throughout the mantle along an adiabatic geotherm, which itself is calculated from the mineral physics parameters of the particular composition model, thus ensuring self-consistency between the calculated density, bulk sound velocity, and geotherm. The purpose of this research is to critically evaluate the conclusion that chemical and thermal stratification exists at the 660 km seismic discontinuity as reached by recent Chapter 2, page 45 studies (e.g. Jeanloz, 1989; Bina and Silver, 1990; Hemley, et al., 1992; Stixrude et al., 1992; Ita and Stixrude, 1992; 1993; Zhao and Anderson, 1994). Such chemical stratification at the 660 km seismic discontinuity (or at any of the other seismic discontinuities) demands layered convection and has major implications for the efficiency of chemical mixing (Olson, 1984; Kellogg and Turcotte, 1990; Kellogg, 1992) and the isotopic (O'Nions and Tolstikhin, 1996; Allegre et al., 1996) and thermal evolution (e.g. Schubert and Spohn, 1981; Spohn and Schubert, 1982; Kenyon and Turcotte, 1983; Davies, 1983) of the Earth's mantle. If the mantle possesses a uniform bulk chemistry then the major seismic discontinuities represent only phase transitions, and consequently, the mantle is likely to undergo whole mantle convection with the phase boundaries providing little, or only temporary (e.g. Tackley et al., 1994), impedance to convective flow. In contrast, if the bulk composition of the mantle changes at any of the seismic discontinuities (or elsewhere within the mantle), then mantle convection is restricted to a limited number of separate layers that greatly reduces the efficiency of chemical mixing and heat transport (Silver et al., 1988). In general, for this type of comparative mineral physics tests, two limitations are recognized. The most fundamental limitation is that the necessary elastic properties for some of the key minerals have not been measured. For example, in virtually all studies prior to the early 1990's that modeled Vs and Vp profiles, many of the minerals were "assigned" values for the temperature (<9u,/dr)5, and pressure {d\i/dP)T derivatives of the shear moduli, p. These two parameters, which are used to correct the standard T and P reference values of \i(Tie{,Pref) to the high temperature and pressure conditions of the mantle, were largely "best guesses" that were sometimes based on the properties of minerals of similar crystal Chapter 2, page 46 symmetry and sometimes based on fitting the calculated profiles to the observed profiles. Consequently, the conclusions regarding the success or failure of a particular assemblage to match observed shear (Vs) and compression (Vp) velocity profiles, where Vs(T,P)^^(T,P)/p(T,P) and V11(T,P)^yl(K(T,P) + %[i(T,P))/p(T,P) were often controversial. Similarly, controversy over the appropriate value for the thermal expansion coefficient a(T) for magnesium perovskite, the mineral that dominates the petrology of the lower mantle 70 vol% (Navrotsky, 1989; Hemley and Cohen, 1992)), has lead to uncertainty and controversy over the density of perovskite bearing assemblages, and thus, the ability of uniform or layered compositions to fit the seismic density profile (see Zhao and Anderson, 1994; Anderson et a l , 1995). However, in this study I model density (p) and bulk sound velocity (VQ) profiles where V^ equals *JKS /p or equivalently yjVp -\Vl (Ks is the adiabatic bulk modulus). Unlike modeling Vs and Vp, the required elastic data to calculate p and V® is indeed measured, and furthermore, this data has, for key minerals, been reproduced and refined by duplicate experiments at different laboratories. Consequently, the precision and confidence in such comparisons between extrapolated experimental and seismic profiles is greatly improved over previous studies. As noted by Duffy and Anderson (1989) the elasticity data set for mantle minerals is growing at such a rapid pace that compilations which are only 3 or 4 years old are out of date and thus, the conclusions drawn from such studies may be considered suspect. Indeed, I conclude that the use of the latest thermoelastic data for Mg and Ca perovskite phases are the principle reason for the success of this study in obtaining a fit between predicted and observed properties in the lower mantle. Chapter 2, page 47 The second limitation, which often goes unstated, is the uncertainty of the seismic profiles themselves. Since 1981 the one dimensional, globally averaged, seismic model that has been used as the benchmark in mineral physics studies is the Preliminary Reference Earth Model (Dziewonski and Anderson, 1981), or P R E M for short. However, it has been argued that the magnitude of the velocity jumps in Vs and Vp , and hence V0, at 220 km and 400 km depth are in very poor agreement with those inferred from detailed regional seismic studies (Bina and Wood, 1987). This inference has been supported by the velocity profiles in new global seismic reference models (iasp91 (Kennett, and Engdahl, 1991); akl35 (Kennett et al., 1995); akl35-F (Montagner and Kennett, 1996) that lack a discontinuity in velocity or density at 220 km depth (see figure 2.1 and 2.2). Since velocity gradients in the immediate neighborhood of a seismic discontinuity will trade off against the magnitude of an increase across the discontinuity (e.g. Kennett, 1991), it is very likely that the seismic velocity and density profiles in P R E M , are locally biased by the large increase across the 220 km seismic discontinuity. It is interesting to note that CREMO, (for Constrained Reference Earth Model; Montagner and Anderson, 1989a, b), an updated global average upper mantle model that is based on P R E M , and which incorporates independent petrologic constraints, lacks a large seismic discontinuity at 220 km. In addition, recent studies that have concentrated on characterizing the seismic discontinuities themselves have concluded that the 220 km discontinuity is poorly imaged and unlikely to be of global extent (e.g. Revenaugh and Jordan, 1991). Lastly, there is growing recognition that there exists an additional seismic discontinuity at 520 km depth, albeit with velocity jumps that are smaller in magnitude to those inferred for the 410 and 660 km discontinuities (Shearer, 1990; 1996; Gaherty and Chapter 2, page 48 Jordan, 1995; Gaherty et al., 1996). The acceptance of a 520 km discontinuity by the seismological community is so recent that the 520 is only now being incorporated (Guy Masters, personal communication) into the latest global average seismic models (see also Navrotsky et al., 1995). Essentially, prior to 1991 when the publication of the current generation of seismic reference models began (e.g. iasp91, akl35, ak!35-Q), there is the strong likelihood that the use of P R E M as the benchmark with which to judge the success or failure of proposed mineral assemblages has contributed to the failure of a consensus to emerge on the chemical composition of the Earth's mantle. In this study I utilize the new reference seismic models, calculated average profiles derived from many regional studies, and high resolution continental and oceanic seismic models to judge the merits of the predicted p and V® profiles. I focus on modeling density and bulk sound velocity of the mantle because p and Vq,can be calculated independently of the shear modulus and its related temperature and pressure derivatives. For some key mantle minerals of interest, the latter properties remain unmeasured, and consequently, predicted profiles of Vs and Vp are less robust than V0. Numerical experiments for olivine (forsterite) and its high pressure polymorph, p-olivine have tested the ability of different equations of state (e.g. Murnaghan, 3rd order Birch-Murnaghan, 2nd order polynomial) to faithfully reproduce molecular dynamic estimates of bulk and shear moduli, and density up to 14 GPa pressure when the equations are only fit to a subset of the data over the 0 to 3 GPa range (Wall et al., 1993). This simulates the situation where experimental data, available over only a limited pressure range, are extrapolated to much higher pressures. The extrapolated bulk moduli values determined by the 3rd order Chapter 2, page 49 Birch-Murnaghan equation of state agree very well with the molecular dynamic data over the complete pressure range and deviate by only a maximum of +1.0% for p-olivine and +1.5% for olivine at 14 GPa, the highest pressure considered. In contrast, for the shear moduli, the 3rd order Birch-Murnaghan equation of state over predicts the molecular dynamic estimates and reaches a maximum error of + 1.6 % for P-olivine and + 7.6 % for olivine at 14 GPa. Finally, for density, the 3rd order Birch-Murnaghan equation of state predicts values for both minerals that were indistinguishable from the molecular dynamic estimates. Although, Wall et al. (1993) state that the molecular dynamic calculations are not accurate enough to make quantitative, geophysical predictions of seismic velocity, they argue the qualitative change of the bulk and shear moduli with pressure are useful in evaluating the weaknesses of the various equations of state they tested. From their study one may conclude that density and bulk moduli may be extrapolated with confidence, and consequently, the use herein of both p and profiles to evaluate the composition of the mantle is a robust method. Seismologically, bulk sound velocity (V^) is determined from both free-oscillation and body-wave travel time data, and furthermore, since nearly all seismic attenuation occurs in the shear modulus (e.g. Durek and Ekstrom, 1996), the mineral physics estimate of V^, which is calculated from laboratory data collected at frequencies outside the seismic band, may be compared to seismic estimates of with confidence (Bina and Silver, 1990). In contrast, the density profile of the Earth is constrained seismologically by primarily free-oscillation observations (Masters, 1989), and hence, due to the nature of free-oscillations, which average Earth structure over a much greater depth extent than do body-waves, only broad constraints on the exact shape of the density profile of the mantle are available. Chapter 2, page 50 Finally, Bina and Silver (1990) argue that the is relatively insensitive to lateral heterogeneity based on the observation that the ratio of relative magnitude of Vs and Vp velocity anomalies, expressed as {p\nVs/d\nVp)^2, is nearly constant when ever it has been measured in the mantle. They argue this implies that the lateral heterogeneity in V^ ^ ^ / p j i s an order of magnitude less than Vs ^ p / p j for a Poisson's ratio of a = 0.25 (based on the relationship between shear moduli, Poisson's ratio and Vs: and Vs = TPTP ). 1+CT In this study I investigate mantle composition by calculating density and bulk sound velocity profiles along a self-consistent adiabatic geotherm and comparing them to the mean seismic properties of the mantle. I also test the sensitivity of the results by also considering other seismic models as a reference and to uncertainties in the mineral elastic data. The results here supersede those given in a preliminary report of this work (Calderwood, 1996) due to the inclusion of new elastic data (Mg-majorite) and the affects of Fe and A l partitioning into Mg-perovskite on density. A major conclusion is that a pyrolite mineralogy best fits the observed density and bulk sound velocity profiles throughout the whole mantle and furthermore, that no thermal discrepancy exists between the upper and lower mantles at 660 km depth. Together, these two conclusions strongly indicate that the Earth's mantle is not presently chemically layered and that the Earth is currently in a state of whole mantle convection. Chapter 2, page 51 2.3 Previous Work The most recent and thorough studies that have compared extrapolated laboratory measurements with seismic observations have concluded that while the upper mantle (100-410 km depth interval) and transition zone (410-660 km depth interval) is homogeneous and best matched by a pyrolite mineralogy, there exists a thermal and compositional discrepancy at the 660 km seismic discontinuity (Ita and Stixrude, 1992; 1993). They found that the lower mantle geotherm that achieved the best fit between the calculated and observed density and bulk sound velocity profiles was significantly colder than that predicted from the base of the upper mantle (figure 2.3) for either a pyrolite or piclogite mineralogy. To resolve the thermal discrepancy, they concluded that the bulk composition of the lower mantle differed from that of the upper mantle, a conclusion that agreed with earlier studies where only a simplified lower mantle mineralogy of Mg-perovskite and magnesiowustite were considered (Bina and Silver, 1990; Hemley et al., 1992; Stixrude, et al., 1992). Ita and Stixrude (1992; 1993) note that this discrepancy is largely the result of the elastic properties of Ca-perovskite (CaSi0 3), a phase which comprises « 7 - 14 vol. % in the lower mantle (with the exact percentage dependent upon the bulk composition), and which resulted in both pyrolite and piclogite models to overestimate the bulk sound velocity profile and underestimate the density across the lower mantle (figure 2.4 and 2.5). Specifically, they noted that the high room temperature value of the isothermal bulk modulus (KTQ = 301.4 GPa {where the subscript T indicates isothermal properties and the zero indicates standard room temperature and pressure conditions}), attributed to the experimental work of Mao et al. (1989), was largely responsible for this misfit in the lower mantle. However, Mao et al., Chapter 2, page 52 (1989) actually reports a value of KT0 = 281 ± 4 GPa and no where in their work do they discuss a value as large as 301.4 GPa (Tamai and Yagi (1989) report an experimental value of 325 ± 1 0 GPa, and thus, I speculate that Ita and Stixrude (1992; 1993) may have averaged these two results to obtain their tabulated value). Subsequent experimental studies have re-evaluated the thermoelastic parameters for both Ca-perovskite, CaSi0 3 (Wang et a l , 1996) and Mg-perovskite, M g S i 0 3 phases (Wang et al., 1994; Funamori et al., 1996). Of particular interest here is that Wang et al. (1996) experimentally determined a much lower value for the isothermal bulk modulus of CaSiO, (KTQ = 232 ± 8 GPa) than that adopted by Ita and Stixrude (1992; 1993) which, irrespective of the additional refinements in the thermoelastic properties of Mg-perovskite, implies their conclusions regarding thermal and compositional stratification within the mantle is in need of revision. In addition to these lower mantle phases, I also incorporate the latest elastic data for all of the other mantle minerals in an up-to-date compilation that forms the basis for calculating profiles of density and bulk sound velocity throughout the mantle. 2.4 Methods In this section I first briefly outline the two compositional models which will be considered here. Next, the thermoelastic data used in the calculations is discussed with explanations provided where I have used existing experimental measurements to infer un-measured properties. Lastly, the particular steps taken in calculating the radial profiles of density and adiabatic bulk moduli along a self consistent geotherm are presented. Chapter 2, page 53 2.5 Mineralogical Models I evaluate two simple models of mantle chemistry but recognize that these represent end- member idealizations that are certainly not unique. The simplest model is known as Pyrolite, where the whole mantle is of uniform bulk composition (Ringwood (1975, 1979, 1982). This model was originally proposed on the basis of the complimentary relationship between basaltic magmas and peridotite xenoliths. Ringwood argued that since the peridotite xenoliths are strongly depleted in low melting-point components they would be unable to produce the common basaltic magmas that are observed i f these peridotite xenoliths underwent direct partial melting. He proposed that peridotite xenoliths do not represent samples of the fertile upper mantle, but are residues from partial melting, and that when combined with the bulk composition of common basaltic magmas they give the composition of the primitive source region for the magma. Ringwood referred to this hypothetical source material as pyrolite, an olivine rich peridotite. The most notable geochemical problem in applying the pyrolite composition to the entire mantle is reconciling the resulting Mg/Si ratio (1.27 atomic) determined via mass balance calculations (Jagoutz et al., 1979; Ringwood, 1979) with the widely held view that the Earth should have a Chondritic ratio (Mg/Si = 1.05). Because both of these elements are refractory lithophile elements under typical upper mantle conditions, they should be present in the silicate earth (i.e. the whole mantle + crust + lithosphere) in roughly chondritic proportions. If the whole mantle has an upper mantle composition then the bulk silicate earth is missing about 5-7 wt% Si compared to carbonaceous chondrites (Carlson, 1994). Some possible solutions to this are either that the Earth accreted from material with a non-Chapter 2, page 54 chondritic Mg/Si ratio (Ringwood, 1979; 1989) or that the some Si segregated into the core during core formation (Ringwood, 1959; Poirier, 1994). Allegre et al. (1995) recently evaluated the question of composition of the mantle and core through the use of major and trace element ratios, relying on meteorite correlations and ratios for elements that do not enter the core to first constrain the initial Bulk Earth composition. The Bulk Earth is then compared with the composition of the mantle, with the assumption that the upper mantle bulk chemistry represents the whole mantle, to determine, by difference, the chemical composition of the core. They concluded that the core contains about 7.17 ±0.3wt % Si, 2.25 ± 0.2 wt % S, 4.87 ± 0.3 wt% N i , and to satisfy the seismologically determined density deficit of the core under the assumption that oxygen is the sole remaining light element in the core, about 4.1 ± 0.5 wt% O. Of interest is that this Si concentration is within the range of the experimentally determined Si solubility in Fe (Ringwood and Hibberson, 1991). Therefore, contrary to many of the early estimates that only considered Si as the sole light element in the core, and consequently, estimated a very high Si content in the core to satisfy the core density deficit (e.g. 20 wt% Si; Ringwood, 1959; 20-30 wt% Si; Knopoff and MacDonald, 1960; 14-20 wt% Si; Balchan and Cowan, 1966; 8-20 wt % Si; Stewart, 1973), the Allegre et al. (1995) chemical model of the mantle and core is able to reconcile the Mg/Si ratio of a pyrolite whole mantle by placing Si in the core, but also satisfies independent sulfur (Dreibus and Palme, 1996) and nickel concentration arguments, while simultaneously satisfying the observed core density deficit. While the chemical model is not unique (see discussion section in Allegre et al., 1995), it does demonstrate that the non-chondritic Mg/Si ratio of a pyrolite whole mantle is not a fatal flaw in applying this bulk composition to the whole mantle. Chapter 2, page 55 I stress that the precise mineralogy of the pyrolite bulk composition is not known, and therefore, for consistency with previous work, I adopt the petrology and volume percent estimates from Ita and Stixrude (1992, 1993) (reproduced here as figure 2.6). They evaluated and distilled the voluminous experimental and thermodynamic studies to produce estimates of the mineral proportions for a pyrolite composition: details of the construction of the phase diagrams and derivation of the mineral proportions may be found in their papers. I adopt their results with adjustments to the Fe partitioning in the magnesiowustite and Mg-perovskite phases which reflect the experimental results of Irifune (1994) and Wood and Rubie (1996). I also adjust the depth of the mid-point of the 410 and 520 phase transitions such that these depths agree with recent seismic inferences (Shearer, 1996). In contrast, the most widely known chemically layered model is the piclogite model championed by Don Anderson and colleagues (Anderson, 1979a, b; 1981; 1989; Bass and Anderson, 1984; Anderson and Bass, 1984; 1986; Duffy and Anderson, 1989; Zhao and Anderson, 1994). In its original manifestation it was assumed that seismic discontinuities at 220, 410, and 660 km depth mark abrupt chemical changes in bulk composition that were frozen in during quenching of a primordial magma ocean. From top to bottom, the upper mantle down to 220 km consists of peridotite mineralogy (olivine dominated), followed by an eclogite layer (a clinopyroxene-garnet dominated assemblage) from 220 to 410 km, a garnet-rich eclogite layer, sometimes referred to garnetite, from 410 to 660 km, which in turn overlies, an A1 2 0 3 poor assemblage that comprises the lower mantle (figure 2.7). The details on how such chemical layering is preserved against convective disruption and mixing by subduction of oceanic lithosphere over the Earth's history has not been quantitatively addressed although qualitative diagrams have been proposed (figure 2.8 and 2.9). In these Chapter 2, page 56 figures Anderson (1979; 1981) shows cold thermal downwellings in the upper mantle, analogous to subducting oceanic lithosphere, triggering thermally-coupled, convective downwellings in the lower mantle. Taken together, the two thermally coupled downwellings mimics a continuous slab which appears to extend across the seismic discontinuities of the transition zone. Liu (1980), Liu and Bassett (1986, chapter 5) and Bina and Wood (1984; 1986, 1987) have argued that the eclogite to garnetite transition proposed by Anderson (1979a, b) for the 410 km discontinuity would not produce a sufficient velocity jump to match the observed seismic models. Consequently, Anderson and Bass (1984, 1986) and Bass and Anderson (1984) moved the boundary from peridotite to eclogite, originally at 220 km down to 410 km depth, and made successive, and in some cases, substantial changes to the proposed piclogite mineralogy (see table 2.1 and compare the wt% mineralogy given by Anderson and Bass (1984, 1986) and Bass and Anderson (1984) - following the original authors, the mineralogy is listed in both weight and volume percent). Such adjustments to the piclogite mineralogy has drawn sharp criticism (see Ringwood, 1991; 1994; Liu and Bassett, 1986, chapter 5) as, in turn, has the minor changes adopted for the pyrolite model (see Anderson, 1989, pp. 184-186). Chapter 2, page 57 Table 2.1. Estimates of pyrolite and piclogite mineralogy for a representative low pressure mineralogy. Pyrolite low Pressure mineralogy Bass & Anderson, 1984 (March) Anderson & Bass, 1984 (July) Weidner, 1986 Ita & Stixrude, 1992 Wt% wt% vol. % vol. % olivine 57 57 61 62.8 orthopyroxene 17 17 15 7.0 clinopyroxene 12 12 10 16.0 garnet 14 14 14 14.2 Piclogite Bass & Anderson, 1984 (March) Anderson & Bass, 1984 (July) Anderson & Bass, 1986 Duffy & Anderson, 1989 Weidner, 1986 Ita & Stixrude, 1992 Wt% Wt% Wt% Wt% vol. % vol. % olivine 16 22 30 40 16 42.4 orthopyroxene 3 5 6 10 3 9.2 clinopyroxene 44 43 33 37 45 36.7 garnet 37 30 31 13 36 11.7 For consistency, I adopt the piclogite mineral proportions from Ita and Stixrude (1992; 1993) (see figure 2.10) and thereby ensure that the pyrolite and piclogite mineral proportions were constructed with the same data and methods. As a consequence, I am not testing the original hypothesis of multiple chemical boundaries within the upper mantle and transition zone (Anderson, 1979a), since the mineral proportions determined by Ita and Stixrude (1992; 1993) describe the expected mineralogy if the piclogite bulk composition was applicable throughout the temperature and pressure regime of the upper mantle, transition zone, and lower mantle. Hence no abrupt changes in chemistry are assigned to the seismic discontinuities apriori in modeling the piclogite composition. This is largely consistent with recent interpretations of the Piclogite model by Duffy and Anderson (1989) Chapter 2, page 58 and Duffy et al., (1995), where they have stopped interpreting the mineralogy in terms of discrete upper mantle chemical boundaries. I reiterate that the exact mineralogy of these two particular chemical models are not known exactly, nor are pyrolite and piclogite the only two possible models: alternative chemical models such as "Chondrite" based geochemical models that invoke chemical layering (Agee, 1993), and some that do not (e.g. composition C; Ita and Stixrude, 1993) have also been proposed. In addition, Liu (1979, 1980; 1982a, b) has championed a chemically layered mantle that is distinct from piclogite and Gasparik (1990; 1997) has proposed a Na enriched chemically layered upper mantle that differs in detail from piclogite, but is virtually identical in terms of convective isolation. In spite of these diverse models, I restrict the focus to the pyrolite and piclogite models because Ita and Stixrude (1992) have conveniently provided internally consistent mineral proportions for these two compositions, and since the primary purpose here is to focus on the affect of updated thermoelastic parameters on the conclusion that the lower mantle is chemically distinct from the upper mantle and transition zone. Chapter 2, page 59 2.6 Equation of State I calculate density (p) and bulk sound velocity (V^) using third-order Birch-Murnaghan finite strain theory as reviewed by Bina and Helffrich (1992) and outlined briefly below. This equation of state differs from the thermodynamic potentials utilized by Ita and Stixrude (1992; 1993), where they combined the Mie-Gruneisen equation of state with Gibbs free energy minimization; an approach they termed the Universal equation of state. Their method requires fewer parameters (molar volume, VQ; isothermal bulk modulus, KJO', the pressure derivative of the bulk modulus, (dKT0/d P) ; the Debye temperature, Te ; and the Gruneisen parameter, y) than that adopted here and has the additional advantage that the formalism contains all the thermodynamic information about the model system. However, Ita and Stixrude (1993) demonstrate that these two techniques give indistinguishable results for the predicted density and bulk sound velocity profiles for olivine across the whole mantle (figure 2.11), and consequently, I assume that a third-order Birch-Murnaghan equation of state will not contribute to any systematic difference between this work and theirs. 2.1 Elasticity Data Set The values for the thermal expansion coefficients and their data sources are listed in table 2.2, while table 2.3 presents the elastic parameters used here and their references. Tables A1...A18 in the appendix list the elastic data for each mineral and compares it to recent experimental values - these tables allow a quick comparison to the very recent published values. I attempted to utilize the most up-to-date data for the various parameters and kept within the reported experimental error. Following convention (e.g. Bina and Chapter 2, page 60 Helffrich, 1992) the elastic properties of a phase are estimated by averaging on the mole fraction of the end member phases assuming ideal mixing where the material properties of the end-members combine linearly as a function of composition. When experimental constraints are unavailable, I follow Ita and Stixrude (1992) and estimate the unknown isothermal bulk moduli using velocity-density systematics: K V = K V where Kjrej\s> the known bulk modulus of the reference mineral, VM is its molar volume and the Kf is the unknown bulk modulus and V0 is the molar volume of the unknown. While the appendices document the values used here there are a few specific entries that warrant comment. 2.8 Olivine Phases The bulk moduli of the olivine phases are taken as a function of iron content. This follows the trend in the elastic data set of Ita and Stixrude (1992; 1993) but the values used here differ in detail because new experimental values are adopted, including new data to extrapolate for the fictive pure Fe-end member molar volume along the Mg-Fe join. The molar volumes (and hence density) for the beta and gamma olivine phases differ from those values in Ita and Stixrude (1992; 1993). They adopted values from Jeanloz and Thompson (1983) whereas I use the latest published x-ray diffraction data of Hazen et al., (1990) for wadsleyite to determine a new linear fit along the Mg-Fe join (figure 2.12 and 2.13). This gives a Mg-wadsleyite molar volume of V0 = 40.31 cnvVmole (40.52 cmVmole) and Fe-wadsleyite V0 = 42.68 cmVmole (43.22 cmVmole) as compared with the values of Ita and Stixrude (1992; 1993) which are given in brackets. Next, the Mg-wadsleyite adiabatic bulk Chapter 2, page 61 moduli determined by Zha et al. (1996) and L i et al. (1996) is converted to the isothermal equivalent (KJQ = 168.50 GPa) and used together with the bulk moduli pressure derivative estimated by Zha et al. (1996) to determine the appropriate isothermal bulk modulus from the trade off curve (figure 2.14) between KJQ and (d Kro/d P) for the compression data of Fei et al. (1992) for an iron bearing wadsleyite, (Mg 0 8 4Fe 0 l 6 ) 2 Si0 4 . This yields the Fe end-member bulk moduli of Fe-wadsleyite (KJQ = 183.86 GPa; figure 2.15). For the iron content considered here («12 mol%), the resulting value for wadsleyite (Kfo = 170.3 GPa) is slightly less than that deduced by Fei et al. (1992) but significantly less than that of Ita and Stixrude (1992; 1993; £ 7 / 0 = 174 GPa). In contrast, re-reducing new x-ray diffraction data for y-olivine (Hazen, 1993) results in molar volumes that do not differ from that adopted by Ita and Stixrude (1992; 1993; Mg-olivine V0 = 39.65 cmVmole (39.65 cmVmole) and Fe-olivine V0 = 42.06 cmVmole (42.02 cmVmole; figures 2.16 and 2.17). After converting the adiabatic bulk moduli of Weidner et al., (1984) to its isothermal equivalent I use this as a fixed point and force a linear fit through it and the isothermal bulk moduli values for the iron bearing samples of Hazen (1993; figure 2.18). This gives a predicted value for the Fe end-member isothermal bulk moduli of KJQ = 207.48 GPa (192.00 GPa) while for the Mg end member the value is KJO = 182.60 GPa (183.00 GPa; with the values of Ita and Stixrude, 1992 in brackets). Again, for the iron content considered here, the resulting bulk modulus for an Fe-bearing y-olivine is only slightly greater than that used by Ita and Stixrude (1992; 1993). 2.9 Orthopyroxene Chapter 2, page 62 I initially followed Ita and Stixrude (1992; 1993) in modeling orthopyroxene as a mixture of pure iron and magnesium end members. However, recent experimental work on natural samples containing Ca + 2 and A l + 3 have demonstrated that substitution of only small amounts of either element causes the isothermal bulk modulus to increase significantly as compared to KJQ of the pure end member phases (Hugh-Jones and Angel, 1997 in press; Chai et al., 1997 in press). Consequently, I adopt the values for Kj ,(8Kr/dP) , u. and S P J derived from fitting a 4th order equation of state to acoustic compression experimental data that extended to pressures up to 12.5 GPa on a natural sample Chai et al., (1997) rather than approximate orthopyroxene by a mixture of pure end members. This sample's composition is: (Mg, 6 3 Fe 0 . l v Ca 0 . 0 4 Mn 0 0 1 )(Al 0 . 1 2 Cr 0 0 1 )(Si , . 8 9 Al 0 ,,)0 6. which is only slightly greater in aluminum content than that studied by Hugh-Jones and Angel, (1997 in press); (Mg, 6 6 Fe 0 2 4 Cao. 0 1 2 Al 0 0 8)(Si, 9 4 A1 0 0 6 )O 6 The motivation for adopting the results of Chai et al. (1997) over that of Hugh-Jones and Angel (1997) is that Chai et al., (1977) provide the shear modulus (p) and its pressure derivative ((p JI /d P \ ) in addition to Kj , (d KT/d P) T , and (s2 Kr /d P2 j while Hugh-Jones and Angel (1997 in press) give only the isothermal bulk modulus and its pressure derivative. While the focus of this study does not require the shear moduli, later chapters do. Thus, I adopted the Chai et al. (1997) results simply because it provides a greater number of self-consistent elastic properties. Note that Chai et al. (1997) found that the bulk modulus Chapter 2, page 63 must be fit by to a fourth order Birch-Murnaghan equation of state while the shear moduli could be fit by a 3rd order equation of state. Thus, I extend from 3 to 4, the number of terms in the Birch-Murnaghan equation of state to accommodate their results. 2 .10 Majorites Unlike Ita and Stixrude (1992), who were forced to treat the Mg-, Fe-, and Ca-majorite isothermal bulk moduli and their related pressure derivatives as free variables to be adjusted within reasonable estimates to provide the best fit with seismic properties, this study uses values for the isothermal bulk modulus based on direct experimental measurements for Mg-majorite (Pacalo and Weidner (1997); Sinogeikin et al., 1997). Furthermore, I estimate the affect of Fe on the molar volume and bulk and shear moduli by a simple linear fits between the pure Mg-end member and Fe-bearing majorites. Specifically, for the change in molar volume (and hence, density), I fit the experimentally observed unit cell volumes for Fe-bearing majorites listed in Ohtani et al. (1991) and Sinogeikin et al. (1996) and for pure Mg-majorite given by Pacalo and Weidner (1997), Sinogeikin et al. (1997), and Yagi et al. (1992) (see figure 2.19). This gives a predicted unit cell volume for the pure Fe-majorite of 1575 A 3 , which translates to a molar volume of 118.59 cmVmole and a density of 4.449 g/mole. To account for the affects of Fe on the bulk moduli I performed a linear fit to the experimentally determined bulk moduli (figure 2.20) for the Fe bearing majorite recently reported by Sinogeikin et al. (1996) with the values used here for the pure Mg end member majorite. This resulted in a predicted values of Ks = 179.04 GPa (Kj1 = 177.71 GPa; where the predicted Kf was converted from the predicted adiabatic value via Ks - Kr{\ + a y 7) Chapter 2, page 64 with the coefficient of thermal expansion being that of almandine garnet, the Gruneisen parameter = 1.20, the value for the Mg-end member, and temperature T= 298K). For Ca-majorite this study utilizes the measured molar volume and relative compressibility for a calcium bearing majorite of composition (Cao^Mg^^Si 4 0 1 2 ) determined by Hazen et al., (1994a, b), together with the pure Mg-majorite end member, to estimate the molar volume and isothermal bulk modulus of the pure Ca-majorite phase (Ca 4 Si 4 0 ] 2 ) . This is consistent with the convention of Ita and Stixrude (1992; 1993) but differs from that adopted by Duffy and Anderson (1989) who define Ca-majorite as (Ca 2 Mg 2 Si 4 0 ] 2 ) . The linear fits for molar volume and density are shown in figure 2.21 and figure 2.22, respectively. The adopted isothermal bulk modulus for (Ca 0 4 9 Mg 3 5 ] )S i 4 0 1 2 ) differs from that tabulated by Hazen et al. (1994b). The experimental technique they used was to determine relative compressibilities by preparing a diamond anvil mount with several crystals that have various compositions in it. This allows the small differences in compressibility to be determined in compositionally similar suites of samples - hence, they loaded a pure Mg-majorite along with the Ca-bearing majorite. They note that the relative differences are well resolved, but that absolute values of compressibility, derived from their measurements, may be in error by several percent. In fitting their unit cell data with a Birch-Murnaghan equation of state, they fixed the pressure derivative (dKs/dP)= 4.0 and allowed the values of KJQ and VQ to vary. This resulted in KJQ = 169.3 ±3 .4 GPa and 164.8 ± 2.3 GPa for Mg-and Ca-majorite phases respectively. Because the derived Mg-majorite KJO value is significantly larger than the recent value determined by Brillouin spectroscopy (Pacalo and Weidner (1997) which is adopted here, I infer on the basis of the relative Chapter 2, page 65 compressibility between the Hazen et al. samples (Ca-bearing majorite KJQ is 2.65% lower than the pure Mg end member) that the Ca-bearing majorite should be KJQ « 155.74 GPa relative to the KJQ =160 GPa for the pure Mg-majorite phase. Alternatively, i f I use the simple relationship advocated by Ita and Stixrude (1992; 1993) to predict the isothermal bulk modulus of the Ca-bearing majorite: V K = V K where, in this case, the "unknown" values VQ and Kj are the molar volume and isothermal bulk modulus of the Ca-bearing majorite while the reference values, Vgref and Kjref are taken as the molar volume and isothermal bulk modulus of the pure Mg-majorite. I obtain Kj = 156.70 GPa, a value indistinguishable from that estimated above where I assumed a relative difference of 2.65%. Consequently, the linear fit between the bulk moduli of the Ca-bearing majorite of Hazen et al. (1994a) and the pure Mg-majorite of Pacalo and Weidner (1997) adopts KJQ = 156.22 GPa (the arithmetic average of the two estimates) for (Ca a 4 9 Mg 3 i 5 , )Si 4 0 ] 2 ) and 160 GPa for the Mg 4 Si 4 0 , 2 . This is shown in figure 2.23 and predicts a KJQ = 129.14 GPa for the pure Ca-majorite phase (Ca 4Si 40, 2) (and KJQ = 144.57 GPa for an calcium bearing Ca-majorite (Ca 2 Mg 2 Si 4 0i 2 ) as defined by Duffy and Anderson (1989)). 2.11 Lower mantle phases The mineralogy and composition of the lower mantle is from Ita and Stixrude (1992), but the composition of the magnesiowustite and Mg-perovskite phases is adjusted to reflect recent Fe partitioning experiments. Irifune (1994) synthesized the high pressure assemblage Chapter 2, page 66 for a pyrolite bulk composition at high temperatures and pressures (23-28 GPa = 650 - 770 km; 1,500 - 1,600 °C) to determine directly what phases and their composition should exist at the top of the lower mantle. A major question underlying his study was to determine i f a new aluminous phase was stable in the lower mantle, or if the entire aluminum inventory could be accommodated in solid solution within the major phases of M g S i 0 3 and CaSi0 3 perovskite and (Mg,Fe)0 magnesiowustite. He determined that Al-bearing majorite garnet, the high pressure phase of pyroxene that is stable immediately above the lower mantle, had completely disappeared in the experimental charges at pressures > 27 GPa leaving only Mg-Pv, Ca-Pv and magnesiowustite as the stable phases. X-ray analysis revealed that the lattice parameters of the Mg-perovskite were significantly greater than pure Mg-Pv with the values consistent with it incorporating most of the A1 2 0 3 inventory (minor amounts were incorporated into the Ca-Pv phase). His calculated mineral proportions agree with the mineral proportions of Ita and Stixrude (1992) and, although his results are obtained at a shallower depth, also agree with the a mineral proportions found in single synthesis experiment at 54 GPa (O'Neill and Jeanloz, 1990). Additional synthesis experiments with greater aluminum contents (Irifune et al., 1996) in the system M g 3 A l 2 S i 3 0 1 2 - M g S i 0 3 confirm the previous results. The relevance of these experiments to this study was demonstrated by Wood and Rubie (1996) in synthesis experiments designed to constrain the Fe and Mg partitioning between perovskite and magnesiowustite. They found that the Fe content in perovskite is strongly coupled to the A1 2 0 3 concentration. In pure end member experiments that lacked aluminum and that had a bulk Fe concentration typical of pyrolite (Fe/(Fe + Mg) = 0.11), most of the iron was partitioned into magnesiowustite (Fe/(Fe + Mg) = 0.17) compared to the Chapter 2, page 67 Mg-perovskite phase which had a value of 0.04. These results are in agreement with previous partitioning experiments in the pure MgO-FeO-Si0 2 system (Fei et al., 1991; Katsura and Ito, 1996). For A1 2 0 3 concentrations expected for the lower mantle, Wood and Rubie (1996) found that the Mg-Al-perovskite now had approximately the same Fe content as the coexisting magnesiowustite (to test the sensitivity to the oxidation state of the experiments both reducing (Fe capsule) and oxidizing (Re capsule) runs were performed and showed no systematic trend). The results of Wood and Rubie (1996) for aluminum bearing and the A1 2 0 3 free results of Fei et al. (1991) and Katsura and Ito (1996) are illustrated in figure 2.24 and 2.25. Figure 2.24 emphasizes the distribution of Mg and Fe between coexisting magnesiowustite and perovskite for the A l 2 O s free case, while figure 2.25 is an enlargement of the experimental results of Wood and Rubie (1991). Also plotted are the results of Irifune (1994) for the natural pyrolite bulk composition which is adopted here. The observation that perovskite and magnesiowustite have nearly the same Fe content has an impact on modeling density profiles across the lower mantle since perovksite makes up « 76 vol% the mineralogy of the lower mantle, and therefore, even minor changes to its iron content, and thus, zero pressure density, will affect the predicted density profile. Previous attempts to match the density structure of the lower mantle have utilized A1 2 0 3 free Fe partitioning coefficients (e.g. Stixrude et al., 1991; Ita and Stixrude, 1992; 1993; Chopelas and Boehler, 1992; Stacey, 1996; O.L. Anderson, 1997) where the Mg-perovskite has been modeled with very low Fe contents of 0.05-0.06. In this study I account for both the aluminum content and the Fe content by adopting the composition of Irifune (1994) and expressed in terms of unit cell volume via (O'Neil and Jeanloz 1994): Chapter 2, page 68 F 0 ( A 3 ) = 162.59 + 5.86xM V O 3 +10.70*^ For the average composition of Irifune (1994; XPe - 0.10; A1 2 0 3 = 0.10) this results in a molar volume for perovskite of 24.73 cmVmole, a value significantly greater than the molar volume of pure Mg-perovskite (V0 = 24.46 cmVmole). I assume that the Fe content in both Mg-perovskite and magnesiowustite remains constant across the whole depth extent of the lower mantle. This is consistent with the results of Kesson et al. (1998) who show that the simple pyrolite mineralogy of Mg-Fe-Al-perovskite, Ca-perovskite, and magnesiowustite is stable at pressures of 70 and 135 GPa («1,500 to 2,900 km depth) and importantly, exhibits no significant change in Fe partitioning (MgPv at 70 GPa has a Mg# of 92.2, while the Mg-Pv at 135 GPa has a Mg# of 92.8; see table 1 in Kesson et al., 1998). Nevertheless, these experiments were performed such that only a central portion of the starting glass fragment was converted to the lower mantle mineral assemblage during laser heating over the experimental run duration (« 30 minutes), and therefore it is possible that non-equilibrium effects may affect the reported iron partitioning. Within experimental uncertainties, the isothermal bulk moduli for Mg, . x Fe x Si0 3 perovskites for x = 0, 0.1, and 0.2 are indistinguishable, implying that iron substitution does not affect the compressibility (Mao et al., 1991). I assume this is equally valid for the addition of both aluminum and iron thus adopt a room temperature isothermal bulk modulus for Mg-Fe-Al perovskite of Kfn = 259.0 GPa and its pressure derivative (dKT/8P) = 3.50, values that are near recommended values (e.g. Jeanloz and Hemley, 1994; KfO = 263 ± 3.0 GPa, (dKT/dP)T= 3.9 ± 0.5). The adopted values are also within experimental uncertainty of the low temperature Brillouin spectrocopy results (Yeganeh-Haeri, 1994; KgQ ~ 264.0 ±5.0 GPa), and lastly, very near the Chapter 2, page 69 "recommended" values from a recent re-evaluation of available thermoelastic data for Mg-perovskite (Jackson and Ridgen, 1996; KJQ = 262A GPa, (dKr/8P) .= 4). To determine the sensitivity to adopting a pure Mg-perovskite KJQ, I use the volume-density relationship (K,V0 = KrrefV0ref) to estimate a KT^~A'~'"'= 256.17 GPa assuming the reference molar volume for pure Mg-perovskite together with a reference KJQ = 259.0 GPa. Ita and Stixrude (1992; 1993) adopted KJQ = 262.6 GPa for pure Mg-perovskite and estimated a similar value for an aluminum bearing perovskite (KJQ = 258.6 GPa). To determine the sensitivity of our predicted profiles, I will also perform some calculations with KPOg~A'~pv = 256.17 GPa. The magnesiowustite molar volume may be determined with the conventional form (e.g. Jeanloz and Thompson, 1983; but again adopting the Fe content of Irifune (1994; XVe = 0.14): V0 (cmVmole) = 11.25 +1.00xpe Unlike Mg-perovskite, the compressibility of magnesiowustite is a function of iron content which I parameterize as KJQ = 160 -1.1 xpe based on adopting the recommended isothermal bulk modulus for MgO of KJQ = 160 ± 0.5 from Richet et al. (1989) and the value of KJQ = 152.3 + 0.2 GPa for Fe 0 9 4 3 O (Jackson et al., 1990). Similar linear relationships have been adopted by other studies (e.g. Zhao and Anderson, 1994; KJQ = 160 - 1.5xpe Duffy and Anderson, 1989; KJQ = 163 - %xpe Richet et al., 1989; KJQ = 160 - 5.5xpe). Since I also adopt additional elastic properties from Fei et al., (1992) for a slightly more iron enriched magnesiowustite [(Mg 0 6Fe 0 4)0] than that used here [Mg 0 8 6 Fe 0 1 4 )0] I am assuming that the effect of iron, in at least the concentrations considered here, does not have a significant affect on these properties (e.g. (dKr/dP)r). This assumption has also been made by other Chapter 2, page 70 researchers (e.g. Yagi and Funamori, 1996), a decision based on the lack of data for our modeled composition, rather than on any rigorous theoretical grounds. Following Ita and Stixrude (1992; 1993) I assume that the no phase transitions occur within the lower mantle when calculating predicted p and profiles. There have been recent suggestions based on diamond anvil experiments on pure M g S i 0 3 perovskite that this mineral undergoes a phase transition from orthorhombic to cubic structure at pressures greater than 64 GPa (Meade et a l , 1995), or alternatively, that it breaks down to magnesiowustite ((Mg,Fe)0) and stishovite (Si0 2) phases (Meade et al., 1995; Saxena et al., 1996). However, these results are in conflict with both early experimental results which observed Mg-perovskite as a stable phase across the lower mantle pressure range (Knittle and Jeanloz, 1987) and more recent diamond anvil cell experiments where Mg-perovskite was stable to 3000°K and 87 GPa (Boehler et al., 1997). Furthermore, a synthetic pyrolite mineral assemblage has been synthesized at pressures equivalent to 1500 and 2900 km depth and it was found upon quenching that the mineral assemblage consisted entirely of Ca-Pv, Mg-Pv, and M w (Kesson et al., 1998). Recent thermodynamic predictions also demonstrate that over the entire temperature and pressure conditions expected within the mantle that (Mg 0 9 0 Fe 0 1 0 )S iO 3 perovskite is stable (Stixrude and Bukowinski, 1992; 1993). They concluded that the breakdown reaction can occur but only for bulk iron contents of > 0.5, a value significantly in excess of the bulk iron content iron content for a pyrolite composition (« 0.12) (figure 2.26). Lastly, molecular dynamic computer simulations have determined the transition temperatures at lower mantle pressures for the orthorhombic to tetragonal to cubic phases of pure MgSi0 3 perovskite (Stixrude and Cohen, 1993; Warren and Ackland, 1996). Chapter 2, page 71 The calculated phase boundaries of Stixrude and Cohen (1993) are shown in figure 2.27 while the orthorhombic to tetragonal of Warren and Ackland (1996) is shown in greater detail in figure 2.28. A comparison between the calculated pyrolite adiabatic geotherm and the Mg-perovskite phase boundaries estimated from either molecular dynamics study strongly suggests that MgSi0 3 perovskite is stable throughout the mantle and its structure remains orthorhombic. By contrast, recent molecular dynamic computer models indicate that CaSi0 3 perovskite, which comprises « 7-12 vol% in the lower mantle, may undergo a high temperature (« 2200 °K at 80 GPa « 1850 km depth) structural phase transition from a distorted tetragonal structure to a cubic structure (Stixrude et al., 1996; see figure 2.28). However, the predicted change in symmetry is slight (<0.7% difference between the distorted and cubic phases) and below the detection limit of static experiments which were used to conclude that CaSi0 3 perovskite existed in a cubic phase throughout the lower mantle (Mao et al., 1989: pressures to 134 GPa; Wang et al., 1996: pressures to 13 GPa). Because the elastic response to the predicted structural phase change in CaSi0 3 perovskite should be slight, it is unlikely to generate a seismically resolvable signature and for the purposes of this study I assume that the experimentally measured elastic properties of CaSi0 3 perovskite hold throughout the mantle. Stixrude et al. (1996) speculated that the structural change in CaSi0 3 perovskite may explain controversial seismological observations of sub-660 km discontinuities. However, the inferred depth of the phase transition (1850 km) lies well below the depths of the seismically inferred discontinuities at 700 km, 900 km, and 1200 km depth (Kawakatsu and Niu, 1994; LeStunff et al., 1995). Chapter 2, page 72 The upper (<660 km depth) and lower mantles (660-2891 km depth) are modeled separately: this allows the flexibility of adjusting the temperature structure of the lower mantle independently of the upper mantle if the need arises. 2.12 Steps in Calculating p and I start by adopting the upper and lower mantle geotherms of Ito and Katsura (1989) and Akaogi and Ito (1993), respectively. This provides only an initial geotherm, since I later substitute an internally consistent adiabatic geotherm calculated directly from the elastic data and iteratively repeat this substitution until the geotherm and elastic parameters remain unchanged. This ensures that the geotherm used in the calculations is self-consistent with the adopted mineralogy, an approach outlined by Graham and Dobrzykowski (1976). I follow the recommendation of Bina and Helffrich (1992) regarding the temperature and pressure path to the T and P conditions of interest; to reach the high T-P conditions of the mantle, I first "step up" in temperature at room pressure (Tref-+T, Prej), followed by a second correction in pressure at high temperature (T, Prej^>P) with 298 K and 1 bar being taken as the reference state. This reflects the fact that volumetric thermal expansion data (ct(7)) are available for most minerals at room pressure, but this parameter is largely unmeasured at high pressure. The adiabatic geotherm is used to correct the standard temperature and pressure value of the isothermal bulk modulus to mantle temperatures using the following relationship: KT(T,Pre/) = KT(Tref,Pref) + T dT (r-298) p Chapter 2, page 73 where {dKr/dT) is the isobaric temperature derivative of the isothermal bulk modulus, T = the temperature of interest along the geotherm, and 298°K represents the reference state at room temperature. In a similar fashion I correct the molar volume from room temperature and pressure v(Tref, Pmf ) to mantle temperatures (but room pressure) using the expression; V(T, Pref ) = V(Tref,Pre/ ) expf }a(T) dT) ^298 / where a(7) is the thermal expansion coefficient and is used to express the volume change of a mineral due to a temperature change (Fei, 1995). Commonly the thermal expansion coefficient is reported as a polynomial expression: a(r) = a 0 + a i r + a_r~2 where a 0 , a , , and cc2 are constants determined by fitting experimental data. Substituting the polynomial expression in the above expression for molar volume and integrating gives: V(T,Pref) = V(Tref,Pref)exp a 0 (r-298) + ^ L ( r 2 - 2 9 8 2 ) - a 2 ( r _ 1 -298'1) Alternatively, for some minerals (see table 2-2) I have used expressions for the thermal expansion coefficient from Saxena and Shen (1992) that are given in the following polynomial expression: a(7') = a 0 + a , r + a 2 r 1 +aT Chapter 2, page 74 To evaluate the pressure dependence of the volume at high temperature, V{T, P) I insert the high temperature value of the isothermal bulk modulus, Kr(T, Pref), the volume at high temperature and 1 bar v{r,Pref^, the pressure derivative of the isothermal bulk modulus(9^ 7 , /9/ J ) T , and pressure, P (from PREM) into the 3rd order Birch-Murnaghan equation and iteratively solve for V{T,P) in 1 km intervals over the pressure range of interest for the particular mineral: P= - Kr(T,Pref) [V{T>P«)\ \V(T'P«)] 1- f -1 A (Mr) \ViT^f)) { V(TtP) J { V{T,P) ) ,4 . t — V { dP) r) { V(T,P) ) This equation follows from the fourth order Taylor series expansion in finite strain if) of the potential energy (Helmholz free energy, F) in response to an applied hydrostatic strain (Davies, 1973; Davies and Dziewonski, 1975); P = - 3 Kn(T) f (1 + 2f)% ji - 2 £ / + [9KT0 K'T0 +4^4-3K'T0)+s(3 K'T0 - s)]j where v{T,Pref) x 2/ V 3 -1 V(T,P) and KT0(T), Kro ={d2 KT/dP2)T, KT0 = (d KT/d P)r are evaluated at zero pressure (as denoted by the subscript 0). While here I predominantly utilize a third order truncation of this 4 t h order expansion (KT0 = 0), in later chapters some minerals are re-evaluated using the full 4 t h order expansion, so for completeness, I introduce it now. Following Bina and Chapter 2, page 75 Helffrich (1992) I determine the pressure dependence of the isothermal bulk modulus at high temperature via the formulation of Davies and Dziewonski (1975): KT {T, P) = KT0 (T) (1 + 2f)% j l - / (5 - 3 KT0)+ [9 Kro KT0 + (3 KTQ - 7^3 Kr0 - 5)] | . This expression is the full fourth order expansion and reduces to the third order when the terms containing the second pressure derivative, Kro are set to zero. I do not attempt to incorporate mixed P, T derivatives for the pressure derivative of the isothermal bulk modulus (e.g. Isaak, 1993; Chen et al., 1996). The mixed derivative, defined as { d2KT^ may be used to correct the pressure derivative of the isothermal bulk KdPdTJ modulus to the temperature conditions of interest via 'ax,) v dPjT ^ J x ( r - 2 9 8 " 4 Pi P AT I V / dPdTj While experimental studies are beginning to measure this property, Chen et al. (1996) note that PVT data with precision better than 0.3% are required to resolve values for (d2KT/dP dT^j and this assumes that the pressure and temperature data are free from errors. Isaak (1993) estimated the affect of neglecting the mixed derivative term would be on the predicted olivine content of the upper mantle by comparing the contrast in adiabatic bulk moduli across 410 km phase transition for the a - and p-olivine phases with and without the mixed derivative (note that the mixed derivative term for the p-olivine phase is unmeasured, while that for a-olivine may be extracted from experiments). He determined that ignoring this term may cause the olivine content to be overestimated by « 3 % assuming that the other Chapter 2, page 76 elastic terms are free from error. Chen et al. (1996) adopted the value [d2KT/dP dT)= 0.5 x 10~3 K"1 and estimated that the bulk sound velocity of olivine to the base of the upper mantle (i.e. 14 GPa and « 1500 K). They found that the bulk sound velocity was underestimated by « 2 % when {d2KT/dP dT^j is ignored. Because measured values for the mixed derivatives of nearly all of the minerals studied here are unavailable, and because I believe these estimated errors are small relative to the uncertainty in the measured elastic properties that I do use, I do not attempt to incorporate this term in the calculations. The pressure dependence of thermal expansion coefficient at high temperature is evaluated using the empirical expression (Anderson, 1967; Chopelas and Boehler, 1989; Anderson, et al., 1990); a(7,P) *(T,Pref) V(T,P) V(T,Pref)j where 5 r is the isothermal Anderson-Gruneisen parameter and is, following convention for upper mantle phases, assumed to be a constant. However, in the lower mantle, 87. for Mg-Pv decreases according to the relationship (Anderson and Masuda, 1994; Anderson et al., 1995); <T,P) a(7,0) • exp 5, ( rv{T,py K 1 V(T,0) where K= 1.5 (Anderson and Masuda, 1994). For Ca-perovskite and magnesiowustite, I adopt the empirical relationship suggested by Chopelas and Boehler (1992) based on mineral systematics because the data for these minerals have yet to be analyzed within the framework used by Anderson and Masuda (1994). Hence, 5rdecreases according to the relationship: Chapter 2, page 77 5 7 , = f V{T,P) " V(T,Pref)) • m-l where m is a constant and equal to 6 for magnesiowustite (Chopelas and Boehler, 1992) while for Ca-perovskite, I simply assume m = 6. The Gruneisen parameter, defined as y = \ ? C V J is corrected to high pressure by the following relationship: y[T,P) y(T,Pref) V{T,P) V ( T > P r e f \ The exponent q is often assumed to be a constant equal to 1, but I have followed the conclusions of Anderson, et al. (1993) on MgO and linearly decreased the exponent q from a value of 1.09 across the mantle to a 0.8 at the base of the lower mantle. Independent arguments in support of decrease in q with increasing pressure have also been raised by Duffy and Ahrens (1993). Ita and Stixrude (1992; 1993) assume that q = 1 ± 1. The high temperature and pressure adiabatic bulk modulus, KS(T,P) is calculated from the isothermal value, KT(T,P) via the accepted conversion (e.g. Anderson et a l , 1992): KS(T,P) = KT(T,P)[\ + Ta(T,P)y(T,P)] Where T is the high temperature of interest, a(T, P) is the thermal expansion coefficient, and Y(r,P)is the Gruneisen parameter, with both parameters at the high T-P conditions of interest. Finally, the density, p(T, P), and bulk sound velocity V^(T, P) are calculated by substituting the adiabatic bulk modulus, KS(T, P), the molar volume, V(T, P), both at high T-P conditions, into their definitions: Chapter 2, page 78 p(r,p)= V(T,P)' M KS(T,P) where M i s the molar mass of the mineral. 2.13 Self-Consistent Adiabatic Geotherm As mentioned briefly above, I calculate an adiabatic geotherm from the mineral physics parameters that were calculated to estimate density and the bulk sound velocity: this geotherm is then used in subsequent calculations for refined estimates of p(T, P) and V^(T, P). Although I am assuming that the appropriate geotherm for the Earth's mantle is indeed adiabatic, this assumption is immediately tested when the predicted density and bulk sound velocity profiles are compared to the observed seismic profiles. A close match between the predicted and observed density and bulk sound velocity profiles across the full depth extent of the mantle implies that, to first order, the geotherm is adiabatic (in addition to placing constraints on bulk composition). If the mantle deviated progressively with depth to a sub-adiabatic geotherm (e.g. Jeanloz and Morris, 1986; 1987) then a progressive and systematic divergence between the predicted and observed p(T, P) and V^,(T, P) profiles would be expected (see Weidner, 1986, p. 262). The adiabatic temperature gradient is calculated via the following expression (e.g. Graham and Dobrzykowski, 1976): dT) _Ty(T,P) VdP)s KS(T,P) Chapter 2, page 79 where y(T,P)and KS(T,P) are the V R H average (see below) of the Gruneisen parameter and the adiabatic bulk moduli respectively. To anchor the adiabatic temperature profile, I assign a temperature at 100 km depth in the upper mantle, which is taken as the "top" of the upper mantle in this study. In the lower mantle, the anchor point is located on the underside of the 660 km seismic discontinuity. The temperature at 100 km depth is chosen such that when the upper mantle adiabat is extrapolated to the surface, the resulting potential temperature is consistent with independent estimates of the mantle potential temperature determined from decompression melt studies of MORBs (1330-1350 °C; White and McKenzie, 1995; Iwamori et al., 1995). I initially elected to tie the anchor temperature of the lower mantle geotherm to the temperature predicted from the upper mantle geotherm. In subsequent numerical experiments, this assumption is relaxed. The temperature jumps associated with the latent heat of phase changes at the 410, 520, and 660 km seismic discontinuities are calculated via the method of Navrotsky and Akaogi (1984) but with the modification that instead of calculating the change in molar volume associated with the phase change from reference molar volumes at room temperature and pressure (e.g. AV(Tref, Pref), values at the mantle temperature and pressure of interest are utilized: where T is the temperature immediately above the onset of the phase change, and yd is the Clapeyron slope of the phase change where the subscript d denotes the depth of the phase boundary in km. I adopt Y 4 1 0 = +3.0 MPa/K for the 410 km and y 5 2 0 = +5.1 MPa/K for the 520 km olivine phase boundaries from Katsura and Ito (1989), and y 6 6 0 = -2.0 MPa/K for the 660 AT1, phase change AV(T,P) Chapter 2, page 80 km y-olivine to Mg-Pv + M w phase change (Bina and Hellfrich, 1994). C p is the heat capacity with appropriate values adopted from Akaogi and Ito (1993) and Akaogi et al. (1989). The adiabatic geotherm is calculated from 100 km depth downwards until it intersects the top of a phase change. The width of the transitions are taken from the widths given in the diagram of mineral proportions of Ita and Stixrude (1992; 1993) (see figure 2.6 and 2.10 for the location and widths of the phase transitions). Thus, the thickness of the phase change is not calculated, but assigned in constructing the adiabatic geotherm. Seismological studies which imply relatively thin phase changes, are in conflict with the equilibrium width calculated via thermodynamics for the 520 km, and to a lesser degree, the 410 km phase changes. I stress that this discrepancy is not addressed in constructing our geotherm since I am adopting "as fixed" the equilibrium widths inferred by Ita and Stixrude (1992; 1993). A more comprehensive study that incorporates the changing phase boundary width as a function of temperature (e.g. Helffrich and Bina, 1994) or incorporates curved phase boundaries (e.g. Helffrich and Wood, 1996) is beyond the scope of this study. The total temperature jump associated with the phase change is distributed linearly over the full transition width. The temperature at the base of the phase change is then used as the anchor point for the next leg of the geotherm. In this way, the upper mantle geotherm is calculated down to, and through, the 660 km phase change. In the lower mantle I assume, as discussed earlier, that there are no phase changes within this region. To ensure convergence, I substitute the new adiabatic geotherm calculated above, back into the calculations for density and bulk modulus and iterate through all the Chapter 2, page 81 above steps until both the geotherm and elastic parameters remain unchanged for a particular set of temperature anchor points. Following Ita and Stixrude (1992; 1993), I use the Voigt-Reuss-Hill averaging scheme (Watt et al., 1976) to determine volume averaged properties for the mineral assemblages. Implicit in this scheme is that the mineral assemblage is a homogeneous, isotropic aggregate. This is a reasonable assumption since tomographic studies that include the affects of anisotropy in the seismic model find that strong anisotropy is largely concentrated above « 250 km depth and decreases rapidly within the depth interval of 250 to 350 km depth and is small enough that it cannot be resolved below 400 km depth (Montagner and Tanimoto, 1991). While more restrictive schemes are available for averaging material properties such as Hashin-Shrikman bounds, Bina and Helffrich (1992) demonstrate that while the Hashin-Shrikman method gives tighter bounds than the V R H method, the averages for both are identical. Chapter 2, page 82 2.14 Results 2.15 Adiabatic Geotherm In the upper mantle the calculated pyrolite adiabatic geotherm (figure 29) is virtually identical to the preferred upper mantle geotherm of Ita and Stixrude (1992; 1993). Their geotherm is actually an isentrope - constructed by finding contours of constant entropy in pressure and temperature space. Consequently, it is based on the same thermodynamic relations that they use in calculating their elastic parameters, and thus, like the geotherm calculated in this study, is a self-consistent geotherm. It is interesting to note that in spite of significant differences between the equation of state used in this study and in theirs, and differences between the elastic database, there is no fundamental difference between the predicted upper mantle and transition zone temperature profiles. In contrast, in the lower mantle where they find a thermal discrepancy between their predicted upper and lower mantle geotherms of « 250 °C across the 660 km phase change (see figure 2.29), I am able to fit the lower mantle with an adiabatic geotherm that is anchored to the temperature predicted from the upper mantle geotherm. In addition, the calculated temperature jump at 660 km is significantly less than they determined -1 speculate on the basis of their phase diagrams (not shown here) that this discrepancy reflects their use of greater Clapeyron slope for the 660 km y-olivine breakdown reaction. Figure 2.30 illustrates the pyrolite adiabatic geotherm throughout the whole mantle along with the starting geotherms of Ito and Katsura (1989) and Akaogi and Ito (1993). A full discussion of the pyrolite geotherm and previous estimates of the temperature structure of the mantle (e.g. Stacey, 1977) will be presented elsewhere. Chapter 2, page 83 2.15 Upper Mantle Density Figure 2.31 compares the calculated upper mantle and transition zone density profiles for the total assemblage for both pyrolite and piclogite with the mean and standard deviation determined by Ita and Stixrude (1992) for 12 published Earth models (Derr, 1969; Haddon and Bullen, 1969; Mizutani and Abe, 1971; Wang, 1972; Jordan and Anderson, 1974; Gilbert and Dziewonski, 1975; Kind and Muller, 1975; Hart et al., 1976; Nakada and Hashizume, 1983; Lerner-Lam and Jordan, 1987; Montagner and Anderson, 1989; Dost, 1990). Also shown is P R E M (Dziewonski and Anderson, 1981), which Ita and Stixrude (1992, 1993) deliberately left out of the average as test of the average density. Finally, the density profile of akl35 (Kennett, Engdahl, and Buland, 1995) is also plotted. Pyrolite agrees very well with mean density in the upper mantle, the uppermost part of the transition zone, but is slightly and systematically higher across the middle of the transition zone. Below the p-to-y-olivine phase transition the density converges back towards the average density (and P R E M and akl35 p profiles). In general, piclogite displays similar behavior; within the upper mantle the density profile is offset slightly to lower densities than pyrolite but still agrees well with the mean density. However, across the 410 discontinuity, it is significantly less dense and remains so until the intersection of the beta-to-gamma olivine phase change whereupon the density rises to greater values such that across the remainder of the transition zone it is systematically denser than pyrolite (the small, abrupt, jogs in the piclogite density profile at « 500 and 530 km depth reflect minor, abrupt changes in mineral volume percent. I ascribe no significance to these jogs as they reflect imperfections in the mineral volumes that are due to digitizing the original figures from Ita and Stixrude (1992)). Inspite of slightly over Chapter 2, page 84 predicting the density in the lowermost part of the transition zone, the piclogite assemblage, while providing a worse fit than pyrolite, cannot be rejected on the basis of its predicted density. Figure 2.32 plots the pyrolite mineral physics density profile against density profiles from two new global reference models (akl35-Q and akl35-F) and two recent high resolution regional models (AU3 and PA5). Models akl35-Q and akl35-F (Montagner and Kennett, 1996) are constructed by adding free-oscillation constraints to akl35 (Kennett et al., 1995) with the model akl35-Q representing a version where only the density structure of the akl35 model was perturbed to satisfy the free-oscillation data, while the model akl35-F represents a version where both velocity and density was freely adjusted. The predicted pyrolite density profile significantly misfits these new density profiles; the new akl35-F exhibits very large density jumps at the 410 km discontinuity with a negative density gradient across the transition zone with density actually decreasing with increasing depth in this region. This is clearly anomalous as no known mineral of geophysical interest will become less dense with increasing pressure. Likewise, the akl35-F density profile, while less extreme than akl35-Q, still exhibits an unusually steep density profile through the transition zone. Both akl35-Q and akl35-F have steep gradients in density that extend from below the 660 km discontinuity to intersect the their lower mantle profiles at 850 and 800 km depths respectively. These depths are substantially deeper than the predicted depth for the pyrolite model which intersects the predicted lower mantle density profile at 730 km (this represents the termination of the progressive breakdown of garnet and majorite phases into Mg-perovskite). Chapter 2, page 85 Independent seismological studies on global stacks of SS precursor data that represent underside reflections off the 410, 520, and 660 km seismic discontinuities (Shearer, 1996) demonstrate that a steep shear wave velocity gradient is required immediately below the 660 km discontinuity and that it intersects the lower mantle velocity profile at « 727 km depth. This depth is virtually identical to that in the pyrolite model, supporting the inference that by 730 km depth (and along the average adiabatic geotherm) the upper mantle phases have completely converted to their lower mantle equivalents. This implies that the ak!35-Q and akl35-F models are likely to be in error (in constructing global reference models it is convention that discontinuities in the velocity and density profiles are placed at the same depth - thus shifting the depth of the base of the high gradient in the density profile to match the pyrolite model implies that a similar shift is required in the S- and P-wave velocity profiles). I suspect that the large swings in the akl35-Q and akl35-F density profiles may in part reflect errors in parameterization - these models do not include a 520 km discontinuity, and they allow the high gradient zone beneath the 660 km discontinuity to extend too deep into the lower mantle. By contrast, the density profiles for AU3 (Gaherty and Jordan, 1995) and PA5 (Gaherty et al., 1996), which represents average density profiles inferred for old continents and oceans respectively, are much closer in shape to the predicted pyrolite profile than either of the new global models. While the transition zone density profiles in the two high resolution regional models are offset to lower density than the pyrolite profile, the shape of the three profiles are similar. Nevertheless, like akl35-Q and ctkl35-F, both AU3 and PA5 intersect the lower mantle density profile at too great a depth (AU3 = 861 km; PA5 = 791 km), a feature which largely reflects the parameterization of these models (AU3 and PA5 were tied to P R E M velocity and density profiles at these depths). Thus, it is unclear i f the Chapter 2, page 86 systematic offset to higher densities for the predicted pyrolite density profile across the transition zone is real or i f the offset is an artifact reflecting how the seismic models are parameterized. 2.17 Lower Mantle Density Figure 2.33 compares the calculated lower mantle density profiles for pyrolite and piclogite together with the P R E M density profile and the standard error estimates of Ita and Stixrude (1992; 1993). Their initial lower mantle mean density profile is based on the statistical average of 12 seismic models. While this profile matches P R E M across the upper one third of the lower mantle, it becomes systematically less dense than P R E M across the bottom two thirds of the lower mantle (see figure 3 of Ita and Stixrude, 1993). Although the calculated standard deviation of the mean density profile encompasses P R E M in this region, the misfit led Ita and Stixrude (1992; 1993) to adopt P R E M as the "true" mean for the lower mantle density profile, and assign to it the calculated standard deviation determined from the 12 seismic models, an assumption that I follow here. The density profile of akl35 (Kennett, Engdahl, and Buland, 1995) is shown in figure 20 and is indistinguishable from P R E M (as are the lower mantle density profiles of akl35-Q and akl35-F). The average standard error in density (± 0.6%) estimated by Ita and Stixrude (1993) is very similar to that of Silver et al. (1988; ± 0.5%). Inspection of figure 2.33 shows that the Pyrolite density profile is in excellent agreement with seismic lower mantle density profile. A measure of how well the calculated pyrolite density profile fits akl 35 is given in figure 2.34 which is presented as a percentage difference via: Chapter 2, page 87 pyrolite Pa* 135 x l O O . V Potl35 J It is clear from this figure that the calculated pyrolite profile never deviates away from the expected profile by more than ± 0.2%. Figure 2.35 shows the percentage error when akl35-F and akl35-Q density profiles are adopted as the reference model and demonstrates that the excellent fit of pyrolite to the lower mantle density structure is not sensitive to the particular choice of the reference density profile. Furthermore, the deepest part of the lower mantle (bottom « 300 km) where the greatest misfit occurs, is also the region of the mantle, that by convention, is excluded from consideration of comparisons between predicted and mean properties (Chopelas and Boehler, 1989; Ita and Stixrude, 1992; 1993; Bina and Silver, 1990; Zhao and Anderson, 1995; Anderson and Masuda, 1994) because of the anomalous velocity gradients that exist in the D" region (e.g. Kendall and Shearer, 1994; Loper and Lay, 1995). The D" region is believed to represent a thermal and chemical boundary layer with a temperature jump in excess of 1500 °K from the solid mantle to the hotter, liquid core (Boehler, 1996). Ignoring the complications of chemical heterogeneity, a temperature increase of this magnitude forces the geotherm within this region to be super-adiabatic. Consequently, the method followed here, where an adiabatic gradient is explicitly assumed, is clearly inappropriate for this region, and therefore, a large misfit over this particular depth interval is not significant. Lastly, figure 2.36 shows the density profiles of magnesiowustite, Ca-perovskite and Mg-perovskite phases together with the predicted pyrolite and akl35 profiles. Of note is that the Mg-perovskite density profile is slightly more dense than the akl 35 profile at the top of Chapter 2, page 88 the lower mantle, but it becomes progressively less dense with depth such that it crosscuts the akl35 profile and terminates at the base of the lower mantle slightly below the akl35 profile. By contrast, magnesiowustite exhibits an opposite behavior; it starts out at the top of the lower mantle less dense than the akl 35 profile, but magnesiowustite becomes progressively denser with increasing depth, such that it too crosscuts the reference profile but ends up being more dense than the akl35 profile. These features have been previously documented (see figure 5 of Chopelas and Boehler (1992)) and Zhao and Anderson (1994) stress that one byproduct of the cross over in relative densities in the lower mantle is that studies which only use density as a discriminant (e.g. Chopelas and Boehler, 1989; 1992) and/or simply consider a single point in depth (e.g. 1071 km Wang et a l , 1991; 1994; 721 or 1171 km depths, Yagi and Funamori, 1996) cannot resolve between different petrological models that possess different bulk iron or silica contents. 2.18 Upper Mantle Bulk sound velocity Bulk sound velocity profiles for pyrolite and piclogite are shown in figure 2.37 along with the mean and standard error calculate by Ita and Stixrude (1992; 1993). They estimated the mean VQ by combining 34 published Vp and 32 Vs profiles (Chinnery and Toksoz, 1967; Hales et al., 1968; Herrin, 1968; Fairborn, 1969; Hales and Roberts, 1970; Buchbinder, 1971; Randall, 1971; Robinson and Kovach, 1972; Wright and Cleary, 1972; Wiggins et al., 1973; Gilbert and Dziewonski, 1975; Hart, 1975; Kind and Muller, 1975; Dey-Sarkar and Wiggins, 1976; Hart et al., 1976; King and Calcagnile, 1976; Fukao, 1977; Burdick and Helmberger, 1978; Sengupta and Julian, 1978; McMechan, 1979; 1981; Uhrhammer, 1979; Given and Chapter 2, page 89 Helmberger, 1980; Hales et al., 1980; Burdick, 1981; Dziewonski and Anderson, 1981; Vinnik and Ryaboy, 1981; Fukao et al., 1982; Nakada and Hashizume, 1983; Grand and Helmberger, 1984a; b; Walck, 1984; 1985; Lyon-Caen, 1986; Lerner-Lam and Jordan, 1987; Paulssen, 1987; Grad, 1988; Graves and Helmberger, 1988; Montagner and Anderson, 1989; Lefevre and Helmberger, 1989; Bowman and Kennett, 1990; Dost, 1990; Kennett and Engdahl, 1991). These profiles are from studies that postdate 1974, under the belief that after this time researchers attempted to account for the affects of attenuation and thus, the profiles are largely free of this systematic bias. Ita and Stixrude (1992; 1993) first determined the mean and standard deviation of the Vp and Vs profiles and then calculated the mean and standard deviation of V$, through formal propagation of errors. They checked this procedure by simulation of the probability distribution of V® when all possible combinations of Vp and Vs profiles are considered and found the two approaches gave indistinguishable results. Note that unlike the density profile, P R E M and iasp91 were included when calculating the mean In the upper mantle both pyrolite and piclogite fall within the standard error, although pyrolite gives a noticeably better fit to the average profile. I also plot the akl35 V® profile calculated from combining this models Vp and Vs profiles via the relationship VQ = yj{Vp +%Vs) . This Vo profile deviates systematically from both the mean seismic profile and the two predicted mineral physics profiles within the upper mantle, but it is not clear what significance to ascribe to this. Kennett (1991) presented three preliminary pairs of Vp and Vs velocity profiles (reproduced in figure 2.38) that were under consideration as a basis for a new global reference seismic model. It is clear from inspection of this figure that Chapter 2, page 90 significantly different, yet acceptable, upper mantle velocity models exist (compare MD89ps and iasp89) and consequently, it may be premature to consider the upper mantle portion of akl35 as "absolute ground truth" with which to evaluate predicted mineral physics profiles. In other words, the discrepancy between the predicted mineral physics profiles and the upper mantle akl 35 profile may not reflect shortcomings of the mineral physics model, but instead, reflects shortcomings of the seismic model. While there exists minor differences between the predicted and seismic V0 profiles in the upper mantle, the pyrolite and piclogite models exhibit major differences across the 410 km phase change. In the pyrolite model, the bulk sound velocity increases strongly across the 410 km and then gradually increases with depth to a peak value at « 520 km depth, whereupon the velocity gradient abruptly changes to a steeper slope which is relatively constant down to the 660 km discontinuity. Below this discontinuity is a zone with a shallow velocity gradient where the calculated profile rapidly increases with depth to intersect the mean profile at 730 km depth. In contrast, the piclogite model under predicts the increase in velocity across the 410 km with the subsequent profile lying systematically well below the mean velocity for the top part of the transition zone down to « 500 km depth. At this depth the piclogite profile has increased enough to re-enter the standard error bounds of the mean profile (the small, abrupt jogs in the piclogite profile at « 500 km and 540 km depth reflect imperfections in digitizing the mineral volumes from the original figures of Ita and Stixrude (1992; 1993) and therefore I ascribe no significance to these jogs). If I compare the pyrolite V® profile to the profiles derived from high resolution regional seismic models (AU3 and PA5; figure 2.39) it is evident that there is no significant Chapter 2, page 91 difference in V® velocity gradient in the upper mantle between the predicted and these particular regional models. While the two regional models are offset to faster velocities, this may be a function of the data used in constructing them. Since Gaherty and Jordan (1995) and Gaherty et al., (1996) used primarily S-wave data, they obtained a tightly constrained shear wave velocity structure, while the corresponding Vp velocity profile was simply scaled to the Vs profile so that their calculated VQ, was broadly consistent with independent estimates at 6 discrete depths taken from the pyrolite model of Ita and Stixrude (1992). Consequently, the Vp velocity profile may be shifted to lower values (and hence, reduce the associated V0 profile), without altering the ability of the Vs profile to satisfy their data. In the transition zone there still exists a distinct difference between the predicted pyrolite V& profile and the AU3 and PA5 profiles. Nevertheless, this difference decreases with increasing depth since the pyrolite profile becomes progressively faster down to « 520 km where it intersects the two regional profiles. From 520 km down to the 660 km discontinuity, the pyrolite and regional models are in very good agreement. Below the 660 km discontinuity, the regional profiles do not exhibit a zone of high velocity gradients. As noted earlier, this reflects the parameterization in constructing the seismic Vs and Vp profiles since they were constructed without inclusion of a narrow gradient zone, and instead, were allowed to intersect the P R E M velocity profiles at great depth (AU3 = 861 km; PAS = 791 km). 2.19 Lower Mantle Bulk Sound Velocity Chapter 2, page 92 In the lower mantle the pyrolite model is an excellent match to the akl35 VQ profile (figure 2.40). Figure 2.41 displays how well the calculated profile fits akl35 where the percentage difference between the two is calculated via: (\v -V 11 1 x 100 V \ * Oa*135 J and is plotted as a function of depth. It is clear from figure 2.41 that deviations of the calculated profile for pyrolite never exceeds seismic profile by more than the standard error (the estimated mean error from Ita and Stixrude (1992) is ± 0.8%). Figure 2.42 shows the percentage error when other seismic models are adopted as the reference model (akl35-F and akl35-Q; Montagner and Kennett, 1996), and indicates that the very good fit between predicted and observed is insensitive to the particular V0 reference model. Figure 2.43 displays the predicted bulk sound velocity profiles for the individual minerals in the lower mantle. Inspection of this figure clearly shows that Ca-perovskite is not the fastest mineral in the lower mantle, as Ita and Stixrude (1992; 1993) had found. This reflects the use here of a much lower value for the Ca-perovskite KfQ, (232 GPa versus 301 GPa) than the value they adopted. The piclogite model provides nearly as good as fit as the pyrolite model in the lower mantle when density (p) and bulk sound velocity (V^) are calculated along geotherms that are anchored to the same temperature as the pyrolite model (figure 2.33 and 2.40). This is not unexpected since Ita and Stixrude (1993) find that the pyrolite and piclogite calculated bulk sound velocity profiles systematically overestimate the seismic observations by 1 and 2 % respectively. I would expect that the relative misfit between the two models would remain Chapter 2, page 93 even after the new elastic data for Ca-perovskite and Mg-perovskite is incorporated, and indeed, this is what is found; the pyrolite still fits the seismic observations better than the piclogite model, but both models now lie well within the standard error of the seismic model. Note, however, this is not the case if the piclogite model is calculated along a hotter lower mantle geotherm, as is demanded if the lower mantle is chemically distinct from the upper mantle and transition zone. This is also shown in density and bulk sound velocity plots (figures 2.33 and 2.40) for a piclogite geotherm anchored at the top of the lower mantle to a temperature of 108 K. In this case, neither predicted piclogite density nor predicted bulk sound velocity profiles fit the observations. I comment further on this below. Chapter 2, page 94 2.20 Discussion O f the two compositions, only pyrolite agrees with both the density and bulk sound velocity observations throughout the upper mantle and transition zone, a result that is consistent with that reached earlier by Ita and Stixrude (1992; 1993). In the region of the 410 k m seismic discontinuity, the piclogite model significantly misfits the observed bulk sound velocity, and to a lesser degree, the density profiles. It can not account for the magnitude of the observed jump in across this discontinuity and for « 80 km below this depth, it falls well outside the lower error bound of the mean profile. The low olivine content of piclogite (« 40 vol%) is responsible for the smaller jump in bulk sound velocity across the 410 km discontinuity, while Ita and Stixrude (1992; 1993) state that it is the relatively low A l content in piclogite that delays the breakdown of pyroxene to majorite to greater depths than that of the pyrolite (compare figures 6 and 10) and that this feature results in the anomalously low velocities and densities below this discontinuity. To estimate the sensitivity of the predicted lower mantle profiles to the adopted KJQ value for Mg-perovskite I estimated the unmeasured F e - M g - A l perovskite isothermal bulk modulus {KJQ) via velocity-density systematics( (KTV0) M g F e A l p v =(KTre/voref) Mg_pv) w h e r e the reference values are the measured molar volume and isothermal bulk modulus of M g -perovskite (V0 = 24.46 cmVmole and KJQ = 259 GPa), VQ is the calculated molar volume (V0 = 24.73 cmVmole) for F e - M g - A l perovskite for an iron and aluminum content consistent with Irifune (1994), and Kj is its unknown isothermal bulk modulus. I obtain a predicted value of KJQ = 256.17 GPa, similar to that determined by Ita and Stixrude (1992; 1993). When this value is substituted into the pyrolite model, the resulting density and bulk sound velocity Chapter 2, page 95 profiles differ little from that calculated earlier (see figures 2.44 and 2.46 for the new p and V® profiles and figures 2.45 and 2.47 for the percentage error). While the misfit between the predicted and seismic profiles increases, the predicted profiles are still well within the uncertainty of the seismic models. Consequently, assuming that the Kpn value estimated here is an accurate approximation for an aluminum bearing (Mg, Fe)-perovskite, I may deduce that the excellent fit to the seismic observations over the lower mantle is insensitive to the exact value adopted in this study for Mg-perovskite. 2.21 Thermal Boundary Layers at Chemical boundaries As noted earlier, when the piclogite model is calculated along an adiabatic geotherm that is anchored to that predicted from the upper mantle geotherm, the resulting density and bulk sound velocity profiles do not fit the seismic profiles as well as the pyrolite model does, although the difference is minimal. Zhao and Anderson (1994) have performed similar calculations across the lower mantle for a pyrolite and piclogite composition, albeit for Vs and Vp rather than density and and for an adopted geotherm with a mantle potential temperature of 1500 °C. They concluded that since both models satisfied the seismic constraints, neither the pyrolite nor piclogite model could be rejected as suitable compositional models for the lower mantle. However, this claim is misleading and illogical: the pyrolite composition must be calculated along a geotherm consistent with an upper mantle geotherm - which at the surface, is independently constrained from decompression melting studies on M O R B to lie within a narrow range from 1330-1350°C. Thus, it is inappropriate for a pyrolite composition to adopt a geotherm with a mantle potential Chapter 2, page 96 temperature (defined, following McKenzie and Bickle (1988), as the surface temperature of the mantle adiabatic geotherm, when it is projected to the surface without melting) of Tp = 1500 °C, a value which falls within the potential temperature field for hotspots, rather than mid-ocean ridges. In contrast, the predicted piclogite p and (and Vs and Vp) profiles should be calculated along a lower mantle geotherm that is systematically offset to higher temperatures than that determined for the upper mantle to reflect the affects of a thermal boundary layer which must exist at the chemical boundary that separates the shallower pyrolite mantle from the deeper piclogite mantle. Chemical layering within the mantle demands that a thermal boundary layer coexists at the boundary separating the different layers (Jeanloz and Richter, 1979; Schubert an Spohn, 1981; Spohn and Schubert, 1982; Jeanloz and Morris, 1986). Thus, if one accepts that the upper mantle and transition zone is best fit by a uniform pyrolite bulk composition with the 660 km seismic discontinuity marking a phase and chemical boundary, then the appropriate lower mantle geotherm must be significantly hotter than the geotherm in the transition zone and upper mantle. While there is complete agreement that such a thermal boundary layer must coincide with a chemical boundary, the magnitude of the temperature jump across it is less constrained with estimates ranging from 500-1500 K (e.g. Jeanloz and Richter, 1979, Richter and McKenzie, 1981; Spohn and Schubert, 1982; Kenyon and Turcotte, 1983; Glatzmaier and Schubert, 1993). Here, I adopt a 1200°K jump in temperature across the 660 km seismic discontinuity as determined by three-dimensional numerical simulations of enforced layered convection (Glatzmaier and Schubert, 1993). It follows that the average offset between the whole mantle and layered mantle geotherms calculated in that study is also 1200°K. The two geotherms Chapter 2, page 97 from these numerical simulations are shown in figure 2.48 along with the pyrolite adiabat. For our purposes, I simply add this offset to the anchor temperature for the piclogite lower mantle geotherm (due to the systematic offset between the whole mantle 3D convection geotherm and the pyrolite adiabatic geotherm calculated here, I do not simply adopt the absolute values of the 3D layered convection geotherm). Note that while the 3D layered convection geotherm of Glatzmaier and Schubert (1993) may exceed the proposed dry lower mantle solidus of Ahrens and Holland (1996) in the upper region of the lower mantle, i f it, and its associated 3D whole mantle numerical convection geotherm were shifted to cooler temperatures to match that determined here, then the enforced layered convection geotherm would just fall beneath the hypothesized dry solidus. Figure 2.33 plots the predicted density profile for the piclogite model when its geotherm is anchored to 3108 K at the top of the lower mantle. It is clear from this figure, that when an appropriate "layered" geotherm is adopted, the predicted p profile is inconsistent with the seismic observations and falls well outside the estimated error of the seismic model over the upper half of the lower mantle. Likewise, the predicted bulk sound velocity profile (figure 2.40) for a piclogite model on a layered geotherm anchored to 3108 K falls well bellow the seismic estimate and may be rejected throughout the full extent of the lower mantle. Prior studies that reached the conclusion that a different chemical composition in the lower mantle could fit the seismic observations (e.g. Hemley et al., 1992; Stixrude et al., 1992; Zhao and Anderson, 1994) used estimates for the thermal properties of Mg-perovskite that conflict with the latest experimental observations (see discussion in Anderson etal., 1995). Chapter 2, page 98 Thus, claims that a piclogite composition can satisfy the lower mantle seismic data must be evaluated carefully; this statement is true i f a "cold" geotherm, such as an extrapolated upper mantle geotherm, is adopted in the calculations. Nevertheless, adopting such a geotherm for a chemically distinct composition in the lower mantle is invalid. In this study I find a piclogite composition fails to satisfy the seismic data when a "hot" geotherm, appropriate for a chemically layered mantle, is used in calculating the predicted properties. 2.22 Independent Constraints on Mantle Geotherms and chemistry In this study I adopted an upper mantle anchor point for the adiabatic geotherm, that when projected to the surface, falls with the temperature range of the mid-ocean ridge mantle potential temperature (Iwamori et al., 1995). McKenzie and Bickle (1988) theoretically modeled decompression melting to determine the major element composition and volume of melt produced during adiabatic decompression of the upper mantle across the dry solidus and determined that the volume of melt produced was very sensitive to the inferred mantle potential temperature and the degree of extension during melting. Subsequent studies have supported this conclusion in spite of adding in additional complexity associated with different parameterizations of melting (e.g. McKenzie and Bickle, 1990; White et al., 1992), the affects of changing spreading rate (Brown and White, 1994; Su et al., 1994; Minshull and White, 1996), finite duration of extension as opposed to instantaneous extension (Pedersen and Ro, 1992; Williamson et al., 1995; Brown and White, 1995), and greater details of mantle flow and melt migration (Spiegelman and McKenzie, 1987; Su et al., 1994; Shen and Forsyth, 1995). Linking decompression melting to trace and isotopic elements and converting Chapter 2, page 99 from a forward to an inverse modeling approach have also been undertaken (e.g. McKenzie and O'Nions, 1991; Brodie et al., 1994). A l l of the studies support the original conclusion, that globally, the upper mantle as sampled by mid-ocean ridges has a near uniform mantle potential temperature with a variance of only « ± 50°C (e.g. Brown and White, 1994; Su et al., 1994). While the absolute value for the M O R B mantle potential temperature has slightly increased from the initial inference of 1280°C (McKenzie and Bickle, 1988) to between 1320-1350 °C (Iwamori et al., 1995), in response to changes in the value for the entropy of fusion, AS (earlier calculations used 250 J/kg/°C, while Iwamori et al., (1995) adopt 350 J/kg/°C base on experimental calorimetric studies, see Iwamori et al., p. 255), whether or not the melt generation was by fractional melting or by batch melting, and to uncertainties in the final depth of melting, the inferred variance around in the normal M O R B value has stayed small (<± 50°C). This reflects the observations that the total thickness of oceanic crust derived from seismic measurements, away from the influence of fracture zones, hotspots, and marginal basins, appears to be almost insensitive to changes in spreading rate (changes in rate from 20-150 mm/year) and constant at an average value of 7+1 km (White et al., 1992; Brown and White, 1994; Su et al., 1994; Minshull and White, 1996). Oceanic crust is formed at mid-ocean spreading centers as a result of decompression melting of upwelling mantle beneath the ridge in response to plate separation. The uniform crustal thickness implies that the melt production beneath the spreading ridge increases in direct proportion to the spreading rate. If the mantle is relatively volatile free, and consequently, the dry peridotite solidus applies, and if the flow beneath the ridge is well represented by simple corner flow models', then theoretical models indicate the volume of the melt generated is largely Chapter 2, page 100 dependent upon the mantle potential temperature. The near uniform global thickness of oceanic crust indicates that away from hotspots, the mantle potential temperature beneath normal ridges has little variation (White et al., 1992; ± 40 °C; Brown and White, 1994; ± 40 °C; Su et al., 1994; their figure 3 indicates ± 30 °C). These studies have also demonstrated that the predicted melt composition agrees well with observations when the melt source region is a pyrolite-like composition with high olivine contents (>55 vol. %). As noted above, I based the choice on the anchor temperature at 100 km depth for the upper mantle geotherm on the results from these petrologic studies such that when the pyrolite adiabatic geotherm was projected to the surface, it fell with the tight bounds suggested by Iwamori et al. (1995). Other mineral physics studies that compared predicted seismic velocities and densities to observations, within the upper mantle (100-400 km depth) show that the absolute velocities can be matched well by either a piclogite or pyrolite composition, especially by trading off temperature against the volume % of the respective minerals (e.g. Bass and Anderson, 1984). While it is indeed possible to trade off temperature against the adopted mineralogy in terms of mineral physics modeling, the independent decompression melt studies cited above, demonstrate that this is an invalid approach - the average mantle potential temperature exhibits very little variation (+50 °C) globally and it's absolute value is relatively well constrained at between 1330-1350 °C. Furthermore, both the predicted melt volume and major element composition is satisfied by a mineralogy very similar to the pyrolite mineralogy adopted in this study. Saxena (1996) recently used a thermodynamic database to calculate, by minimization of Gibbs free energy, the mineralogical composition of a pyrolite and piclogite mantle and Chapter 2, page 101 compared the predicted density and bulk sound velocity profiles to P R E M . Such a modeling approach is desirable in that internally consistent thermodynamic estimates of the phase equilibria are calculated at each pressure of interest (see also Kuskov and Panferov, 1991; Kuskov and Galimzyanov, 1986) and the development of a public domain computer program to do this is one of the stated goals in establishing the next generation of Reference Earth Models (Navrotsky et al., 1995). In spite of the theoretical rigor in Saxena's approach, his tabulated geotherms are anomalously cold with a mantle potential temperature of 1135°C, a value which is in conflict with the above cited studies. This is shown in figure 2.49 for the whole mantle and figure 2.50 in an enlargement of just the upper mantle and transition zone which also shows the dry solidus and liquidus melting curves based on experimental studies of Zhang and Herzberg (1994), Herzberg and Zhang (1996), and Iwamori et al. (1995). Also shown is a calculated conductive geotherm for 120 Ma old oceanic lithosphere that has been spliced onto our pyrolite geotherm and represents the typically thermal structure inferred for cooling oceanic lithosphere of this age. To place the mantle potential temperature value of Saxena (1996) in context with the decompression melt studies, I show in figure 2.51 a plot from Su et al., (1994) which illustrates the sensitivity in the predicted crustal thickness for oceanic lithosphere as a function of mantle potential temperature. For temperatures only 20 °C colder than their adopted normal mantle potential temperature of 1317°C, the crustal thickness is reduced by about 3 km (down from the normal thickness of 7 km). The pyrolite mantle potential temperature in Saxena (1996) is about 180°C below the normal mantle temperature and would predict essentially zero oceanic crust being produced at modern spreading ridges! Chapter 2, page 102 While it is clear from figures 2.49 and 2.50 that Saxena's (1996) pyrolite geotherm fails to satisfy the above mentioned constraints for the surface mantle potential temperature, since it falls well below the range of 7> = 1330-1350 °C cited above, this figure also demonstrates that it is inconsistent with independent experimental constraints on the temperature at the 660 km seismic discontinuity determined by Boehler and Chopelas (1992). They bracketed the transition temperature and Clapeyron slope via direct laser heating in a diamond anvil cell with pure forsterite, converting it to y-spinel, and then subsequently to perovskite. They note that the experimental results of Ito and Takahashi (1989) demonstrate that the phase transition to perovskite is sharp and only insignificantly affected by iron content (up to 20 %) and the phase boundary as documented by their experiments is almost the same for MgSi0 3 or M g 2 S i 0 4 starting material. As Boehler and Chopelas (1992) note this makes the perovskite phase transition nearly ideal to constrain the temperature of the 660 km seismic discontinuity since the temperature at this depth is insensitive on the inferred mineralogical model (i.e. a pyrolite model has a different Mg/Si ratio than a piclogite model and for layered compositions, the lower mantle is inferred to be enriched in iron with respect to the upper mantle). Their direct experimental estimate of the temperature at 660 km depth is 1900 ±100 K, a value which agrees with thermodynamic estimates (Ito and Katsura, 1989; 1900 ±100 K). In contrast, the temperature at 660 km depth for the pyrolite geotherm estimated by Saxena (1996) is only 1733 K, well below the uncertainty of the above estimates. While Saxena (1996) concludes, like this study, that a uniform mantle of pyrolite composition can satisfy the seismic observations (density and V0), it is unclear how Saxena Chapter 2, page 103 (1996) can match the observed properties for both a pyrolite and piclogite composition along a geotherm that is so much colder than that adopted here. I find that a piclogite composition cannot satisfy the bulk sound velocity constraints, and inspection of the predicted piclogite F 0 in figure 2.37 shows that while it is possible to improve the fit of the predicted piclogite to the upper mantle and top of the transition zone by shifting it to faster velocities, as would happen i f the temperature is uniformly reduced, the same affect would drive the predicted in the lower part of the transition zone to a worse fit with the seismic observations. Unfortunately, the calculated profiles of for either pyrolite or piclogite in the upper mantle or transition zone are neither plotted, nor tabulated in Saxena (1996) so it is not possible to make a quantitative comparison with his results. I note that Saxena (1996) did not include Ca-perovskite in modeling the lower mantle (all Ca phases and majorite garnet were excluded), and his method differs from that used here in that he has attempted to model a temperature dependence for the pressure derivative of the isothermal bulk modulus, whereas I take {dKr/dP) as a constant. It is unclear i f this is warranted since the required cross derivatives {{d2Kr/d PDT)T, see Chen et al., 1996) are, with the exception of olivine, unmeasured for other mantle minerals. 2.23 Can a Chemically Distinct Lower Mantle be seismicallv invisible? While I have focused largely on the 660 km seismic discontinuity and the question of whether or not the bulk chemistry changes across this, I note that Wen and Anderson (1995) have concluded from excellent correlations between the predicted volume and location of subducted oceanic lithosphere and zones of seismically high velocity observed in different Chapter 2, page 104 seismic tomographic models within the 800-1100 km depth range, that subducting lithosphere does indeed penetrate the 660 km seismic discontinuity. Because laboratory tank experiments and numerical computer simulations of the interaction of subducting lithosphere with a chemical boundary demonstrate that subducting slabs should be deflected at a chemical boundary and not penetrate into the lower mantle, the results of Wen and Anderson (1995) strongly indicated that the 660 km discontinuity is not a chemical boundary. Nevertheless, they claim there is no requirement that a chemical boundary coincide with the known phase change at the 660 km discontinuity (where y-olivine breaks down to magnesiowustite and Mg-perovskite), and speculate that a global discontinuity may exist deeper within the lower mantle somewhere within the 900-1000 km depth interval (based on the regional seismic study of the Western Pacific by Kawakatsu and Niu (1994) who argued for a seismic discontinuity at 920 km depth). I note that Castle and Creager (1996) have recently looked closely at converted S-to-P phases within the area studied by Kawakatsu and Nui (1994) and found that conversion depths are uniformly distributed between 900 and 1300 km depth, a result that is not consistent with a nearly horizontal chemical boundary. Instead they suggest that the 920 km discontinuity inferred by Kawakatsu and Niu (1994) is a product of stacked subducted slabs with a "dead" slab stacked below the present day, active subducting plate. In a subsequent study analyzing events from this region that were recorded in the Western United States, Castle and Creager (1997) found no evidence for a sharp seismic discontinuity with a S-velocity jump greater than 1% that is coherent over large horizontal spatial scales such as thousands of kilometers, a feature that should exist for a global change in bulk composition. Thus, re-investigation of the region where the deep velocity discontinuity is purported to exist is not supporting the earlier conclusions of Chapter 2, page 105 Kawakatsu and Niu (1994), and consequently, significantly weakens the arguments of Wen and Anderson (1995) that a global chemical boundary exists at this depth. Lastly, I note that Wen and Anderson (1997) recently have modeled the Earth's long wavelength geoid using viscous flow techniques (e.g. Hager and Clayton, 1989) and argued that a chemically layered mantle with a boundary at 920 km depth may satisfy the geoid observations. However, they assumed the velocity to density scaling factor (dlnp/dlnl 7 , .), a parameter required to convert (or scale) the seismic tomographic velocity anomalies linearly into density anomalies, was a constant in the depth intervals 0-400 km, 400-670 km, and 670 - 2891 km and treated these three constants as free parameters to be adjusted to minimize the misfit between the observed and predicted geoid fields. In spite of invoking a chemical boundary at 920 km depth, I note that the velocity to density scaling factor is constant across the depth of their purported chemical boundary. This assumption is implausible given that the density signal of a chemical change should be substantial (Jeanloz, 1991) - indeed one may obtain an indication for the likely density contrast by comparing the predicted density profile for the hot piclogite model in figure 2.20 to the predicted pyrolite density profile. It is clear that there should exist a substantial density jump across a chemical change, a conclusion also reached by Jeanloz (1991), but for the case when temperature affects were not considered. In light of its large seismic signature, I contend that the 660 km seismic discontinuity remains the best candidate for a chemical boundary, contrary to the claims by Don Anderson and co-workers. While it is possible to retreat ever deeper into the lower mantle in search of possible discontinuities, I note that none of the global reference seismic models constructed to date have required a density or velocity discontinuity within the lower mantle (excluding Chapter 2, page 106 the D" region at the base of the lower mantle).Consequently, the 660 km seismic discontinuity is the deepest global discontinuity and thus, represents the deepest and last seismically visable "potential boundary" within the mantle. Lastly, I point out that i f one abandons the 660 km seismic discontinuity as the boundary separating chemically distinct layers, then advocates of a chemically layered mantle are left without a seismically distinct chemical boundary, and hence, the hypothesis of chemical layering within the lower mantle becomes largely untestable, since it becomes very difficult to test a hypothesis for which there is no visible means of detection. 2.24 Implications for the Next Generation of Reference Seismic Models I have shown that the predicted pyrolite V® profile matches the averaged upper mantle profile very well, both in velocity gradient and in absolute values, and also provides a good fit to the recent high resolution, regional upper mantle velocity structure beneath old continents and oceans. In spite of this success, the predicted pyrolite profile does not fit the profile from the latest global seismic reference model, akl35; the predicted velocity gradient is significantly different, such that while the two profiles intersect at 150 km, they rapidly deviate away from one another with increasing depth such that by 410 km depth, the difference is very large. This feature also exists in recent models based on ak!35 that have included free-oscillation travel time data (akl35-Q, akl35-F). It is disturbing that the seismic global reference model deviates so much from both the recent high resolution regional models (AU3 and PA5) and from the pyrolite mineral physics model. The fact that the mineral physics model is using the latest thermoelastic data and that I am applying it in a Chapter 2, page 107 region of the mantle where I have confidence in the assumed mineralogy (based on direct sampling at mid ocean ridges, dynamic melt modeling of the volume and composition of melts at mid-ocean ridges, thermodynamic modeling of the stable phases, and experimental synthesis studies) leads me to conclude that the source of the misfit does not lie in the pyrolite mineral physics model, but in the akl35 seismic model. This model was originally constructed as a radially stratified velocity model that gave calculated travel times that best matched the observed teleseismic arrival times of P, S, and core phases (see figure 2.52) listed in the International Seismological Center (ISC) database. This data base is huge (> 6 million readings of arrival times) and extends over 20 years. As noted by Kennett and Engdahl (1991) the resultant velocity model, iasp91, is intended as a summary of seismic travel times and does not necessarily represent a simple average of the Earth. iasp91 was parameterized with discontinuities in both Vp and V$ taken at 20, 35, 410, and 660 km depth with the velocities in each layer being represented by a linear gradient in depth. While discontinuities were allowed at 120 and 210 km, the final model did not require them and instead, a slight change in gradient occurred at 210 km. Likewise, a change in velocity gradient was allowed at 760 km depth. Kennett and Engdahl (1991) admit that iasp91 is a compromise between two alternative preliminary upper mantle velocity models, iasp89, and md89ps (see figure 38) that while being very close to one another in the lower mantle, differed largely in upper mantle velocity structure. iasp89 was characterized by large velocity jumps at the 410 and 660 km discontinuities, whereas md89ps had smaller jumps but higher velocity gradients. Although an improvement of the existing velocity modes such as P R E M , the calculated Vs arrival times of iasp91 appeared to suffer from a baseline shift, and Chapter 2, page 108 this, and other minor deficiencies resulted in the development of an improved global radial velocity model akl35 (Kennett et al., 1995). This model relied upon empirical traveltime curves for all the major seismic phases which had been derived from the ISC database after the entire set of earthquakes were relocated using the P-wave arrival times with the predicted iasp91 traveltimes. After relocation a subset of 6000 earthquakes that possessed good global coverage and depth distribution were selected and their reported arrival times were corrected for the new earthquake parameters (depth and position). The resulting data base of new arrival times (« 1.6 million) for the major seismic phases were plotted as a function of epicentral distance and then smoothed to interpolate over data gaps. Lastly, this set of smoothed empirical travel times is used to refine the radial velocity structure of iasp91 based on improving the fit between the empirical times and predicted times from the refined model. Figure 2.52b, taken from Kennett et al. (1995; their figure 2), is a composite diagram which gives the traveltime residuals as a function of epicentral distance between the predictions of the iasp91 velocity model and the empirical times for the major seismic phases that would be subsequently used to refine iasp91. Of note is that while this figure shows residuals for some phases in the epicentral distance range 0 to 25°, Kennett et al., (1995) state that in refining iasp91, they excluded P- and S- arrivals from 0 to 25° under the assumption that the crust and upper mantle, the region of the Earth that is primarily sampled by these phases in this epicentral distance, is too laterally heterogeneous to warrant producing an average. Thus, in constructing akl35, Kennett et al. (1995) adopted a continental style crust and upper mantle, and excluded some data that would significantly constrain the velocity structure in the upper mantle. Chapter 2, page 109 Consequently, I believe that the major reason why the high resolution, regional seismic models (AU3 and PA5) and the averaged regional velocity profile are in excellent agreement with the predicted pyrolite profile, yet the mineral physics profile systematically misfits the upper mantle portion of akl 35, is that akl 35 does not include sufficient data over this depth region. Indeed, in terms of mineral physics modeling, nearly all the elastic parameters for the major mineral phases in the upper mantle have been measured (new state-of-the-art thermoelastic data for natural clinopyroxene is needed) and thus, the upper mantle of the Earth is where the predictions are most accurate. Moving deeper, the pyrolite model still misfits akl 35 in the upper most part of the transition zone, but the two V0 profiles converge with the deviation between the two decreasing to 520 km depth, where the two models intersect. While beyond the scope of this study, one avenue of approach to improve the next generation of global reference Earth models is to adopt as a starting velocity model, the pyrolite model with the shallow upper 400 km "fixed" to the mineral physics model. Adjustments would then be made on the magnitude of the velocity jumps across the 410, 520, and 660 km seismic discontinuities and on the velocity gradients in the intervening parts of the velocity profile, while keeping the shallowest structure fixed. 2.25 Conclusions The purpose of this chapter is to analyze the pyrolite and piclogite geochemical models for the Earth's mantle by comparing calculated profiles of density and bulk sound velocity to their seismic estimates. These two chemical models, while not unique, represent Chapter 2, page 110 end members for the composition of the mantle: the pyrolite model represents a uniform bulk composition which is based on combining the observed composition of mafic magmas and xenoliths to predict the composition of the upper mantle source region. This composition is then applied throughout the mantle and implies whole mantle convection with the seismic discontinuities representing pure phase transitions that offer little or no permanent impedance to convective flow. The piclogite model represents a heterogeneous bulk composition where it is argued that large scale chemical heterogeneity, reflected by distinct layers within the mantle, represent quenched products initially produced during differentiation of a primordial global magma ocean. The piclogite model was originally proposed in the context of a three-layer convecting mantle with boundaries between the chemical layers coinciding with seismic discontinuities at 220 km, 410 km, and 660 km depth (Anderson, 1979a, 1980). With the application of new experimental and elastic data this model has undergone progressive and significant changes in mineralogy with the inferred olivine content increasing progressively from «16 to « 40 vol. %, and in it current mutation, the piclogite model still represents a chemically layered mantle, but now only between two layers separated at 660 km depth (or perhaps deeper; Wen and Anderson, 1995; 1997). The principal focus in this study was to re-evaluate the conclusion reached by Ita and Stixrude (1992; 1993) that thermal and chemical stratification existed within the mantle with the 660 km discontinuity marking the boundary separating a chemically distinct lower mantle from a uniform upper mantle and transition zone. Internally consistent adiabatic geotherms were calculated so that the associated mantle potential temperature was in agreement with independent constraints derived from studies of decompression melting at mid-ocean ridges. These studies provide a very narrow temperature range for acceptable mantle geotherms and Chapter 2, page 111 this is a constraint which must be satisfied when undertaking mineral physics modeling of the upper mantle and transition zone. The resultant adiabatic geotherm is utilized in estimating p and profiles - the assumption that an adiabatic gradient is appropriate for the whole mantle is tested when the predicted profiles are compared against the seismic profiles. If there existed regions within the mantle where the "true" geotherm progressively and systematically deviated away from an adiabatic geotherm, then the predicted p and profiles would show a similar deviation away form the seismic profiles with increasing depth (assuming that the adopted bulk composition is accurate). I do not find a systematic difference between the predicted p and profiles and the seismic observations, and thus, within the uncertainty of the calculations, I conclude that the temperature structure of the mantle is adiabatic. To evaluate the sensitivity of the predicted profiles to the adopted elastic data, I substituted different values for KJQ for aluminum-bearing Mg-perovskite based on velocity-density systematics. In the lower mantle, the use of an estimated KJQ value for aluminum-bearing Mg-perovskite has little effect on the fit between the predicted and observed p and profiles, and hence, I conclude that uncertainty about the appropriate KJQ for Mg-Fe-Al perovskite is unlikely significantly affect our results. I believe that the use of the latest thermoelastic data for lower mantle phases is the principle reason for the success in matching the seismic p and profiles for a uniform pyrolite mantle. Ita and Stixrude (1992; 1993) argued that the principle cause for the misfit between the predicted p and profiles for both a pyrolite and piclogite composition was the high bulk modulus of the Ca-perovskite (CaSi0 3) phase. Subsequent experimental studies have reported much lower values (Wang et al., 1996), which I use here. Therefore, it may not Chapter 2, page 112 be surprising that I are able to obtain an excellent fit between predicted and observed profiles when this change is made. However, I note that Ita and Stixrude (1992; 1993) adopted the Fe-Mg partition coefficient between magnesiowustite and perovskite from the experimental study of Fei et al., (1991) which is based on experiments with only pure Fe-Mg end members. This results in the majority of iron being partitioned into magnesiowustite. In contrast, guided by the results of Wood and Rubie (1996), who noted that the Fe-Mg partitioning between these phases is quite different in the presence of A1 2 0 3 , I adopt the observed iron and aluminum contents for co-existing magnesiowustite and Mg-Al-perovskite from synthesis experiments of a pyrolite bulk composition (Irifune, 1994). The resultant molar volume, and hence density, of the Mg-Fe-Al perovskite phase is significantly different from the pure Mg-perovskite end member. Since Mg-Fe-Al perovskite makes up « 75 vol% of the mineralogy of the lower mantle, only slight changes in density for this phase will have a significant affect on the predicted density. In spite of this effect I were able to obtain an excellent fit between the predicted and observed density profiles and I believe that the use here of the latest thermal expansion data for Mg-perovskite of Funamori et al. (1996) compensated for the significant change in density caused by adopting an increased Fe contents. I note that contrary to the conclusions of Bina and Silver (1990) for the lower mantle, I find that ability of a uniform pyrolite composition to satisfy the seismic p and profiles is largely insensitive to the seismological model used in the comparisons. As before, I believe the difference between their study and ours reflects the thermoelastic data adopted here, rather than any difference in methodology or seismic models. Chapter 2, page 113 While I find that a piclogite model can provide nearly as good a fit as pyrolite to the seismic p and V^, profiles in the lower mantle, this result is dependent upon utilizing a "cold" lower mantle geotherm that is concordant with the upper mantle and transition zone geotherms. However, a thermal boundary layer must coincide with a chemical boundary at 660 km depth and when an appropriate lower mantle geotherm that reflects the large temperature jump that must exist across the thermal boundary layer separating the two chemical layers is adopted, the predicted piclogite p and profiles fail to fit the seismic profiles, and thus, the piclogite model may be rejected. Because the upper mantle and transition zone seismic properties are best fit by a pyrolite composition with a geotherm that is consistent with independent constraints on the mantle potential temperature, and since the variance in mantle potential temperature is slight, it is invalid to arbitrarily adjust the upper mantle and/or transition zone temperature structure to reduce the magnitude of the temperature jump across 660 km discontinuity. The results I obtain when an appropriate "hot" lower mantle geotherm are used demonstrate clearly that claims that a piclogite model can satisfy the seismic constraint equally as well as the pyrolite model are misleading and illogical. Likewise, claims that a change in composition across the 660 km discontinuity would be seismically invisible (e.g. Jeanloz, 1991) are also not supported by the results of this study. While this study has focussed on the presence or absence of chemical layering at the 660 km discontinuity, I note that retreating ever deeper into the lower mantle to place a chemical boundary is not a productive approach because there is no known global seismic discontinuity within the lower mantle, and consequently, any invoked change in chemical composition in this region, must be invisible to seismology. Therefore, I firmly agree with Chapter 2, page 114 Allegre et al., (1995, p. 517) who state, "...it appears that the defenders of the chemically stratified mantle for major elements must resort to ever more elaborate models in order to evade the obvious conclusion, namely that this is an idea whose time has come and gone". In the upper mantle and transition zone our results are in agreement with those reached earlier by Ita and Stixrude (1992; 1993): a pyrolite mineralogy best fits the seismic properties for this region. In contrast, the piclogite model, which was originally constructed to explain the transition zone seismic properties, significantly underestimates the seismic V0 profile at the top of this region. Our major conclusion is that, away from the chemical and thermal boundary layers that characterize the Earth's surface and the core-mantle boundary, a pyrolite composition gives an excellent fit to the seismic observations throughout the whole mantle along a concordant, adiabatic geotherm. While the pyrolite bulk composition is not unique, it is consistent with inferred source compositions used in successfully modeling the major and trace element composition of melts produced by decompression melting. In conclusion, there is no need to invoke any chemical or thermal stratification within the Earth's mantle: this strongly suggests the Earth is currently in a state of whole mantle convection. Chapter 2, page 115 2.26 References Abramson, E.H., Brown, J.M., Slutsky, L.J. , and Zaug, J., 1997. 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Mineral Formula thermal expansion coefficients a(T) = a0+atT+<x3T~2, or a(T) = a0+alT+a2T'1 +a3T"2 a 0 a! a 2 a 3 Forsterite1 M g 2 S i 0 4 2.77 x 10° 0.97 x 10"8 -0.32 Fayalite2 Fe 2 Si0 4 0.5673 x 10"* 0.0163 x 10"' -0.2517x 10"z -1.6133 Enstatite3 OPX M g 2 S i 2 0 6 2.86 x 10"3 0.72 x 10"8 Ferrosilite4 OPX F e 2 S i 2 0 6 2.64 x 10° 1.574 x 10"8 -0.16279 Diopside5 C P X CaMgSi 2 0 6 0.3206 x 10"* 0.0811 x 10"' 0.1347 x 10"z -1.8167 Hedenbergite6 C P X CaFeSi 2 0 6 2.383 x 10"5 9.07 x 10"9 Pyrope7 Mg3Al 2 Si0! 2 0.0991 x 10"4 0.1165 x 10"7 1.0624 x 10"2 -2.5 Almandine8 Fe 3 Al 2 SiO ] 2 0.1776 x 10"4 1.2140 x 10"8 -0.5071 Grossular9 C a 3 A l 2 S i 0 1 2 2.649 x 10° 3.066 x 10"y -0.6605 Mg-Majorite1 0 M g 4 S i 4 0 1 2 Fe-Majorite" F e 4 S i 4 0 i 2 Ca-Majorite12 Ca 4 Si 4 0] 2 Mg-Wadselytie13 M g 2 S i 0 4 0.2711 x 10"* 0.6885 x 10"5 -0.5767 Fe-Wadselyite14 Fe 2 Si0 4 0.2319 x 10"* 0.7117 x 10"8 -0.2430 Mg-Ringwoodite15 M g 2 S i 0 4 0.1872 x 10"4 0.4210 x 10"8 -0.6537 Fe-Ringwoodite16 Fe 2 Si0 4 0.2455 x 10"4 0.3591 x 10"8 -0.3703 Mg-Fe-Al perovskite17 M g S i 0 3 1.982 x 10"5 0.818(± 0.257) x IC 9 -0.4740 ±0.118 Pv this study 1.982 x 10"5 0.918 x 10"9 -0.4740 Ca-perovskite18 CaSi0 3 3.06 x 10° magnesiowustite 19 (Mg,Fe)0 3.768 x 10"5 7.404 x 10"9 -0.7446 1, Gillet et al., 1991; 2, Fei et al., 1992, equation 10, p. 4 1 9 ; 3, Zhao et al., 1995; 4 , fit to Yang and Ghose, 1994; 5, Saxena and Shen, 1992; 6, fit to Cameron et al., 1973; 7, Saxena and Shen, 1994; 8, Fei, 1995; 9, fit to Issak et al., 1992; 10, assumed equal to pyrope garnet following Yusa et al., ( 1 9 9 3 ) ; 11, assumed equal to almandine garnet; 12, assumed equal to grossular garnet; 13, Fei et al., 1992; 14, Fei et al., 1991; 15, Meng et al., 1994; 16, Fei et al., 1991; 17, Funamori et al., 1996, note I slightly adjusted the coefficient oq within the stated experimental errors by 0 .100. This is shown in the row directly below; 18, Wang et al., 1996, I use the empirical relationship of O . L . Anderson et al., 1992 to extrapolate this value to high temperatures (their eq # 31): ( a ( 7 ) / a 7 > e ) = l / | l + a R > E 8 7 ( r - 7 E ) ] , where 0 is the Debye temperature for Ca-perovskite (TQ = 1100 K ) , 8j is the Anderson-Gruneisen parameter which for Ca-perovskite S T = 4 .65 . O . L . Anderson et al. ( 1 9 9 2 ) apply this to Mg-perovskite due to the paucity of high temperature thermal expansion data for that mineral; 19, Fei 1995. p CfQ CD c/3 OJ vo o On oo bo os O P i T3 CD I-I o <: £tl NJ On O O N O N O N O N O N O © NJ o O N O N On © O N O N O J o O N O N CD CD 1-1 o < Stl CD NJ OJ p^ Or, P> N j NJ OJ NJ © O NJ OS On o P^ O N oo o VO O N On O N Oo O OJ OJ o o © VO on P^ O o P^ o p^ Or, 4^ OS On p^ Or, on o -fe. o o O N -fe. 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Note the significant differences at 220 and 410 km depths between the two seismic models. Chapter 2, page 169 3.20 3.40 3.60 3.80 4.00 4.20 4.40 4.60 d e n s i t y ( g / c m 3 ) Figure 2.2 PREM (Dziewonski, and Anderson, 1981) and akl35 (Kennett, et al., 1995) density versus depth. Chapter 2, page 170 Mid-Ocean Ridge Hot-Spot mantle potentid temperature m a n t l e p o t e n t i a l temperature 1330-1350 C (- 1603-1623 K ^ i 4 5 o . l 5 5 0 C (=1723-1823 K ) o 100 E-E 200 E-300 | -400 E E 1 Q 600 E -700 900 1575 K best fit pyroli 800 E- lower mantle adtabat I Mg-Pv, Ca-Pv, &\iw J L _ T Ita & Stixrude (1992; 1993) predicted temperature 1822-1841 K E L 1 1 1 1200 1400 1600 1800 2000 2200 2400 T e m p e r a t u r e ( K ) Figure 2.3 The 1700 K pyrolite isentrope of Ita and Stixrude (1993). Note the offset between the predicted temperature at the top of the lower mantle determined from the upper mantle isentrope and the best fit lower mantle pyrolite isentrope. Chapter 2, page r 71 2800 8.00 8.50 9.00 9.50 10.00 10.50 1 B u l k S o u n d V e l o c i t y ( k m / s e c ) 1.00 Figure 2.4 Comparison of the predicted bulk sound velocity profile for the pyrolite and piclogite compositions with the seismic profile from PREM. Figure redrawn from Ita and Stixrude (1993). Q 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500 2600 2700 2800 U Pyrolite% Chapter 2, page 172 I ' I ' 4.40 4.60 4.80 5.00 5.20 5.40 D e n s i t y ( g / c m 3 ) Figure 2.5 Comparison of the predicted density profile for the pyrolite and piclogite compositions with the seismic profile from PREM. Figure redrawn from Ita and Stixrude (1993). Chapter 2, page 173 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 V o l u m e % P y r o l i t e Figure 2.6. Volume percentage of the mantle minerals present in the pyrolite model as a function of depth. Figure redrawn from Ita and Stixrude (1992). Chapter 2, page 174 0 100 200 300 Al2q-rich stable Al2Or poor assemblage stratification assemblage r-< 400 O H Q 500 h 600 h-700 h 800 Olivine + Cpx + plagioclase Peridotite Garnet + CPX p = 3.5 g/cm3 \-Garnet solid solution p = 3.6 g/cm3 Ilmenite p = 3.9 g/cm3 Olivine + OPX p = 3.2 g/cm3 ~ \fi-spinel + OPX p= 3.3 g/cm3— P - spinel + stishovite p= 3.55 g/cm3 y - spinel + stishovite p = 3.60 g/cm3 Ilmenite + spinel = 3.7 g/cm3 Figure 2.7 Mineral phase relations proposed by Anderson (1979). Note the inferred stable stratification sketched in the center column of peridotite, eclogite, and garnetite. Chapter 2, page 175 Trench Ridge Trench swell y )/ x v tl Continent ZZ~v jCZZS; " L o n C7 67 Ohm A Y Figure 2.8 Schematic plate tectonic cycle for the chemically stratified mantle of Anderson (1979). Chapter 2, page 176 Figure 2.9 Schematic illustration of the convective flow in a chemically stratified upper mantle (Anderson, 1983). In the upper figure, the eclogite layer now forms the transition zone and acts as the source and sink of oceanic lithosphere. In hte lower figure isotherms of convection are illustrated with the locations of descending flow in the lower mantle is thermally linked to the location of cold convective downwelling in the upper mantle and transition zone.. Chapter 2, page 177 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 V o l u m e % P i c l o g i t e Figure 2.10 Volume percentage of the mantle minerals present in the piclogite model as a function of depth. Figure redrawn from Ita and Stixrude (1992). Chapter 2, page 178 1 I I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 I i i i i i i i i i i i i i i — I J 0 1000 2000 3000 D e p t h ( k m ) Figure 2.11 Composite figure of density and bulk sound velocity calculated along a 2000oK adiabat for a pure olivine composition using a Birch-Murnaghan finite strain equation of state (solid line) and the Universal equation of state (dashed line). Figure redrawn from Ita and Stixrude (1993). Chapter 2, page 179 43 1 I 1 I 1 I Fe-end member 42,6810 I 1 I 1 I 1 I 1 I O a 42 S o > S 3 41 40 Fit 1: Linear, Y=B*X+A Equation: Y = -2.36732 * X + 42.681 Hazen etal., 1990 average 0 GPa values 1 Mg-end member 40.3130 0.00 0.20 0.40 0.60 0.80 a m o u n t o f M g b e t a O l i v i n e 1.00 Figure 2.12 Inferred linear relationship of molar volume for betta-olivine as a function of Mg content. Chapter 2, page 180 5 4 4 4 4 ^ 4 8 4 . f 4 3. 3. 3. 3. 3. 00 90 80 70 60 50 40 30 20 10 00 90 80 70 60 50 1 I 1 I 1 I 1 I 1 I 1 I 1 I Fe- end member 4.8281 g/cm3 40 0.00 Fit 1: Linear, Y=B*X+A Equation: Y =-1.33655* X+4.82819 1 1 Mg- end membel 3.4916 g/cm3 0.20 0.40 0.60 0.80 1.00 A m o u n t o f M g i n b e t a O l i v i n e Figure 2.13 Inferred linear relationship of density for betta-olivine as a function of Mg content. Chapter 2, page 181 190 180 170 h-160 h 150 i i i i i i i i i l i i i i i i i i i l i i i i i i i i i ( M g 0 . 8 4 F e 0 . 1 6 ) 2 S i O 4 H Fei et al., (1992) trade off curve between isothermal bulk modulus and the adopted K\ pressure derivative (their figure 2). Polynomial Coefficients Degree 0: 218.719 Degree I: -13.2196 Degree 2: 0.491126 Zha et al, 1996 pressure derivative 4.3 ± 0.2 ' ' i i i i i i i i i i I I 3.0 4.0 5.0 (dKjdp) 6.0 Figure 2.14 Estimated isothermal bulk modulus for the iron bearing b-olivine studied by Fei et al. (1992) for (8KT0ldP)T = 4.3. This estimate rests on the assumption that the Zha et al. (1996) pressure derivative, determined for a pure Mg end-member, is also applicable to this composition. Chapter 2, page 182 0.00 0.20 0.40 0.60 0.80 1.00 A m o u n t o f M g B e t a O l i v i n e Figure 2.15 Inferred linear relationship of the isothermal bulk modulus for betta-olivine as a function of Mg content. Chapter 2, page 183 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 A m o u n t o f M g i n g a m m a - o l i v i n e Figure 2.16 Inferred linear relationship of molar volume for gamma-olivine as a function of Mg content. Chapter 2, page 184 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Amount of Mg in gamma-olivine Figure 2.17 Inferred linear relationship of density for gamma-olivine as a function of Mg content. Chapter 2, page 185 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Amount of Mg in gamma-Olivine Figure 2.18 Inferred linear relationship of the isothermal bulk modulus for gamma-olivine as a function of Mg content. Chapter 2, page 186 1580 m < 1570 O £2 1560 ^ 1 5 5 0 M 1540 FzY 7: Lwear, Y=B*X+A Equation: Y= 61.0121 *X+ 1514.41 Data sources: Ohtani etal, 1991 Sinogeikin et al, 1996 (AGU abstract) Sinogeikin et al, (1997) Pacalo & Weidner (1997) Yagi et al, 1992 t: > 1510 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Fe content of Majorite 1.0 Figure 2.19 Inferred linear relationship of unit cell volume for Majorite as a function of Fe content Chapter 2, page 187 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 F e c o n t e n t M a j o r i t e Figure 2.20. Inferred linear relationship of the adiabatic bulk modulus for Majorite as a function of Fe content. Chapter 2, page 188 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 a m o u n t o f C a i n M a j o r i t e Figure 2.21 Inferred linear relationship of the molar volume for Ca bearing Majorite as a function of Ca content. Chapter 2, page 189 3.55 3.54 ,3.52' 3.51 '3.50 cn s o 3 49 ^ 3 . 4 8 3.46 3.45 _ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I [Pacalo & Weidner (1997) — _ Hazen et al, 1994a — Fit 1: Linear, Y=B*X+A — Equation: Y = -0.0489799 * X + 3.522 — " , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 I 1 1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 a m o u n t o f C a i n M a j o r i t e Figure 2.22 Inferred linear relationship of density for Ca bearing Majorite as a function of Ca content. Chapter 2, page 190 170 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I t Pacalo & Weidner, 1997 Ca-majorite of Hazen et al. 1994b Fit 1: Linear, Y=B*X+A j Equation: Y= -30.8571 *X+ 160 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 a m o u n t o f C a i n m a j o r i t e Figure 2.23 Inferred linear relationship of isothermal bulk moduli for Ca bearing Majorite as a function of Ca content. Chapter 2, page 191 0.0 0.2 0.4 0.6 0.8 1.0 F e / ( F e + M g ) i n P e r o v s k i t e Figure 2.24 Iron partitioning between silicate perovskite and magnesiowustite. Figure 2.25 Enlargement of iron partitioning between silicate perovskite and magnesiowtlstite. Chapter 2, page 193 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 M§ > S i 0 4 XFe F ^ S i Q Figure 2.26 Theoretical stability field of silicate perovskite at 3500 K across the lower mantle. Figure redrawn from Stixrude and Bukowinski (1992). Chapter 2, page 194 0 5000 10000 15000 20000 25000 30000 T e m p e r a t u r e ( K ) Figure 2.27 Theoretical temperature-depth phase boundaries for the structural polymorphs of silicate perovskite as determined by Stixrude and Cohen (1993). Chapter 2, page 195 0 200 h -400 600 h -800 h -1000 ^ 1 2 0 0 ^ 1 4 0 0 •g & 1 6 0 0 9 1800 2000 2200 2400 2600 2800 I 1 I 1 I 1 I 1 I 1 I 1 I Mineral Physics Pyrolite geotherm Calculated Phase boundary— /Warren & Ackland, 1996 I Ca-Pv distorted orthorhombic h Orthorhombic Mg-Pv \ I Tetragonal I Mg-Pv Ca-Pv cubic 'Ca-Pv calculated phase boundary transition tempe\ P = 80GPa (depth = 1850 T = 2200 K Stixrude et al., 1996 _ — l zone of reduced \ — — l\ seismic velocity gradients \ — - I D" region r i , i , \\ , l i r^i I . I . 1500 2000 25^0 3000 3500 4000 4500 5000 5500 T e m p e r a t u r e ( K ) Figure 2.28 Theoretical temperature-depth phase boundary for the orthorhombic to tetragonal structural polymorph of silicate perovskite (Warren and Ackland, 1996). Also shown is the theoretical phase boundary for the structural transition in Ca-perovskite (Stixrude et al., 1996) and tentative lower mantle discontinuities (Kawakatsu and Niu (1994: 700 km & 900 km); LeStunff et al., 1995: 1200 km). 0 100 200 300 J2400 &500 Q 600 700 800 900 Mid-Ocean Ridge mantle potential temperature 1330 -1350 C (= 1605-1625 K) Chapter 2, page 196 I 1 I 1 I Ita & Stixrude (1992; 1993) Ho & Katsura, 1989 V (assumed a constant | adiabatic gradient) + 60K Pyrolite adiabatic geotherm (3 y -> M g - P v i 1 i 1 j change + 38.1 K +35 K + 23.6 K - 30.2 K J experimentally bracketed 660 transition temperature (1900 ± 10( from a C 0 2 laser D A Q study (Boef & Chopelas, \992). Ita & Stixrude (1993) best fit lower mantle geotheYm ' ' ' I ' ' l_J I J I l _ L Pyrolite LM geotherm J I L 1200 2200 1400 1600 1800 2000 T e m p e r a t u r e ( K ) Figure 2.29 The calculated pyrolite adiabatic geotherm for the upper mantle, transition zone, and the upper part of the lower mantle. 0 200 400 600 800 1000 1200 1400 g<1600 1800 2000 2200 2400 2600 2800 43 P Q Ita & Katsura am) 1 I 1 I 1 I Mineral Physics Pyrolite geotherm Chapter 2, page 197 T Akogi & Ito, 1993b (Mg-Pv + 1/2 Mw) 1 1 1 1 1 1 I \ 1 1 1 1 1 Mill 1 1 1 1 1 1 V 1 , l \ , 1 1 1 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 T e m p e r a t u r e ( K ) Figure 2.30 The calculated pyrolite adiabatic geotherm for the whole mantle compared to the initial upper and lower mantle geotherms that were used in the calculations. Chapter 2, page 198 3.20 3.40 3.60 3.80 4.00 4.20 4.40 4.60 D e n s i t y ( g / c m 3 ) Figure 2.31 Predicted bulk density of pyrolite and piclogite as a function of depth in the upper mantle. The mean and standard deviation of the seismic densities are represented by the orange and yellow lines, respectively. The PREM and akl35 density profiles are also plotted. Chapter 2, page 199 900 3.00 3.20 3.40 3.60 3.80 4.00 4.20 4.40 4.60 d e n s i t y ( g / c m 3 ) Figure 2.32 The adopted bulk density of pyrolite as a function of depth compared to the global reference models akl35-Q and akl35-F density profiles (Montagner and Kennett, 1996) and the high resolution regional models AU3 and PA5 (Gaherty and Jordan, 1995; Gaherty et al., 1996). 700 800 900 1000 1100 1200 1300 1400 1500 Chapter 2, page 200 a i6oo h ^ 1 7 0 0 F-•g 1800 h-&1900 Q 2000 2100 2200 2300 2400 2500 2600 2700 2800 4.30 4.50 4.70 4.90 5.10 5.30 D e n s i t y ( g / c m 3 ) 5.50 Figure 2.33 Predicted bulk density of pyrolite and piclogite as a function of depth across the lower mantle. 700 h ' I ' I 800 -900 -Chapter 2, page 201 Q2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 -4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 Density error (%) Pyrolite composition Figure 2.34. Percentage difference of the predicted pyrolite density profile from PREM or akl35 density profiles. Chapter 2, page 202 2900 -4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 D e n s i t y e r r o r (%) P y r o l i t e c o m p o s i t i o n Figure 2.35. Percentage difference of the predicted pyrolite density profile from akl35-Q or akl35-F density profiles. Chapter 2, page 203 4.40 4.60 4.80 5.00 5.20 5.40 5.60 D e n s i t y ( g / c m 3 ) Figure 2.36 The predicted density profiles for the lower mantle mineral phases. 100 150 200 250 300 ^ 3 5 0 ^ 4 0 0 0,450 ^ 5 0 0 550 600 650 700 750 1/2 - J \ Chapter 2, page 204 1— 1—I— 1—I— 1—I Seismic v* = (v; - ivs2) Mineral Physics PREM •akl35 111111 Piclogite \ Pyrolite -% -Ita & Stixrude (1992). mean profile i i i 5.50 6.00 6.50 7.00 7.50 8.00 8.50 B u l k S o u n d v e l o c i t y ( k m / s e c ) Figure 2.37. Predicted bulk sound velocity for pyrolite and piclogite as a function of depth. The mean and standard deviation of the seismic densities are represented by the dot-dash and triple dot-dash lines, respectively. PREM and akl35 bulk sound velocity profiles are also plotted. 700 800 900 Chapter 2, page 205 Miiilin imiiiii|in I , i , i , i , i , i \-t a 05 C 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 V e l o c i t y ( k m / s e c ) Figure 2.38 Upper mantle S- and P- wave velocity profiles from proposed global reference models MD89ps, and iasp89 (Kennett, 1991). Chapter 2, page 206 5.50 6.00 6.50 7.00 7.50 8.00 8.50 B u l k S o u n d v e l o c i t y ( k m / s e c ) Figure 2.39. Predicted bulk sound velocity for pyrolite as a function of depth compared to AU3 (Gaherty and Jordan, 1995) and PA5 (Gaherty et al., 1996). Chapter 2, page 207 2900 8.0 8.5 9.0 9.5 10.0 10.5 11.0 B u l k S o u n d V e l o c i t y ( k m / s e c ) Figure 2.40. Predicted bulk sound velocity for pyrolite and piclogite as a function of depth across the lower mantle. Chapter 2, page 208 0 2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 -4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 B u l k S o u n d V e l o c i t y E r r o r % P y r o l i t e Figure 2.41 Percentage difference of the predicted pyrolite bulk sound velocity profile from the akl35 profile. 2900 -4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 B u l k S o u n d V e l o c i t y E r r o r % P y r o l i t e Figure 2.42. Percentage difference of the predicted pyrolite bulk sound velocity profile from the ak!35-Q and akl35-F profiles. Note that akl35-Q = akl35. 700 F Chapter 2, page 210 "T~ Mg-perovskite Ca-perovskite — 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 B u l k S o u n d V e l o c i t y ( k m / s e c ) Figure 2.43 The predicted bulk sound velocity profiles for the lower mantle mineral phases. Chapter 2, page 211 2000 2100 2200 2300 2400 2500 2600 2700 2800 4.30 5.50 4.50 4.70 4.90 5.10 5.30 D e n s i t y ( g / c m 3 ) Figure 2.44. Predicted bulk density of pyrolite and piclogite as a function of depth across the lower mantle for a Mg-Fe-Al bearing perovskite pyrolite assemblage. 700 F 1 i • on 800 -900 -1000 -1100 -1200 h 1300 1400 I— 1500 -1600 -^ 1 7 0 0 £ 1800 &1900 Q2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 A i L . Pakl35 \-pegion of reduced seising velocity gradients Mg- Ft'-AI pero vsk ite pyrolite versus ok 135 estimated average erroj_ of seismic model (0.7%) (Ita & Stixrude, 1993)— Chappr 2^ page 212 -4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 D e n s i t y e r r o r ( % ) P y r o l i t e Figure 2.45. Percentage difference of the predicted Mg-Fe-Al bearing perovskite pyrolite density profile from the akl 35 density profiles. 4.0 Chapter 2, page 213 2800 2900 8.0 8.5 9.0 9.5 10.0 10.5 11.0 B u l k S o u n d V e l o c i t y ( k m / s e c ) Figure 2.46. Predicted bulk sound velocity of pyrolite and piclogite as a function of depth across the lower mantle for a Mg-Fe-Al bearing perovskite pyrolite assemblage. 700 800 900 1000 1100 I— 1200 1300 1400 1500 1600 ,1700 £ 1800 0. Q &1900 V*>akl35 region of reduced seismi |_ velocity gradients 2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 -4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 B u l k S o u n d V e l o c i t y E r r o r % P y r o l i t e Figure 2.47. Percentage difference of the predicted Mg-Fe-Al bearing perovskite pyrolite bulk sound velocity profile from the akl 35 density profiles. nated average error Ijeismic models (± 0.8%J1 & Stixrude, 1993) _ J Chapter 2, page 214 Mg- Fe-A I pero vsk itc wrolite versus akl35 Chapter 2, page 215 i Q &1600 2600 2800 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 T e m p e r a t u r e ( K ) Figure 2.48 Pyrolite geotherm compared to the whole mantle and enforced layered mantle geotherms calculated from 3D numerical simulations of mantle convection (Glatzmaier and Schubert, 1993). 0 200 400 600 800 1000 j^l200 w 1 4 0 0 &1600 Q 1800 2000 2200 2400 2600 L minimization model 2800 •Saxena, 1996 Pyrolite compositi .Gibbs Free Energy Chapter 2, page 216 1 I 1 I 1 I T T Pyrolite adiabatic geotherm -j this study i i 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 T e m p e r a t u r e ( K ) Figure 2.49 Mineral physics pyrolite geotherm from this study compared with the pyrolite geotherm calculated by Saxena (1996). Chapter 2, page 217 Saxena (1996) mantle potential temperature of 1135 C Mid-Ocean Ridge mantle potential temperature 1330-1350 C (=1603-1623 K) Hot-Spot 1450-1550 C 900 250 500 750 1000125015001750200022502500 T e m p e r a t u r e ( K ) Figure 2.50 Enlargement of the upper mantle and transition zone temperature structure comparing the Pyrolite geotherm calculated in this study to that determined by Saxena (1996). Chapter 2, page 218 Tp is 185 C colder-^ than this mantle potential temperature. i i i fe I -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 p e r t u r b a t i o n s i n m a n t l e p o t e n t i a l t e m p e r a t u r e ( G ) Figure 2.51. Oceanic crustal thickness versus mantle temperature for half spreading rates of 1 cm/yr and 5 cm/yr. The axes are normalized to the intersection point of the curves where 7 km thick oceanic crust is produced from decompression melting of a mantle with a potential temperature of 1317 C. Figure redrawn from Su etal., (1994). Chapter 2, page 219 1 * • • 1 • 1 • 1 1 1 1 1 1 1 • 1 1 • 1 1 1 1 1 1 1 1 1 1 1 1 '1 20 40 60 80 100 120 140 160 180 A degrees Figure 2.52a. Theoretical iasp91 travel times superimposed on the times for test events (dots). Figure redrawn from Kennett and Engdahl (1991). P PP PcP S SS ScS SP ScP PKPdf PKPbc PKPab SKSac SKKSac SKPdf SKPbc P'P' fcM t j j I I | i i I | I I i | i i 1 I I | I I I | I • I I I I I I I 1~T~T i I i i i K M i I t CD i n 0 20 40 60 80 100 120 140 160 180 delta degrees Figure 2.52b. Composite figure of the residual travel times predicted for the iasp91 model and the smoothed empirical traveltimes for 18 seismic phases. Figure from Kennett etal., (1995). Chapter 3, page 220 Chapter 3 Mineral Physics constraints on the Chemical Composition of the Earth's upper mantle from Vs and VP velocity profiles; a test of the Pyrolite model. Chapter 3, page 221 3.1 Abstract Recent studies that have compared predicted Vs and Vp velocity profiles for various chemical compositions to equivalent seismological profiles have concluded that the transition zone and lower mantle are chemically distinct from the upper mantle. The preferred mineralogy, termed piclogite, has an olivine content of « 42 vol% (Duffy and Anderson, 1989; Ridgen et al., 1992; Duffy et a l , 1995). However, I have demonstrated in a previous chapter, from a comparison between predicted and observed density (p) and bulk sound velocity (K 0 ) profiles, that a pyrolite mantle (olivine content of « 62 vol. %) is consistent with the observed seismic observations throughout the whole mantle, while piclogite is not. To address this discrepancy I extend the modeling to calculate Vs and Vp for a pyrolite mantle. The decision to model Vs and Vp profiles for only the pyrolite model is that it, but not a piclogite mineralogy, satisfies the more stringent test of matching the p and V0 profiles throughout the mantle. Therefore, I am assuming that since pyrolite already successfully fits the mantle p and V0 structure, it should also match the related Vs and Vp structure. To test i f this is indeed the case, all of the parameters used in modeling p and V0 are held "fixed" - then the focus of this study is largely concerned with values for unmeasured temperature (d\x/dT) and pressure (d[i/dP)T derivatives of the shear moduli, u. that are required in calculating Vs and Vp profiles. Fortuitously, measured values of (du/9P) exist for the a-, P- and y-olivine phases, and {d\\./dT) for the a-, P-olivine phases, leaving only the temperature derivative of y-olivine as an unknown. I utilize both the high temperature thermodynamic approximation of Isaak (1992) and the mineral systematics of Anderson (1988) to predict high temperature values for {d\i/df) for the y-olivine, diopside and hedenbergite phases. The initial value for y-olivine was then perturbed, i f necessary, to optimize the fit between predicted and calculated velocity profiles from 520-660 km depth interval where the high resolution, regional oceanic velocity model PA5 was used as a reference over this interval. The resulting values for (d\i/df) and (du./dP) are then tested as a set to check they are mineralogically plausible following the recommendation of Duffy and Anderson (1989). Our adopted value is consistent with their claim that the temperature derivatives of the oc-,P-, and y-olivine phases should all be similar. However, unlike their earlier calculations, the temperature derivatives used here result in predicted Vs and Vp profiles for a pyrolite mantle that are in excellent agreement to the observed velocity profiles. Specifically, the predicted pyrolite Vs and Vp velocity profiles are able to; 1) fit the absolute velocities and velocity gradients across the upper mantle and transition zone, especially the gradients exhibited in the latest high resolution, regional seismic models that incorporate a 520 km discontinuity; 2) give mutually consistent estimates of the olivine content (« 62 vol. %) using the observed Vs, Vp, and V& jumps across the 410 km seismic discontinuity; 3) predict normal incidence shear wave reflection coefficients at the 410, 520, and 660 km discontinuities that are in excellent agreement with independent i? S c S estimates based on ScS reverberations; and 4) predict normal incidence P-wave reflectivity at the 410 Chapter 3, page 222 and 660 km discontinuities that are in excellent agreement with independent long period seismologic estimates. An unexpected byproduct of the modeled V$ and Vp profiles is that they predict both the absence of PP precursor reflections, yet the presence of strong SS precursor reflections from the underside of the 660 km discontinuity, an observation that was previously interpreted to favour a low olivine content 40 vol. %) mantle. Therefore, a mineralogically plausible estimate for the unmeasured temperature derivative for the y-olivine phase results in predicted Vs and Vp profiles for a pyrolite model that are entirely consistent with seismic observations throughout the upper mantle and transition zone. Hence, there is no need to invoke changes in bulk chemical composition within the upper mantle or transition zone of the Earth. Chapter 3, page 223 3.2 Introduction This chapter reports and interprets mineral physics calculations of shear (Vs) and compression (Vp) velocity profiles for a pyrolite composition using Birch-Murnaghan finite strain theory (e.g. Bina and Helffrich, 1992). In this study, both Vs and Vp (where transition zone along an adiabatic geotherm that is directly calculated from the mineral physics parameters, ensuring self-consistency between the calculated velocities and the geotherm. I concentrate here on the upper mantle (100-410 km) and transition zone (410-750 km) and defer consideration of the lower mantle (750-2891 km) until chapter 4 and 5. The purpose of this research is not to differentiate between different compositional models by comparison between extrapolated laboratory data and seismic observations. Although this has been the purpose of many previous studies where predicted Vs and Vp profiles have been used as a discriminant of compositional models (e.g. Anderson and Bass, 1984; 1986; Bass and Anderson, 1984; Lees et al., 1983; Duffy and Anderson, 1989), I take a different approach. Based on a comparison of calculated density (p) and bulk sound velocity (V0) profiles, I concluded earlier that while a pyrolite mineralogy successfully satisfies the observed seismic constraints throughout the whole mantle, a piclogite model does not. Because the thermoelastic data required to calculate p and V0 are experimentally measured, these properties are a robust test of the compositional models and are better suited than predicted Vs and Vp profiles to discriminate between the pyrolite and piclogite compositions. Hence, on the basis of p and V0, I subject only the pyrolite composition to additional mineral physics tests - there is no logical reason to pursue study of the piclogite calculated throughout the upper mantle and Chapter 3, page 224 model, especially in terms of calculating Vs and Vp since for these properties, the elastic data base is incomplete, and hence predicted Vs and Vp profiles are inherently more uncertain than p and F 0 profiles. Consequently, I adopt a pyrolite mineralogy, its self-consistent adiabatic geotherm, and importantly, the thermoelastic parameters used in calculating the p and F 0 profiles, and treat all of these properties as "fixed" for the purposes of modeling Vs and Vp. By making these assumptions I am significantly reducing the number of adjustable variables; for example the mineralogy can not be simply adjusted to improve the fit between calculated and observed profiles, as was done in successive studies by Bass and Anderson (1984), Anderson and Bass (1984; 1986), and Duffy and Anderson (1989). Nor can I arbitrarily pick a geotherm from the geophysical literature. For example, in attempting to place constraints on the olivine content of the upper mantle by modeling the seismic velocity jump across the 410 km discontinuity, Duffy et al. (1995) adopt an upper mantle geotherm with a mantle potential temperature of 1,250 °C, while Duffy and Anderson (1989) and Ridgen et al. (1991; 1994) adopt a geotherm with a mantle potential temperature of 1,400 °C, while finally, Ridgen et al. (1992) use a 1,300 °C geotherm. Since the magnitude of the calculated velocity jump is primarily sensitive to the value for the temperature derivative of the P-olivine shear modulus, a requirement in performing such a calculation is that the temperature structure of the mantle around 410 km depth is accurately known. Lastly, I am not free to adjust the isothermal bulk moduli, KJQ nor its temperature, (dK.JdT)^ and pressure, (<9 KT /'d P) derivatives to improve the fit between calculated and observed Vs and Vp profiles; these properties were used in modeling p and V&, and hence, Chapter 3, page 225 are treated as "fixed" in this study. For example, Bass and Anderson (1984) and Anderson and Bass (1984) adopted a high value for the isothermal bulk modulus of majorite, Kj = 221 GPa (from the experimental study of Jeanloz, 1981), a mineral that forms greater than « 50 vol% in the transition zone for the particular piclogite mineralogy they advocated. In a subsequent study, Duffy and Anderson (1989) altered the volume percent of majorite (as well as other transition zone minerals) but also adopted a lower value for majorite Kj = 175 GPa based on the preliminary experimental values of Weidner et al. (1987). Subsequent experimental work has indicated that an even lower value is appropriate (Pacalo and Weidner, 1997; Sinogeikin et al, 1997). In contrast, this study does not alter the pyrolite mineralogy to improve the fit. Lastly, values for the thermal expansion coefficients of the various minerals that were used earlier are also held fixed. In short, the purpose of this research is to determine i f a pyrolite compositional model can satisfy the seismic observations in the upper mantle and transition zone. Thus, I wish to determine i f the discrepancy between earlier studies, based of Vs and Vp profiles, that favoured a piclogite model (« 42 vol% olivine), and the results from the previous chapter, based on p and V0 profiles, that favors a pyrolite model (« 62 vol% olivine), is indeed real. For example, Bass and Anderson (1984) and Anderson and Bass (1984), using a different data base of thermoelastic properties than which used here, claim that a pyrolite mineralogy can not satisfy the seismic observations. It was demonstrated earlier that when the latest experimental values for the thermoelastic properties of Ca- and Mg-perovskite are used in modeling density and bulk sound velocity throughout the lower mantle, the difficulty, found by previous studies, in obtaining a fit between the predicted and observed profiles along a concordant adiabatic geotherm, is resolved. Likewise, previous studies which are based on Chapter 3, page 226 comparisons between calculated and observed V$ and Vp profiles, should be re-evaluated, since the thermoelastic data base for upper mantle and transition zone mineral phases has undergone significant changes as better and more experimental data has been published. Specifically, because of advances in experimental design, many of the required parameters that earlier studies were forced to estimate have recently been measured, with the result that predicted Vs and Vp profiles may be constructed and interpreted with much greater confidence than ever before. I reiterate that a pyrolite bulk composition is not unique, and it is not the only bulk composition that can fit the seismic p and V& observations; I have no doubt that other "pyrolite-like" compositions can be concocted which also fall within the seismic observations. On the other hand, low-olivine compositions that may satisfy some seismic constraints, may be ruled out on the basis of other information. For example, Ita and Stixrude (1993) present, along with pyrolite and piclogite models, a third compositional model of an aluminum enriched piclogite (40 vol% olivine), that fits the seismic p and V& profiles across the transition zone far better than a traditional piclogite does. While such a model is capable of satisfying the seismic constraints, it is not possible to take this mineralogy up to the Earth's surface - independent modeling of the volume and major-, trace-, and isotopic-chemistry of melts produced by decompression melting at mid-ocean ridges constrains the shallow pressure (<100 km) mineralogy to be essentially a pyrolite composition with > 55 vol. % olivine (e.g. McKenzie and Bickle, 1988; 1990; McKenzie and O'Nions, 1991). Thus, i f an aluminum enriched piclogite were accepted as the composition of the bulk of the upper mantle and transition zone, then a chemical boundary between the shallow olivine dominated mantle and the [Al]+ piclogite mantle must exist and lie shallower than the 410 km seismic Chapter 3, page 227 discontinuity. On the other hand, such a chemical boundary must also lie deeper than the maximum depth of the continental roots (« 300-350 km; Grand, 1994; Nolet et al. (1994)). I note that the earlier chemically layered models of Anderson (1979a), Bass and Anderson (1984), Anderson and Bass (1984) placed the boundary between the shallow olivine dominated assemblage and the deeper chemical layers at 220 km depth, coincident with a large seismic discontinuity in P R E M (Dziewonski and Anderson, 1981), the global-average, seismic reference model that was then available. Furthermore, Anderson (1979a; 1987a, b; 1990; 1995) argued that continental roots extend no deeper than 150 km, although recently Polet and Anderson (1995) admit that the roots to some continental shields reach > 300 km depth. Subsequent global reference seismic models (e.g. iasp91; Kennett and Engdahl (1991); and akl35; Kennett, et al., (1995)), and high resolution regional studies (e.g. AU3, Gaherty and Jordan, 1995; PA5, Gaherty et al., 1996) have not required a 220 km discontinuity to fit the seismic observations with the implication that there is no global discontinuity at this depth. Furthermore, many regional seismic tomographic models that cover continental shields resolve continental roots to > 300 km depth (Su et al., 1994; Vasco et al., 1993; 1994; 1995; Zhou, 1996; Grand, 1987; 1994; Marquering and Snieder, 1996; Masters et a l , 1996) with the consensus that Jordan's tectosphere hypothesis of deep cratonal roots (Jordan, 1975a, b; 1978; 1979; 1981, 1988; Learner-Lam and Jordan, 1987; Jordan et a l , 1989) is confirmed (Nolet et a l , 1994). Therefore, i f the [Al]+ piclogite mineralogy is adopted for the upper mantle and transition zone, then there exists the problem that the shallow chemical boundary which must exist, is seismically invisible. A further difficulty is that a thermal boundary layer must accompany a chemical boundary layer - thus, it is invalid to adopt a geotherm that is tied to Chapter 3, page 228 the present-day, mantle potential temperature of« 1330 °C when modeling a bulk composition in the upper mantle that is not a pyrolite composition (e.g. Duffy et al., 1995). In a layered mantle, a 1330 °C adiabat is appropriate for the shallow pyrolite mantle, but not for the underlying, chemically distinct layer: this must be significantly hotter (estimates for the temperature jump across such a thermal boundary layer range from +500°K (Kenyon and Turcotte, 1983) to +1,500 °C (Glatzmaier and Schubert, 1993). I will return to the problem of an "invisible" shallow chemical boundary and its thermal boundary layer in the Discussion section. I stress that a major advantage in adopting as the pyrolite mineralogy, its self-consistent adiabatic geotherm, and the thermoelastic parameters used in the earlier study of p and V0 [Kp, [dKT/dT^ , [dKr/dP^ , a(7), 5 T , y] is that I may now focus largely on the temperature derivative |3u./srj of the y-olivine shear modulus and its affect on the calculated Vs and Vp profiles (recall that Vs =• ^u/p and V,, = ^J(K + %n)/p ). The temperature derivative [dyijdT^ is used to correct the standard room temperature and pressure reference values of the shear moduli, \x(Tref, Pre{) to the high temperature conditions of the mantle, and it is primarily in the last 3-5 years that high precision experiments have been performed to measure the (d\i/df)s (and {d\i/dP) ) properties of mantle minerals over a sufficiently large range of temperature (or pressure). Prior studies that compared calculated Vs and Vp profiles to seismic observations were forced to adopt values that were largely "best guesses" based on the properties of minerals of similar crystal symmetry (e.g. Lees et al., 1983; Bass and Anderson, 1984; Anderson and Bass, 1984; 1986; Bina and Chapter 3, page 229 Wood, 1987; Weidner, 1985; Weidner, 1986; Weidner and Ito, 1987; Irifune, 1987; Duffy and Anderson, 1989). I also note that these studies were also free to adjust the mineralogy, the geotherm, and the other thermoelastic properties (thermal expansion coefficient, bulk moduli and related temperature and pressure derivatives). Consequently, the conclusions reached by these studies regarding the success or failure of a particular assemblage to match the observed Vg and Vp velocity profiles were controversial since the results were largely dependent upon the particular values adopted for the unmeasured thermoelastic properties. The paucity of experimental measurements for temperature and pressure derivatives is rapidly changing. Values for {d\i/dP)T, which are derived from elastic moduli measured across the full pressure range of the upper mantle, are just now being reported for key mantle minerals (Mg 2 Si0 4 , forsterite to 16 GPa, Duffy et a l , 1995; Zha et al., 1996; L i et al., 1996; (Mg 0 9 Fe 0 1 ) 2 SiO 4 olivine to 17 GPa, Abramson et a l , 1997; Zaug et al., 1993; Mg 2 Si0 4 , wadsleyite to 12 GPa, L i et al., 1996a, b; to 14 GPa, Zha et al., 1997). The pressure range of these measurements ensures that the pressure derivatives are much more tightly constrained than before: previous estimates for (9p./3P)7. were often determined from fitting data from very low pressure ultrasonic experiments (< 1 GPa) (e.g. Kumazawa and Anderson, 1969; Graham and Barsch, 1969). It is clear that values for (d\i/8P)T, determined from fitting data extending over 16 GPa, are much more robust than estimates made from fitting data that extends over only 1 GPa. A n additional advantage of laboratory experiments that extend over a great range in pressure is the ability to differentiate linear and non-linear pressure dependence. For example, Abramson et al. (1997) document non-linear behavior for the shear moduli, |a (but linear behavior for the adiabatic bulk moduli, K$) of a Chapter 3, page 230 natural olivine [(Mg 0 9Fe 0 ,) 2Si0 4] over a pressure range of 17 GPa. The implication is that for olivine, an extrapolation in pressure of the shear moduli should be made with a 4th order, rather than 3rd order, Birch-Murnaghan equation of state. Although other high pressure experiments on pure forsterite failed to document a non-linear pressure dependence for the shear moduli in spite of spanning a 17 GPa range in pressure (Zha et al., 1996), the experimental error associated with these results was such that a linear fit to the data was acceptable (new, unpublished experimental data by the Zha et al., group that extend to greater pressure have now led them to adopt a non-linear pressure dependence in p. (J.M. Brown, personal communication). The approach taken here to is to use the measured values (within the stated experimental uncertainty) for the temperature {d\x/dTj , and pressure (d\i/dP)T derivatives of the shear moduli for the various minerals, and for those minerals in which these are unmeasured, to adopt values which are both "mineralogically plausible" and which result in predicted Vs and Vp profiles that are in agreement with seismological observations. Unlike previous modeling studies that tested various trial compositions, I am modeling a composition that has already been successfully tested via density and bulk sound velocity modeling. Hence, I assume that pyrolite must also fit the observed Vs and Vp profiles; this is the rational for adopting values for the unmeasured \d\ijdT^j of y-olivine that gives a good match between the predicted and observed Vs and Vp profiles. In spite of the confidence placed in the pyrolite mineralogy, there is no guarantee that a pyrolite composition can, in fact, provide a good fit to the Vs and Vp profiles - for instance, because a 3rd order fit Birch-Murnaghan equation of state is used to extrapolate shear and bulk moduli to high pressure Chapter 3, page 231 for most of the minerals (except for the shear modulus of olivine and the bulk modulus of natural enstatite), this may introduce significant error i f the shear moduli should actually be extrapolated via a 4th order equation of state (e.g. Wall et al., 1993). While such error will have a slight affect i f the particular mineral only forms a small percentage by volume of the total composition, this type of error will, nevertheless, contribute to the misfit between the predicted and observed profiles. As in the previous chapter, where p and V0 profiles were modeled, I find by simple numerical experiments that the calculated Vs and Vp profiles are primarily sensitive to the properties of the olivine phases. This is not surprising since for a pyrolite composition, these phases dominate by volume the mineralogy of the upper mantle and transition zone (see figure 3.1). For example, adjusting the measured values for Mg-majorite within the experimental uncertainty has only a small affect on the calculated transition zone Vs and Vp profiles because this phase does not dominate the transition zone mineralogy. Likewise, the calculated upper mantle velocity profiles are largely insensitive to the temperature and pressure derivatives for the orthopyroxene and clinopyroxene phases, again reflecting their low volume abundance in the pyrolite mineralogy. Previous mineral physics studies have focused on the velocity increase across the 410 km seismic discontinuity as a discriminate between pyrolite and piclogite models (Bina and Wood, 1986; 1987; Duffy and Anderson, 1989; Gwanmesia et al., 1990; Rigden et al., 1991; 1992; Bina, 1993; Duffy et a l , 1995; Zha et al., 1997). Bina (1993) has pointed out that previous studies that focused on fitting the 410 km S-wave velocity jump predicted a significantly lower olivine content than i f the P-wave, or bulk sound velocity, or density jumps had been considered instead. Rather than using only a single velocity type as a Chapter 3, page 232 discriminant, Bina (1993) attempted to find a value for the unmeasured temperature derivative of the shear modulus, (du/srj of P-olivine that gave a consistent estimate of the mantle olivine content when all of the possible jumps across the 410 km discontinuity are considered. Because this parameter was the single unknown in calculating the jumps at this discontinuity, its value is of great interest. Consequently, the experimentally measured value, recently reported by L i et al. (1996) bears directly on the viability of the pyrolite model. Note, however, that the set of thermoelastic properties used here is an up-to-date compilation, and hence, it differs significantly from that used in previous studies (e.g. Duffy and Anderson, 1989; Bina, 1993). Consequently, the previous claims regarding the amount of olivine in the upper mantle for a particular value of the p-olivine [d\i/dT^ need to re-evaluated. This study adopts the value of L i et al. (1996) and uses the approach of Bina (1993) in checking for consistency between the predicted p, F 0 , V$, and Vp jumps across the 410 km discontinuity for the calculated pyrolite Vs and Vp profiles. I also test the predicted Vs and Vp profiles by calculating near vertical shear and compression reflection coefficients and compare these estimates against seismic observations (Revenaugh and Jordan, 1991; Revenaugh and Sipkin, 1994; Lees et al., 1983; Estabrook and Kind, 1996). The reflection coefficients across the phase transitions in the upper mantle and transition zone are dependent on both the density and velocity profiles of interest (i.e. Vs reflectivity combines the p and Vs profiles, while Vp reflectivity requires p and Vp profiles). Thus, calculating S- and P-wave reflection coefficients and comparing these against independent seismic observations is an additional test of the predicted Vs and Vp profiles. A n advantage of calculating near incident reflection coefficients is that observations exist for Chapter 3, page 233 the 410 km, 520 km and 660 km phase transitions. Thus, when considered together, these velocity jumps across the 520 and 660 km discontinuities (note that the velocity and density jumps across the 410 km discontinuity have little bearing on the properties of y-olivine, since this phase is only stable at depths greater than « 485 km). For example, by optimally fitting just the Vs jump across the 410 km seismic discontinuity (e.g. Duffy and Anderson, 1989) there is no guarantee that both of the resultant Vs and Vp profiles will satisfy both the S- and P-wave reflectivity constraints across the 520 km and 660 km seismic discontinuities. A further discriminant to test the predicted Vs and Vp profiles is the high seismic velocity gradients inferred in the transition zone (410 - 660 km depth) (Duffy and Anderson, 1989; Bass and Kanzaki, 1990; Gwanmesia et al., 1991; Ridgen et al., 1991; 1992). It is commonly ascribed that the high velocity gradients determined for this region reflect continuous phase changes that are spread out across this region, with either the pyroxene to majorite reaction, and/or the wadselyite to ringwoodite (P—>y olivine) phase transition, being cited as the reactions most likely to cause the steep gradients. As noted above, the magnitude of the jump calculated across the 410 km discontinuity is sensitive to the value of the temperature derivative of the P-olivine shear modulus. However, Ridgen et al. (1992) point out that since pressure nearly doubles across the transition zone (13 to 24 GPa), while temperature only increases slightly, the calculated velocity gradients are strongly controlled by the pressure derivative of the shear modulus, (dp./5P)7, and insensitive to the temperature derivatives across this interval. Fortuitously, (d\ijdP)T is experimentally observations place tighter constraints on the required value for the unmeasured temperature parameter directly affects the calculated Chapter 3, page 234 measured for both the P- and y-olivine phases, Mg-majorite, and almandine and pyrope garnet, and thus, a comparison between the transition zone velocity gradients for the predicted Vs and Vp profiles and those inferred in recent seismic models provides a direct and robust test of the predicted pyrolite profiles. I repeat that I am not attempting to use the observed Vs and Vp profiles to differentiate between the pyrolite and piclogite compositional models. Recent studies (Zha et al., 1996; Duffy et al., 1995) have concluded that the jumps across the 410 km seismic discontinuity are best fit by an olivine content between 44 % (for 5-waves) and 40 % (for P-waves), a range that is consistent with the Duffy and Anderson (1989) piclogite mineralogy (« 42% olivine), but far below that of a pyrolite mineralogy (« 62% olivine). Taken at face value, these conclusions contradict the result I found earlier in modeling density and bulk sound velocity profiles across the whole mantle; for these properties it is a pyrolite, but not a piclogite, mineralogy that best fits the seismic observations. To address this discrepancy, the question I pursue here is "can a pyrolite model satisfy the observational constraints of seismic F^and Vp profiles?". First, I compile an up-to-date set of thermoelastic properties for the mantle minerals that comprise the pyrolite mineralogy adopted here (Ita and Stixrude, 1992; 1993). Unlike previous attempts to model Vs and Vp profiles, which were forced to estimate many of the temperature and pressure derivatives, the recent advances in experimental design which allow high temperature and pressure measurement of velocities (e.g. L i et al., 1996a; b, c; Gwanmesia et al., 1996; Chen et al., 1997; Duffy et al., 1995; Zha et al., 1996; Zha et al., 1997; Abramson et al., 1997; Chai et al., 1997, 1998; Zaug et al., 1993) provide this study with many of the required derivatives. Second, I use the empirical high temperature Chapter 3, page 235 relationship of Isaak (1992) and the mineral systematics of Anderson (1988) to estimate initial values for the unmeasured temperature derivatives. These values were then adjusted, i f necessary, to optimize the fit between the predicted and observed velocity profiles. Next, the resulting properties are tested to check that they are mineralogically plausible. Lastly, the predicted V$ and Vp profiles are evaluated using a variety of criteria. Specifically, the predicted profiles are tested to see i f they can; 1) satisfy the absolute velocities and velocity gradients across the upper mantle and transition zone, 2) provide a mutually consistent estimate of the p, Vs, Vp, and V0 increase in seismic velocity at the 410 km discontinuity, 3) satisfy normal incidence shear wave reflectivity at the 410, 520, and 660 km discontinuities, and 4) satisfy normal incidence compression wave reflectivity at the 410 and 660 km discontinuities. The major conclusion in this study is that a pyrolite mineralogy provides an excellent fit to the observed Vs and Vp velocity profiles throughout the upper mantle and transition zone using a "mineralogically plausible" value for the unmeasured temperature derivative for the y-olivine phase. Thus, the discrepancy between our conclusions based on modeling density and bulk sound velocity, and conclusions of previous studies (e.g. Duffy and Anderson, 1989; Gwanmesia et al., 1990), based on V$ and Vp velocity profiles, simply reflects the use of inferred, rather than experimentally measured, values for the elastic properties of many of the minerals in those studies. The thermoelastic data base utilized here (and in the earlier chapter utilizing density and bulk sound velocity) is far more complete and reflects improvements in both properties that were measured and considered "known", and in properties that were not, and hence, had to be inferred. In addition, this expanded data base Chapter 3, page 236 of measured properties allows for greater confidence when using empirical systematics to infer unmeasured properties. 3.3 Methodology I calculate shear (Vs) and compression (V^) velocity profiles (where Vs = ^/u-/p and Vp = *J(K + %n)/p ) using third-order Birch-Murnaghan finite strain theory as discussed in detail by Bina and Helffrich (1992) and outlined briefly below. While this form of the equation of state is sufficient for the majority of mineral phases studied here, recent experimental data demonstrate that this should be extended to include 4th order terms for the pressure dependence for the olivine shear moduli (Abrahams et al., 1997) and the enstatite bulk moduli (Chai et al., 1998). A third-order Birch-Murnaghan equation of state is commonly used in extrapolating laboratory properties to the high temperature and pressure conditions of the mantle and has been used by nearly all previous studies that involved modeling Vs and Vp velocity profiles (e.g., Duffy and Anderson, 1989; Gwanmesia et al., 1990; Ridgen et a l , 1992; Bina, 1993; Duffy et al., 1995; Zhao and Anderson, 1994). 3.4 Thermoelastic data base The thermoelastic parameters and the respective data sources for the minerals are listed in Table 3.1, 3.2 and 3.3: in this study those parameters that were utilized in modeling density and bulk sound velocity [V0, Kp, [dKr/dT^ , {dKr/d, 87., y, and a(7)] are held fixed (tables 3.1 and 3.2) at the values used in the chapter two. Consequently, the "new" Chapter 3, page 237 elastic properties [\x, {d]x/dT^, (Su/spj^] introduced here to calculate Vs and Vp velocity are listed in table 3.3. Tables 3.A1...3.A15 in the appendix list the elastic data for each mineral and allows an easy comparison between the adopted values used here and experimental values reported in the literature. Table 3.1. Summary of constants for the coefficient of thermal expansion used in calculations. Mineral Formula thermal expansion coefficients a(T) = a0+a]T+a3T~2, or a(r) = a 0+a,r+a 2r"' +a3T~2 a 0 a 2 a 3 Forsterite1 Mg 2 Si0 4 2.77 x 10° 0.97 x 10"° -0.32 Fayalite2 Fe 2Si0 4 0.5673 x 10"* 0.0163 x 10"' -0.2517 x 10"^ -1.6133 Enstatite3 OPX M g 2 S i 2 0 6 2.86 x 10° 0.72 x 10"8 Diopside5 C P X CaMgSi 2 0 6 0.3206 x 10"* 0.0811 x 10"' 0.1347 x 10"^ -1.8167 Hedenbergite6 C P X CaFeSi 20 6 2.383 x 10° 9.07 x lO"" Pyrope7 M g 3 A l 2 S i 3 0 1 2 0.0991 x 10"4 0.1165x 10"' 1.0624 x 10"2 -2.5 Almandine8 Fe 3 Al 2 Si 3 0 1 2 0.1776 x 10-4 1.2140 x 10-8 -0.5071 Grossular9 C a 3 A l 2 S i 3 0 1 2 2.649 x 10° 3.066 x 10"7 -0.6605 Mg-Majorite1 0 M g 4 S i 4 0 1 2 Fe-Majorite11 Fe 4 Si 4 0 1 2 Ca-Majorite12 C a 4 S i 4 0 i 2 Mg-Wadselytie13 Mg 2Si0 4 0.2711 x 10"4 0.6885 x 10"° -0.5767 Fe-Wadselyite14 Fe2Si04 0.2319 x 10"4 0.7117 x 10"6 -0.2430 Mg-Ringwoodite1 5 Mg 2Si0 4 0.1872 x 10"* 0.4210 x 10"° -0.6537 Fe-Ringwoodite16 Fe2Si04 0.2455 x 10"* 0.3591 x 10"s -0.3703 Mg-Fe perovskite17 MgSi03 1.982 x 10-5 0.818( +0.257) xlO-9 -0.4740 ±0.118 perovskite this stud 1.982 x 10-5 0.918 x 10"9 -0.4740 Ca-perovskite18 CaSi03 3.06 x 10"J i- Q magnesiowustite19 (Mg,Fe)0 3.768 x10" J 7.404 x 10"" -0.7446 Chapter 3, page 238 1, Gillet et al., 1991; 2, Fei etal., 1992, equation 10, p. 419; 3, Zhao et al., 1995; 5, Saxena and Shen, 1992; 6, fit to Cameron et al., 1973; 7, Saxena and Shen, 1994; 8, Fei, 1995; 9, fit to Issak et al., 1992; 10, assumed equal to pyrope garnet following Yusa et al., (1993). Chopelas (1999) report a room temperature value of 2.0 x 10~5 K " l derived from the calculated heat capacity inferred from her Raman spectroscopy measurements of majorite (see Chopelas (1996) for details of deriving a from Raman spectra); 11, assumed equal to almandine garnet; 12, assumed equal to grossular garnet; 13, Fei et al., 1992; 14, Fei et al., 1991; 15, Meng et al., 1994; 16, Fei et al., 1991; 17, Funamori et al., 1996, note I slightly adjusted the coefficient oq within the stated experimental errors by 0.100. This is shown in the row directly below; 18, Wang et al., 1996, I use the empirical relationship of O . L . Anderson et al., 1992 to extrapolate this value to high temperatures (their eq # 31): ( a ( r ) / a r > e ) = l/ '^l + a 7. > e8 7,(7 ,-7^)j, where 0 is the Debye temperature for Ca-perovskite (Tg = 1100 K ) , S T is the Anderson-Gruneisen parameter which for Ca-perovskite 8j = 4.65. O . L . Anderson et al. (1992) apply this to Mg-perovskite due to the paucity of high temperature thermal expansion data for that mineral; 19, Fei 1995. 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O O N t > cn cn CD +-> o "cc? a cd IU m m o •xi-00 |vo C N CD 00 00 1" cd CD IX, in -XT vq O N cn CD H—» bO 00 in vo o C N TI-TS o o £ , bp I fl 2 CD m r-x •xf C N lz? ^ | P H 00 1-IP o Pi I o CN bo cd OH H—> .fl U cd 3*3 13 on, 13 +-» ers 1) d ' > cd is An • o An O N Pi 13 g O N cn r calcul > am cd 13 opside; r calcul o g '8 opside; CD fl -*-» <D opside; G O cn Id S © £ cd Co cd .2 cd —i cd T3 T3 >-< U fl S fl bfi „ w 5 * cd ^ vo • o t~- -!-> >0 _ ON . c d O N O N cr 25 u ^ - <u r H "3 CO" ^ CN 0) bo cd S-I -+-» U fl o • l-H o r - H cd o -a CO ii cd - f l OH I-I <8 a, P ft, ro ro ^1 ro 3. ro cd td -a <+-H ro ro CO j d 3 fl -o o a -fl CO C+H O & a a cd CD fl ° cS o ho o co o o CM 00 r-vo o oo CN CN O CN O o 00 2 V © ON ca cn r-o o o CN 5 CN C O O o CO CM <N O C O O O CO CM ho O o o CM r O CN 00 ho «*i o C O © oo ON o V O o © 00 co V O -a ci 00 I fN CN O o C N C N o o o o VO o O N O o o in o o vo vo o VO O OO o O N IS? o O N 00 o © V O <o o o ho o r-O N CN CN © in |od O N CN o o o 00 CN o © O N 00 ca >n oo C N K. oo O © oo o o o in oo o © oo cd CO G ii 3 I-I 1 CO OH o 1) H—» '5b I-I OH O OH CD fl 1 cd S3 3 CO CO O 00 o 'cd > a 00 D TH-» o 'cd^ a • u fa CD H-» • rH I-I o "cd* CD CD 00 ,3 fa o 00 c 00 CO o o O N -t-> I "3 o I , 00 fl f? CD fa o C O 0 > o 1-1 v , OH I CD Ifa 00 CO m O N f*i f N O o Cv CNJ Ca Ca cs "1 ho o vo CN O © CO i O in r-i C O in 00 > o l-H <D O H cd o CO a CN T r CN <D &0 c3 OH cn •~ <D -+-» & u Chapter 3, page 243 In general, I have utilized the most up-to-date values for the various thermoelastic parameters and i f these parameters were adjusted slightly, the final value was still kept within the reported experimental error. Following convention (e.g. Bina and Helffrich, 1992) the elastic properties of a phase are estimated by averaging on the mole fraction of the end member phases assuming ideal mixing. When experimental constraints are unavailable, I follow Ita and Stixrude (1992) and estimate the unknown shear moduli using velocity-density systematics: where f4.0re / i s the known shear modulus of the reference mineral, V0lt[ is its molar volume and the \x and Vo are the unknown shear modulus and molar volume, respectively. As stated earlier, modeling Vs and Vp velocity profiles has been hindered by the absence of measured properties, principally the temperature and pressure derivatives of the shear and bulk moduli. This forced previous workers to estimate values for these properties (Bina and Wood, 1987; Irifune, 1987; Duffy and Anderson, 1989). To highlight the number of parameters that had to be estimated in previous studies, I show the bulk of the elastic data table used by Duffy and Anderson (1989) in table 3.4. I have not included the elastic properties for jadeite (NaAlSi 20 6), corundum (A1 20 3), stishovite (Si0 2), ilmenite (Mg,Fe)Si0 3, or Na-majorite (Na 2 Al 2 Si 4 0 ] 2 ) since these minerals do not occur within the "normal" mantle temperature and pressure conditions for a pyrolite bulk composition which I adopt from Ita and Stixrude (1992; 1993) - indeed corundum, stishovite, and ilmenite will not occur as distinct mantle phases in a piclogite mineralogy either so it is not clear why Duffy and Anderson (1989) included them. I have shaded the entries in this table to highlight those Chapter 3, page 244 properties that were estimated by Duffy and Anderson (1989) using the mineral systematic framework of Anderson (1988), and it is clear from a casual inspection of this table, that nearly all the mineral phases used in this study, were being to corrected to high temperature and pressure using estimated temperature and pressure derivatives. This situation is not changed if I include jadeite, corundum, stishovite, ilmenite, or Na-majorite in this table, since, with the exception of corundum, these other minerals also had numerous unmeasured properties. Furthermore, the measured values which are highlighted in bold font have now been superseded by subsequent experimental studies. Thus, virtually all of the bulk and shear moduli values have undergone refinement. In contrast, compare the Duffy and Anderson (1989) table with the summary table of the elastic data used here (table 3.5), also highlighted to show the unmeasured properties. Inspite of containing many more mineral phases, it is clear from just a cursory inspection of this table, that many of the unknown properties are now experimentally measured; consequently, the modeling undertaken here is far more robust than prior studies. For instance, Duffy and Anderson (1989) argued that the bulk moduli of the a-, (3- and y-olivine phases show no affect of iron substitution, and hence it was assumed that a single bulk modulus characterized these phases. This assumption is not supported by current experimental measurements, and thus, the Mg and Fe end members for the olivine phases are considered as separate phases here. I comment further on specific differences below. •n CN CD 0 0 OH C O Ul CD H-» u c3 T3 ON oo ON fl O oo !-i CD T3 T 3 3 CD XI H C O \1 a. & I-I o CO CO Anderson-Graneisen Parameter -4.63 -4.44 -4.48 -5.03 -4.57 lililllllll >r, O • r i -4.07 -4.81 -4.70 -3.71 -3.10 -3.42 ft, P w <u U CD i-i TO rd g.x f £ CO o o o 1 o l - H o © 1 «n i - H O © O i — i O ' <n ' O , i T i -er; o o i oo CN - '© '©' . CO r i ©' fN O O i a. P CO CO CD u m g . £ <£ VO o © 1 -© 1 ";•>'© • ro r —i O 1 o l - H CN o © o vo l - H o 1 CN p i ^—v oo 1 © r--o o • © " " ro © © © r 1 © o © VO l - H o © & CO fl. 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(1992) and the pure Mg-end member. For y-olivine there is a great deal of scatter for iron bearing samples. While the value for the hypothetical pure Fe end member is in general agreement with previous estimates, the exact value is poorly constrained (hypothetical in the case that a natural, pure Fe end member does not exist). Nevertheless, this has a secondary affect on the modeling, since the olivine phases considered have compositions of « (Mg 0 8 8 Fe 0 1 2 ) 2 Si0 4 and hence are largely dominated by the Mg end member. In terms of the shear modulus, I used the recently reported value for iron bearing p-olivine of Sinogeikin et al. (1996) along with the value for the pure Mg end member to determine a linear fit which predicts the hypothetical pure Fe end member (figure 3.2) which results in values slightly lower than that inferred by Duffy and Anderson (1989). For y-olivine I adopt the values measured by Weidner et a l , (1984) for the pure Mg end member and Ridgen and Jackson (1991) for the corresponding pure Fe end member phases. 3.6 Majorite phases Duffy and Anderson (1989) estimated the bulk modulus of Mg- and Ca-majorite via the empirical relationship based on elasticity systematics for garnets (Bass, 1986): atomic weight (molecular weight/number of atoms in the molecule). This gave predicted where F 0 is the bulk sound velocity mean Chapter 3, page 248 values of Ks= 177 ± 1 3 GPa and K$= 165 GPa for the Mg- and Ca- end members. To obtain an estimate for the shear modulus, they invoked another empirical relationship: Vp V M = constant where Vp is the compression velocity. By backing out a predicted Ks from the first empirical relationship, they could then use second relationship to estimate the shear modulus in the Vp term (recall Vp = —'•——— ) and they obtained estimates of p. = 99 ± 28 GPa and p. = 91 ± V P 21 GPa for the Mg- and Ca-majorite phases. They noted that i f only Ca-rich garnets are considered, then the predicted value for Ca-majorite is 105 GPa. It is unclear how they predict the affects of iron, because while they state that in their modeling, majorite is considered to have 10 mole Fe, and their tabulated entry indicates that both the bulk and shear moduli vary with iron content, no explanation was given as to how the particular relationship was derived. Their values are compiled below in table 3.6. Table 3.6. Comparison of majorite elastic data from Duffy and Anderson (1989) and this study. Majori te Kp ( £ £ ) D & A 1 9 8 9 Kp this study pD&A1989 p this study M g 4 S i 4 0 1 2 174.23 (175) 160 90 89 Fe 4 Si 4 0 1 2 174.33 (175.1) 177.71 90.8 79.5 Ca 4 Si 4 0 1 2 * (165) 129.12 104 112.24 *note that Duffy and Anderson (1989) define Ca-majorite as C a 2 M g 2 S i 4 0 ] 2 which differs from what I adopt following Ita and Stixrude (1992; 1993). In contrast, this study uses values for the isothermal bulk and shear moduli based on direct experimental measurements for Mg-majorite (Pacalo and Weidner (1997); Sinogeikin Chapter 3, page 249 et a l , 1997), and estimates the affect of Fe on the molar volume and bulk and shear moduli by a simple linear fits between the pure Mg-end member and Fe-bearing majorites. Specifically, for the change in molar volume (and hence, density), I fit the experimentally observed unit cell volumes for Fe-bearing majorites listed in Ohtani et al. (1991) and Sinogeikin et al. (1996) and for pure Mg-majorite given by Pacalo and Weidner (1997), Sinogeikin et al. (1997), and Yagi et al. (1992) (see figure 3.3). This gives a predicted unit cell volume for the pure Fe-majorite of 1575 A 3 , which translates to a molar volume of 118.59 cmVmole and a density of 4.449 g/mole. To account for the affects of Fe on the bulk and shear moduli I performed a linear fit to the experimentally determined bulk (figure 3.4) and shear (figure 3.5) moduli for the Fe bearing majorite recently reported by Sinogeikin et al. (1996) with the values used here for the pure Mg end member majorite. This resulted in a predicted values of Ks = 179.04 GPa {Kf = 177.71 GPa) and p = 79.5 GPa (where the predicted Kpvvas converted from the predicted adiabatic value via Ks = KT(l + a y T) with the coefficient of thermal expansion being that of almandine garnet, the Gruneisen parameter = 1.20, the value for the Mg-end member, and temperature T = 298K). For Ca-majorite this study utilizes the measured molar volume and relative compressibility for a calcium bearing majorite of composition (Ca 0 4 9 Mg 3 5 1 )S i 4 0, 2 ) determined by Hazen et al., (1994a, b) with the properties of the pure Mg-majorite end member to estimate the molar volume and isothermal bulk modulus of the pure Ca-majorite phase (Ca 4Si 40 1 2). This is consistent with the convention of Ita and Stixrude (1992; 1993) but differs from that adopted by Duffy and Anderson (1989) who define Ca-majorite as (Ca 2 Mg 2 Si 4 0 1 2 ) . The linear fits for molar volume and density are shown in figure 3.6 and 3.7, Chapter 3, page 250 respectively. The adopted isothermal bulk modulus for (Ca a 4 9 Mg 3 i 5 1 )Si 4 0, 2 ) differs from that tabulated by Hazen et al. (1994b). The experimental technique they used was to determine relative compressibilities by preparing a mount with several crystals in it. This allows the small differences in compressibility to be determined in compositionally similar suites of samples - hence, they loaded a pure Mg-majorite along with the Ca-bearing majorite. They note that the relative differences are well resolved, but that absolute compressibility may be in error by several percent. In fitting their unit cell data with a Birch-Murnaghan EOS, they fixed the pressure derivative [dKs/d P J = 4.0 and allowed the values of KJQ and VQ to vary. This resulted in KJQ = 169.3 ±3 .4 GPa and 164.8 ± 2.3 GPa for Mg-and Ca-majorite phases respectively. Because the derived Mg-majorite KJQ value is significantly larger than the value determined by Brillouin spectroscopy (Pacalo and Weidner (1997) and adopted here, I simply infer on the basis of the relative compressibility between Hazen et al. samples (Ca-bearing majorite KJQ is 2.65% lower than the pure Mg end member) that the Ca-bearing majorite should be KJQ = 155.74 GPa relative to the KJQ =160 GPa for the pure Mg-majorite phase. Alternatively, i f I use the simple relationship advocated by Ita and Stixrude (1992; 1993) to predict the isothermal bulk modulus of the Ca-bearing majorite: V K =V K where, in this case, VQ and Kj are the molar volume and isothermal bulk modulus of the Ca-bearing majorite, and VQref and Kjref are the molar volume and isothermal bulk modulus of the pure Mg-majorite I Kj = 156.70 GPa, a value indistinguishable from that estimated above. Consequently, the linear fit between the bulk moduli of the Ca-bearing majorite of Hazen et al. (1994a) and the pure Mg-majorite of Pacalo and Weidner (1997) uses KJQ = Chapter 3, page 251 156.22 GPa (the arithmetic average of the two estimates) and 160 GPa for the (Ca 0 4 9 Mg 3 5 1 )S i 4 0 1 2 ) and M g 4 S i 4 0 1 2 phases respectively. This is shown in figure 3.8 and predicts a KJQ = 129.14 GPa for the pure Ca-majorite phase (Ca 4Si 40 1 2) and KJQ = 144.57 GPa for an calcium bearing Ca-majorite (Ca 2 Mg 2 Si 4 0 1 2 ) as defined by Duffy and Anderson (1989). Unfortunately, there are, at present, no measurements for the shear modulus for a Ca-bearing majorite and hence, this property must be estimated (rather than extrapolated from the Mg end member). Using the mineral systematic relationship used by Duffy and Anderson (1989) to estimate this property for Ca-majorite, V,, V M = constant = 43.23, I obtain p = 112.24 GPa. 3.7 Orthopyroxene I initially followed Ita and Stixrude (1992; 1993) in modeling orthopyroxene as a mixture of only the iron and magnesium end members. Recent experimental work on natural samples containing Ca + 2 and A f 3 have demonstrated that even substitution of small amounts of either element causes the isothermal bulk modulus to increase significantly as compared to KJQ of pure end member phases (Hugh-Jones and Angel, 1998; Chai et al., 1998). Consequently, I adopt the values for Kj, (dKT/8P)r , p and | (3p /5PJ derived from fitting a 4th order equation of state to acoustic compression experimental data that extended to pressures up to 12.5 GPa on a natural sample Chai et al., (1998) rather than approximate orthopyroxene by a mixture of pure end members. This sample's composition is: (Mg 1. 63Fe 0. 1 7Ca 0. 0 4Mn 0. 0 1)(Al 0. 1 2Cr 0. 0 1)(Si 1. 8 9Al 0. 1 1)O 6. Chapter 3, page 252 which is only slightly greater in aluminum content than that studied by Hugh-Jones and Angel, (1998); (Mg1.66Fe0.24Ca0012Al0.08)(Si194Al0 06)O6 The motivation for adopting the results of Chai et al. (1998) over that of Hugh-Jones and Angel (1998) is that Chai et al., (1998) provide the shear modulus and its pressure derivative in addition to Kj , (dKr/dP)r, and (d2KT/dP2^ while the experimental technique of Hugh-Jones and Angel (1998) results in only the isothermal bulk modulus and its pressure derivative. Thus, I adopted the Chai et al. (1998) results simply because it provides a greater number of self-consistent elastic properties. Note that Chai et al. (1998) found that the bulk modulus must be fit by to a fourth order Birch-Murnaghan equation of state while the shear moduli could be fit by a 3rd order equation of state. Thus, like olivine (Abramson et al., 1997) I extend from 3 to 4, the number of terms in the Birch-Murnaghan equation of state to accommodate their results. Note too that it is now accepted that virtually all orthopyroxenes near the Mg-end member exhibit anomalously high values for (dKr/dP)r « 9-12, with respect to other mantle silicates (e.g. (dKT/dP) « 4.0 ± 1 ) (Hugh-Jones and Angel, 1998). By contrast, Duffy and Anderson (1989) elected to ignore the experimentally determined temperature and pressure derivatives of Frisillo and Barsch (1972; Kj = 102.5 GPa, [dKT/8P)r = 9.47 which are similar to those determined by Hugh-Jones and Angel (1998) and Chai et al., (1998)), and instead, estimated them via the {DLA} mineral systematics of Anderson (1988). 3.8 Perovskites Chapter 3, page 253 Duffy and Anderson (1989) adopted the isothermal bulk modulus for Mg-perovskite from Knittle and Jeanloz (1987; Ks = 266 GPa) and estimated the shear modulus via the empirical mineral systematic relationship of Bass (1984) based on perovskite analogue compounds: where M is the mean atomic weight (the molecular weight divided by the number of atoms in the molecule), and Vp is the compression velocity. This relationship predicted a shear modulus of p. = 153 GPa whereas the experimentally measured value is 177.3 GPa (Yeganeh-Haeri, 1994). For Ca-perovskite, both the bulk and shear moduli were adopted from Bass (1984) who estimated Ks via: and then by combining Ks with VP\M = 47.0± 1.4 to estimate p.. This gave Ks = 227 GPa; \x = 125 GPa for Ca-perovskite. However, as noted above, the measured shear modulus for Mg-perovskite exceeds that predicted on the basis of the above empirical equations. Specifically, adopting the measured properties for pure Mg-perovskite (M = 20.08, Ks = 261.5 GPa, (a = 177.3, p = 4.108 g/cm3), the empirical relationship predicts a value for the constant of: which is slightly above that based only on the 12 analogue perovskite compounds (47.0 ± 1.4). If I assume that the Mg-perovskite value for the empirical "constant" applies to Ca-V M = 49.333 Chapter 3, page 254 perovskite, I may use it to estimate the unmeasured shear modulus. Thus, for Ca-perovskite the measured properties are M = 23.23, Ks = 232 GPa, p = 4.231 g/cm3 (Wang et al., 1996), and result in a predicted shear modulus of p = 158.4 GPa. Alternatively, I may use the relationship advocated by Ita and Stixrude (1992; 1993) to predict the unmeasured shear modulus: where, in this case, Vo and p are the molar volume and shear modulus of Ca-perovskite, and Voref and Pre/ are m e molar volume and shear modulus of Mg-perovskite. This simple relationship predicts p. = 157.9 GPa, in excellent agreement with the previous estimate. Here I simply adopt 159.0 GPa, a value very near the arithmetic average of the two predictions (p = 158.1 GPa). Note that both of the estimates are significantly greater than the values estimated by Bass (1984) and subsequently adopted by Duffy and Anderson (1989). The difference reflects 1) the density of Ca-perovskite is now well known (p = 4.231 g/cm3) and is significantly greater than the value adopted by Bass (1984; p = 4.13 g/cm3), and 2) the measured elastic properties (Ks and p) of Mg-perovskite are now known with confidence (Yeganeh-Haeri, 1994). Consequently, Mg-perovskite provides a complete set of reference values for a silicate perovskite (as opposed to analogue perovskites) with which to base predictions on for the Ca-perovskite phase. 3.9 Temperature and Pressure derivatives The temperature and pressure derivatives of the elastic properties are central to any modeling study of shear and compression velocities in the mantle. As I note earlier by Chapter 3, page 255 comparing the Duffy and Anderson (1989) data table with the one used here, there has been significant improvement in the number of measured derivatives. Indeed, the pressure and temperature derivatives for the bulk modulus are measured for virtually every major mineral phase in a pyrolite mantle. While there still exists some unmeasured phases, these omissions are no longer critical since the properties are now measured the Mg-end members. For instance are not measured for pure Fe-majorite, but they have been measured up to 7 GPa and 1000 °K on the pure Mg-majorite phase (Granmesia et al., 1996) and since it is commonly accepted that the likely composition of the majorite phase in the mantle will be on the order of « (Mg 0 8 8 Fe 0 1 2 ) 4 Si 4 0 1 2 (Ita and Stixrude, 1992; 1993) the properties of the Mg-end member are the key properties that will largely control the elastic properties. As noted by Duffy and Anderson (1989) and Jeanloz and Hazen (1991) the pressure derivative of the bulk modulus exhibits little variation (with the exception of orthopyroxene, which is now accepted to have an unusually high pressure derivative) with most minerals of interest lying within the bounds of 2 <(dKT/8P)r < 6. Consequently, the assumption made here, that the unmeasured bulk modulus pressure derivative of Ca-majorite has a [dKT/dP^ equal to that measured for grossular, is relatively unimportant to the velocity profiles calculated. The profiles are also insensitive to the particular value because Ca-majorite only comprises a very small component by volume of a pyrolite mineralogy. Likewise, I simply assume that the Fe-majorite has pressure and temperature derivatives equal to the measured values of Mg-majorite - an assumption that may be incorrect, but I contend, will have little affect on the calculated velocities. For example, compare the variability between the measured temperature and pressure derivatives of Chapter 3, page 256 pyrope and almandine garnet. While the values do differ, between the Mg and Fe end member garnets, the differences are modest and I contend, that a similar magnitude in the variability in the derivatives is to be expected for the majorite phases (which are known to form solid solution with garnets). On the other hand, the particular values for [dKT/dT^ and [d KT/dfor the a-, P- and y-olivine phases are of great importance, since these phases dominate the pyrolite mineralogy. To emphasize both the increase in the number of experimentally measured properties and the relatively large variability in the values used in prior studies, I compile in table 3.7 the temperature and pressure derivatives of the bulk and shear moduli for the Mg-olivine phases from recent studies that have modeled the upper mantle and transition zone velocity. As before when I listed tabulated properties, those entries that are estimated, rather than based on experimental measurements, are listed in shaded cells. In contrast, those parameters that are based on measured values are highlighted in bold font. It is clear from this table that the only parameter I need to estimate is the temperature derivative of the shear modulus for y-olivine [d [i/dT j ; all the other properties for the a-, P-, and y-olivine phases have now been measured, a fortuitous situation that it is stark contrast to that faced by previous workers. fl o CD co CD 00 cd C H CD £3 O 00 © rr © © © © © © o © © o PH O ON © © t -© © © vo © © © © VO VO © © o CN CN O r n CN © he K M 1*1-N *+ vo CN © CD 42 A T 3 O !H W 3 i n « g T 3 P H I 4^ ° 3 -2 -S 4 T 1 a oo ™ CD on Cd CD > fl "G ° CD N ^ fl CD 2 fl s 00 fl CD cd T 3 CD cd CD I ^ . 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To obtain initial estimates for the unmeasured temperature derivative I use the empirical relationship between Y , 8T, and {pKT/dP)T observed at high temperature (Isaak, 1992). He found that at a temperature above the Debye temperature, the following approximation was valid: r * 8T*(dKr/dP)r where (dKT/dP)r is the pressure derivative of the isothermal bulk modulus at ambient conditions, 6X is the Anderson-Gruneisen parameter defined as: ( 1 ^ fdK,A \<xKTJ { dTj and r is analogous to the isothermal Anderson-Gruneisen parameter, but defined in terms of the shear moduli: r = - r i ] d p {a(T)ii(T)J [dTj The empirical approximation T « 8X « (dKT/dP) is relevant here because it indicates that estimates for the high temperature value of the temperature derivative of the shear moduli 5p/<9rj may be obtained from the pressure derivative of the isothermal bulk modulus dKj/dP^ . Isaak (1992) found from experimental measurements that at high temperatures, both T and 8T approach, and are approximately equal, to the value of the pressure derivative {dKr/dP)T, which in turn, allows an estimate of the unmeasured Chapter 3, page 259 ( d n / d r ) by assuming T « (dKT/dP)T in the thermodynamic relationship below (Isaak 1992; his equation 16): P(T) P(To). where To refers to room temperature conditions. This expression is first used to obtain a high temperature estimate for the shear modulus, p(7) from the room temperature value using the density ratio and (dKT/8P)r. p(7) is then used, along with a high temperature value of the coefficient of thermal expansion, oc(7) to estimate a value for (<9 p/<3 r ] via: r = -r i i => p { 1 ] \ o p U(r>p(rJ [dTj { dP) T U(r)p(r)J [dTj or rearranging: KdTJp •a(T)n(T) V dP j Isaak (1992) utilized the above relationships to calculate \(d\i/df)p | for the p-olivine phase under the assumption that the approximation T « 5 X « (dKr/dP) is valid for this phase, as it is for oc-olivine. Since our elastic data is slightly different from that used by Isaak d\i/dT (1992) I re-evaluate |( 8 p / 5 T) \ for p-olivine, and also perform the same calculation for y-olivine. Because L i et al. (1996) have recently reported an experimental measured value for |(3p/(3rj for P-olivine, this allows us the opportunity to test the validity of the above approximation. Chapter 3, page 260 For the Mg end member of p-olivine, (dKT/dP)T = 4.3 (Zha et al., 1996, 4.3 ± 0.2), and the room temperature and high temperature (T = 1600 K) densities are p 2 9 g = 3.490 g/cm3 and p(T) = 3.346 g/cm3 where the density is calculated with a room temperature molar volume of 40.313 cmVmole and the coefficient of thermal expansion given by Fei et al., (1992) and listed in table 3.2, was used to correct the molar volume up to high temperature. Combining these parameters with a shear modulus of p298 = 1 13 GPa (Li et al., 1996c), results in a predicted high temperature shear modulus of p 1 6 0 0 = 94.24 GPa. For a temperature of 1600 K, the coefficient of thermal expansion is 3.79 x 10"5 K which taken with p 1 6 0 0 and (dKr/dP)T results in a predicted value of (dp/<37J^= - 0.0154 GPa/K. Isaak (1992) notes that on the basis of direct observations this prediction tends to underestimate the true value for olivine by « 0.0008 GPa/K even when T is exactly equal to (dKT/dP) . Consequently, a "corrected" predicted value is ^d\x/dT^ = - 0.0162 GPa/K. This compares favorably to the experimentally measured value of L i et a l , (1996) of | d \x/d r j = - 0.016 GPa/K. Turning to the Mg end member of y-olivine (dKr/dP) = 5.0 (Ridgen et al., 1991; 1992), and the room temperature and high temperature (T = 1800 K) densities are p 2 9 8 = 3.548 g/cm3 and p(T) = 3.421 g/cm3 where the density is calculated with a room temperature molar volume of 39.645 cmVmole and the coefficient of thermal expansion of Meng et al., (1994) and listed in table 3.2. Combining these parameters with a shear modulus of p 2 9 8 = 119 GPa (Weidner et al., 1984), results in a predicted high temperature shear modulus of p, 8 0 0 = 99.11 GPa. For a temperature of 1800 K, the coefficient of thermal expansion is 2.601 x 10" Chapter 3, page 261 5 K which taken with p 1 6 0 0 and (dKr/dP)r results in a predicted value of |f3p/drj = -0.0129 GPa/K. Again applying 0.0008 GPa/K to correct for underestimation results in a "corrected" predicted value of \d \i/d 71) = - 0.0137 GPa/K. Alternatively, Anderson (1988), on the basis of a compilation of a large number of measurements on compounds, has argued that mineral systematics exist which allow the prediction of the pressure and temperature derivatives. Of interest here is the predicted values for {G} P that he lists in his table 7. This parameter is equal to T in the {DLA} notation of Anderson (1988) and Duffy and Anderson (1989); {G}P=T = -( 1 \ U ( 7 W ) J [dTJ He notes that the average value for the measured silicates resulted in {G} P = 5.4 ± 1.2 and that the mean of olivine was 6.4. On the basis of the similarity between the crystal properties of y - p - and a-olivine, he predicted {G} P = 6.4 for the p-olivine, and {G} P = 6.5 for y-olivine. These values, when combined with the high temperature values for the coefficient of thermal expansion and shear moduli determined above, result in predicted temperature derivatives of (d\i/dT)p = - 0.022 GPa/K for p-olivine and (d\i/dT)p = - 0.0168 GPa/K for y-olivine. While the {DLA} predicted value for y-olivine is in reasonable agreement with the predicted value using the Isaak (1992) empirical relationship, the {DLA} prediction for P-olivine is not, and in addition, is not in agreement with the experimentally measured value of (Sn/dr), = -0.016 GPa/K. Duffy and Anderson (1989) used the {DLA} systematics to predict (d[i/dT)p and derived values for P-olivine (-0.014 GPa/K) and y-olivine (-0.014 GPa/K) that were similar to that of olivine (-0.013 GPa/K) and argued that this was to be Chapter 3, page 262 expected on the basis of the similarity in crystal structure for these 3 phases. The difference between their estimated values and those here is unclear, but may reflect both the use of different thermoelastic data and/or our use of high temperature estimates for the coefficient of thermal expansion and shear modulus, following the recommendation of Isaak (1992). For this study, I simply adopted the value estimated via the Isaak (1992) method for (Sp /dr) , , and then adjusted it to give a better fit to the seismic profiles. Specifically, the criteria that was adopted was that the predicted velocity profiles resulted in a good agreement between the predicted and observed 520 and 660 km shear wave reflection coefficients. The required adjustment was small (e.g. with the value increasing from - 0.0137 G P a / K to -0.0170 GPa/K) . The later value, while higher than the value adopted by Duffy and Anderson (1989), is consistent with the predicted { D L A } parameter given by Anderson (1988, { G } P = 6.5 for y-olivine) when it is combined with the high temperature estimates of a and p determined here. While the pressure derivative (5p/c3P) 7. is experimental measured for y-olivine ((d[i/8P)r =1.73), the experiments cover only a relatively small pressure range of 0-3 GPa (Ridgen et al., 1991; 1992). O f interest is that Zha et al., (1996) and L i et al. (1996) have found from their experiments, which span a much greater pressure range (to 14 GPa), that the resulting values for the pressure derivative (d[i/dP)r o f P-olivine are lower (1.4 ± 0.2) than the values reported earlier determined over the 3 GPa pressure range ((d]x/dP)T = 1.74 -1.90; Ridgen et al., 1992 Gwanmesia et al., 1990). Zha et al. (1997) suggested that this difference may be due to some remaining porosity in the polycrystalline samples used by Ridgen and coworkers. I assume a similar relationship exists for y-olivine, such that the Chapter 3, page 263 reported value of (d[i/dP)T = 1.73 of Ridgen et al. (1992) is slightly too high (by roughly 14%). Correcting the y-olivine value of Ridgen et al. (1991; 1992) downwards leads to a preferred value of (d[i/8P)T = 1.46 which is used here (y-olivine is presently being subjected to the high pressure ultrasonic analysis that L i et al., (1996) applied to P-olivine (Weidner, personal communication). Lastly, I also calculate high temperature estimates for the temperature derivative (8[i/dT)p for diopside and hedenbergite within the framework of Isaak (1992) described above. The resulting estimates give, for diopside (d[i/8T)p = -0.0118 GPa/K, while for hedenbergite, (d[i/8T)p = -0.0096 GPa/K. These values are similar to that inferred by Duffy and Anderson (1989) where it was assumed that all clinopyroxenes had the same value of (8\X./8T)P = -0.010 GPa/K. The predicted values for perovskites are discussed in chapter 4 and 5. 3.10 Mineralogically plausible values for (5 p/5 P)T and (8 p/5 T)p Lastly, to obtain an inference on whether or not the estimated value for y-olivine is mineralogically plausible, I calculate the {DLA} parameter {G} T which Anderson (1988) define as: J [dP) For p-olivine, all the required parameters are measured (Kr = 171.5 GPa, p = 113.0 GPa, (d\x/8P)T = 1.40) and give a calculated value of {G} T = 2.12. When this is combined with the inference for {G} P = T « {dKT/8P)T = 4.3 of Isaak (1992), the ratio {G}T/{G}P = 0.49. Chapter 3, page 264 This value is in good agreement with the values tabulated by Anderson (1988) for silicates (mean) = 0.55, olivine (mean) = 0.45, and total mean for the complete Sumino and Anderson (1984) data base = 0.44. Alternatively, i f the Anderson (1988) estimate for { G } P = 6.4 is used, the resulting ratio {G}T/{G}P =0.33. For y-olivine, the calculated value for { G } T for the parameters used here {Kj = 182.6 GPa, p = 118, (d\i/dP)r = 1.46) is 2.25. When this is combined with the Isaak (1992) approximation for {G} P = F&(dKT/dP)T = 5.0, the resulting value for the ratio {G}R/{G}P = 0.45, which is comparable to a value of {G}R/{G}P = 0.40 i f the predicted value of { G } P = 6.5 of Anderson (1988) is adopted. These various permutations are tabulated below (table 3.8) and it is evident that measured values for p-and y-olivine result in values that are consistent with other silicates (0.55) and the mean value from the total D L A database (0.44). This contrasts with the calculated ratio when the Anderson (1988) values for { G } P are used to predict this ratio; the resulting {G}R/{G}P values of 0.75 and 0.77 for P-and y-olivine respectively, appear to be too high relative to the mean value for silicates (0.55). Inspection of table 3.8 reveals that the major discrepancy between the values inferred by Anderson (1988) and those calculated here appears to be {G} T . Anderson (1988) and Duffy and Anderson (1989) were critical of the choices for the unmeasured temperature and pressure derivatives for the p-and y-olivine phases adopted in previous studies. Specifically, it was argued that the temperature derivatives (d[i/8T)p used by Bina and Wood (1987) were too high, while the pressure derivatives adopted by Weidner (1986) were too low. This is shown in figure 3.9, modified from Duffy and Anderson (1989), which plots the temperature and pressure derivatives of the shear moduli for P-olivine along Chapter 3, page 265 with 55 minerals where both properties are measured. Also shown as large crosses are the various estimates used by the studies listed in table 3.7, and the recent experimental results of Zhao et al. (1996) for (dp/dP)T and of L i et a l , (1996) for (d\i/dT)p . Also plotted are diagonal lines which contour the olivine content in the mantle, based on the magnitude of the shear wave velocity jump at the 410 km seismic discontinuity. Table 3.8. Comparison of calculated and expected {DLA} parameters. Mineral {G} T (DLA88) {G} P (DLA88) { G } T / { G } P (DLA88) {G} T this study {G}P=r> [dKrldP} this study {G} T / (G} this study { G } T / { G } P this study but using DLA88 {G} P a-olivine 2.9 6.5 0.45 2.18 4.29 0.51 0.33 P-olivine 4.8 6.4 0.75 2.12 4.29 0.49 0.33 y-olivine 5.0 6.5 0.77 2.25 4.50 0.50 0.35 Silicates 0.55 Total data base 0.44 In calculating {G} x for a-olivine I adopted (<9p/dP)7, = 1.40 from the 3rd order fit to the shear moduli (Duffy et al., 1995), rather than (d\i/dP)T = 2.28 from the 4th order fit used here (Abramson et al., 1997). Note that the values for (d[i/dP)T and (d\i/bT)p estimated by Anderson (1988, DLA88) and Duffy and Anderson (1989, DA89) are consistent with « 35% olivine while the values of Weidner (1986, W86) and Bina and Wood (1987, BW87) lead to much higher values of « 65-70% olivine. It is interesting to note that the measured value implies an olivine content of « 60%o, a value consistent with that of a pyrolite composition (« 62%). A last point is that the diagonal contours are partially dependent upon the adopted seismic value of the velocity jump at the 410 km discontinuity. Duffy and Anderson (1989) adopted the seismic S-wave Chapter 3, page 266 models T N A and S N A (Grand and Helmberger, 1984) and the P-wave models G C A (Walck, 1984) and CJF (Walck, 1985) to compare with the mineral physics estimates; I adopt global reference models or regional models with both Vs and Vp profiles, since the P-and S-wave profiles are then self consistent. Thus, the slight difference between the implied olivine content of « 60% from the diagonal lines and the olivine content of « 62% for the pyrolite composition adopted here is not significant. Figure 3.10 plots estimates for temperature and pressure derivatives of the shear moduli for y-olivine as well as the various estimates (solid triangles) used by the Vs and Vp modeling studies listed in table 3.7. The open triangle represents this study's estimate for y-olivine. Also shown, as a horizontal band, are the initial estimates (lower and upper lines) for the temperature derivative calculated above using the method of Isaak (1992, r « (dKr/dP)T ) or by adopting the { D L A } value of { G } P = 6.5 = Y. The vertical bands show the adopted value for the y-olivine (d[i/dP)T and the experimentally measured values of Ridgen et al. (1991; 1992). This plot emphasizes the relatively wide range for the inferred values of (d\x/dP)T and (d[i/dT)p adopted by previous workers (compare the value of Bina and Wood (1987) to Weidner (1986)). It is also interesting to note that the adopted values used here for y-olivine (d[i/dP)r and (d\i/dT)p are in better agreement with the {DLA}minera l systematics of mantle silicates than the values advocated by Anderson (1988). In summary, I find that the method of Isaak (1992) gives an excellent prediction of the temperature derivative (d\i/8T)p for P-olivine when compared to the recently reported experimental value of L i et al., (1996). When the Isaak (1992) method is applied to y-olivine, Chapter 3, page 267 this approximation predicts a value of (d^/dT)^ = - 0.0137 G P a / K which had to be increased slightly to -0.0170 GPa /K to match the velocity profiles (see below). When the adopted values are checked using some of the criteria which Anderson (1988) used to predict elastic properties and to highlight implausible choices for the temperature and pressure derivative, it is found that the values used here are consistent with average values tabulated for silicates, and hence, are mineralogically plausible, at least within the { D L A } framework With the values estimated above, I now turn to calculating V$ and Vp velocity profiles. 3.11 Equation of State Steps in calculating V s and V P A s noted above, the adiabatic geotherm, the pyrolite mineralogy, and the thermoelastic properties used in modeling the density and bulk sound velocity profiles are all held fixed in the study. Therefore, the only parameters that are introduced here, are the shear moduli, p(7' r e f,P r e f), and its associated temperature, (dp /d r ) and pressure derivatives, (5 | i / dP) r . The following section explains the general procedure used in calculating the high temperature and pressure elastic properties of the various minerals that were used in this study. The steps are identical to that presented earlier in modeling density and bulk sound velocity profiles throughout the mantle, except the section concerning the shear modulus. 3.12 High Pressure Parameterization; density and bulk modulus I start by adopting the upper and lower mantle geotherms of Ito and Katsura (1989) and Akaogi and Ito (1993) respectively. This provides only an initial geotherm, since I later Chapter 3, page 268 substitute an internally consistent adiabatic geotherm calculated directly from the elastic data and iteratively repeat this substitution until the geotherm and elastic parameters remain unchanged. This ensures that the geotherm used in the calculations is self-consistent with the adopted mineralogy, an approach outlined by Graham and Dobrzykowski (1976). I follow the recommendation of Bina and Helffrich (1992) regarding the temperature and pressure path to the T and P conditions of interest: to reach the high T-P conditions of the mantle, I first "step up" in temperature at room pressure (Tref^T, Prefix followed by a second correction in pressure at high temperature (T, Pref->P) with 298 K and 1 bar being taken as the reference state. This reflects the fact that volumetric thermal expansion data (a(7)) are available for most minerals at room pressure, but this parameter is largely unmeasured at high pressure. The adiabatic geotherm is used to correct the standard temperature and pressure value of the isothermal bulk modulus, [Kr(Tref , JP r t /)jto mantle temperatures using the following relationship: K T (T> Pref ) = K T (Tref > Pref ) + (dKT\ f T - 2 9 8 ) p where {dKr/dT) is the isobaric temperature derivative of the isothermal bulk modulus, T-the temperature of interest along the geotherm, and 298°K represents the reference state at room temperature. Chapter 3, page 269 In a similar fashion I correct the molar volume from room temperature and pressure v{Tref ,Pref jto mantle temperatures (but room pressure) using the expression; V(T,Pref) = V(Tref,Pref) expf ]a{T)dT\ 298 where a(T) is the thermal expansion coefficient and is used to express the volume change of a mineral due to a temperature change (Fei, 1995). Commonly the thermal expansion coefficient is reported as a polynomial expression: a(r) = a 0 +a, r + a 2 IT2 where a 0 , a , , and a 2 are constants determined by fitting experimental data. Substituting the polynomial expression in the above expression for molar volume and integrating gives: V(T,Pref) = V(Tref,Pref) exp! a 0 ( r -298 ) + ^ -(r 2 - 2 9 8 2 ) - a 2 ( T - ' -298"') For some minerals, the polynomial expression for the thermal expansion coefficient is given only as a linear temperature dependence (Bina and Wood (1987, p. 4856) note that over the high temperature range of interest in the mantle such a relation is expected to hold): a(r) = a 0 +a ,7 1 To evaluate the pressure dependence of the volume at high temperature, V(T, P) I insert the high temperature value of the isothermal bulk modulus, Kr (T, Pref), the volume at high temperature and 1 bar v(T,Pref^, the pressure derivative of the isothermal bulk modulus (<9 Kr/d P)T, and pressure, P (from PREM) into the 3rd order Birch-Murnaghan equation and iteratively solve for V(T,P) in 1 km intervals over the pressure range of interest for the particular mineral: Chapter 3, page 270 P = [-)KT(T,PREF) V(T,P) j { V(T,P) \5A dP J J V(T,P) -1 Following Bina and Helffrich (1992) I determine the pressure dependence of the isothermal bulk modulus at high temperature via the third order formulation of Davies and Dziewonski (1975): f - -,5/\ KT{T,P) = KR{T,PREF) 1 + 2 1 (V(T>P«)) -1 / 2 « 1 + f 3 'dKT \ - 5 1 2 { V(T,P) J { dP) T / 2 { V(T,P) J -1 The pressure dependence of thermal expansion coefficient at high temperature is evaluated using the expression (Anderson, 1967; Chopelas and Boehler, 1989; Anderson, et al., 1990); a ( X P ) o~{T,Pref) V(T,P) V(T,PRET re/ J where 87. is the Anderson-Gruneisen parameter and is constant for upper mantle minerals. The Gruneisen parameter, defined asy = following relationship: , is corrected to high pressure by the J(T,P) yiref) V{T,P) V ( T > P « \ The exponent q is often assumed to be a constant equal to 1, but I have followed the conclusions of Anderson, O.L., et al. (1993) on MgO and linearly decreased the exponent q from a value of 1.09 across the mantle to a 0.8 at the base of the lower mantle. Independent Chapter 3, page 271 arguments in support of decrease in q with increasing pressure have also been raised by Duffy and Ahrens (1993). Ita and Stixrude (1992; 1993) assume that q = 1 ± 1. The high temperature and pressure adiabatic bulk modulus, KS(T,P) is calculated from the isothermal value, KT(T,P) via the relationship: KS(T,P) = KT(T,P)[\ + Ta(T,P)y(T,P)] where T is the high temperature of interest, a(T, P) is the thermal expansion coefficient, and y(r ,P)is the Gruneisen parameter, with both parameters at the high T-P conditions of interest. 3.13 High Pressure Parameterization: Shear Modulus I correct the room temperature and pressure value of the shear modulus, \^(Tref ,Pref) to mantle temperatures using the linear relationship; p(r,pre/) = p(7;rf,pre,)+ ref •>± ref , (P-298) where {d \x/dT)p is the temperature derivative of the shear modulus. Again, following Bina and Helffrich (1992), I determine the pressure dependence of the shear modulus at high temperature via the third order formulation of Davies and Dziewonski (1975): p(r,p) = p(r,p. re/) 1+2 v(T,Pref) V(T,P) \2A -.$A /2 -1 -1 J 1-V(T,P) 8PJ where (d p/5 P ) T is the pressure derivative of the shear modulus. Chapter 3, page 272 Finally, density, p(T, P), and the isotropic Vs and F p velocities are calculated by substituting the shear modulus, \i(T, P), the adiabatic bulk modulus, KS(T, P), the molar volume, V(T, P), all at high T-P conditions, into their definitions M 9{T,py V(T,P) Ks(T,P) + ±\i(T,P) VP(T,P) = -p K p(T,P) where M i s the molar mass of the mineral. 3.14 Shear Modulus; non-linear extrapolations in pressure Although I use third order Birch-Murnaghan equation of state to extrapolate to the pressures of the Earth's interior, I stress this choice is largely one of convenience since the experimental data for many of the minerals does not warrant expanding the terms to fourth order. However, this situation has changed for olivine and orthopyroxene, where,high precision experimental work at both high temperature and pressure is documenting a non-linear pressure dependence for the shear modulus (e.g. Abramson, et al., 1997) and bulk modulus (Chai et al., 1998). To model the shear modulus pressure dependence of olivine I use a 4th order Birch-Murnaghan equation of state, which is expressed as: Chapter 3, page 273 [x(T,P) = ^(T,Pref) 1 + 2 V(T,P) x 2/ \/3 5 ^ /2 \{v{T,Pref)f _x V(T,P) ySPjT KT(T,PJ V{T>PJ V(T,P) -1 (*r(T,Pjy ^ W p J -+ - WPJ + 35 I fit,the data of Abramson et al. (1997) to determine the values for (<3p/c3P)T, and ( a 2 p / 5 P 2 ) T and obtain ( d p / 5 P ) T = 2.28 and ( d 2 p / 5 P 2 ) T = -0.0687 GPa"1. This is shown in figure 3.11 where a 4th order Birch- Murnaghan fit is shown together with data points. Bina and Helffrich (1992) note that the higher order pressure derivatives appear to be of order y based on molecular dynamics simulations and laboratory experiments of the / P-o elastic properties of MgO (Isaak et al., 1990) and suggest that one may approximate {d2 p / d P 2 ) t as or ignore the 4th order term completely (as is commonly done). 3.15 Self-consistent Adiabatic Geotherm I adopt without modification the adiabatic geotherm calculated earlier in modeling density and bulk sound velocity profiles, but for completeness, I document below how this geotherm was constructed. I calculate an adiabatic geotherm from the mineral physics parameters that were calculated to estimate density and the bulk sound velocity: this geotherm is then used in Chapter 3, page 274 subsequent calculations for refined estimates of p(T, P) and V^(T, P). Although I am assuming that the appropriate geotherm for the Earth's mantle is indeed adiabatic, this assumption is tested when the predicted density and bulk sound velocity profiles are compared to the observed seismic profiles. A close match between the predicted and observed density and bulk sound velocity profiles across the full depth extent of the mantle would imply, that in addition to placing constraints on bulk mineralogy, to first order, the geotherm is adiabatic. If the mantle deviated progressively with depth to a sub-adiabatic geotherm (e.g. Jeanloz and Morris, 1986; 1987) then I would expect to see a progressive and systematic divergence between the predicted and observed p(T, P) and V^{T, P) profiles (Weidner, 1986, p. 262). The adiabatic temperature gradient is calculated via the following expression (Graham and Dobrzykowski, 1976): rdT\ _Ty(T,P) KdP)~ KS(T,P) where y (T, P) and Ks (T, P) are the V R H average of the Gruneisen parameter and the adiabatic bulk moduli respectively. To anchor the adiabatic temperature profile, I assign a temperature at 100 km depth in the upper mantle, the "top" of the upper mantle considering in this work, while in the lower mantle, the anchor point is located on the underside of the 660 km seismic discontinuity. The temperature at 100 km depth is chosen such that when the upper mantle adiabat is extrapolated to the surface, the resulting potential temperature agrees with independent estimates of the mantle potential temperature determined from decompression melt studies of MORBs (1330-1350 °C; White and McKenzie, 1995; Iwamori et al., 1995). I initially elected to tie the anchor temperature of the lower mantle geotherm to Chapter 3, page 275 that temperature predicted from the upper mantle geotherm. In subsequent numerical runs, I relaxed this assumption. The temperature jumps associated with the latent heat of phase changes at the 410, 520, and 660 km seismic discontinuities are calculated via the method of Navrotsky and Akaogi (1984) but with the modification that instead of calculating the change in molar volume associated with the phase change from reference molar volumes at room temperature and pressure (e.g. AV(TREF,PREF), values at the mantle temperature and pressure of interest are utilized: where T is the temperature immediately above the onset of the phase change, and y j is the value of the Clapeyron slope of the phase change and the subscript d indicates the depth of the phase change. I adopt y 4 1 0 = +3.0 MPa/K for 410 km and y 5 2 0 = +5.1 MPa/K for 520 km from Katsura and Ito (1989), and y 6 6 0 = -2.0 MPa/K for the 660 km phase change (Bina and Hellfrich, 1994). C p is the heat capacity with appropriate values adopted from Akaogi and Ito (1993) and Akaogi et al. (1989). The adiabatic geotherm is calculated from 100 km depth down until intersecting the top of a phase change, the thickness of which is taken from the widths given in the diagram of mineral proportions of Ita and Stixrude (1992; 1993) and reproduced and used here (see figure 3.1). Thus, the thickness of the phase change is not calculated, but assigned in constructing the adiabatic geotherm. Seismological studies which imply relatively thin phase changes, are in conflict with the equilibrium width calculated via thermodynamics for the 520 km, and to a lesser degree, the 410 km phase changes. I stress, that this discrepancy is AT, phase change AV(T,P) c„ Chapter 3, page 276 not addressed in constructing our geotherm since I am adopting as fixed, the equilibrium widths inferred by Ita and Stixrude (1992; 1993). A more complete study that incorporates the changing phase boundary width as a function of temperature (e.g. Helffrich and Bina, 1994) is beyond the scope of this study. The temperature jump associated with the phase change is linearly added to the geotherm. Once the depth region of the phase change is exited, the temperature at the base of the phase change is used as the anchor point for the next leg of the geotherm. In this way, the upper mantle geotherm is calculated down to, and through, the 660 km phase change. In the lower mantle I follow Ita and Stixrude (1992; 1993) and assume there are no phase changes within this region, an assumption supported by thermodynamic calculations on the stability of the assemblage of Mg-perovskite and magnesiowustite (Stixrude and Bukowinski, 1992; 1993), and molecular dynamics simulations on the structural stability and breakdown of Mg-perovskite (Stixrude and Cohen, 1993; Warren and Ackland, 1996). To ensure convergence, I substitute the new adiabatic geotherm calculated above and iterated through all the above steps until both the geotherm and elastic parameters remain unchanged for a particular set of temperature anchor points. 3.16 Aggregate properties Following Ita and Stixrude (1992; 1993), I used the Voigt-Reuss-Hill averaging scheme (Watt et al., 1976) to determine volume averaged properties for the mineral assemblages. Implicit in this scheme is that the mineral assemblage is homogeneous, isotropic aggregate. This is a reasonable assumption since tomographic studies that include the affects of anisotropy in the seismic model find that strong anisotropy is largely Chapter 3, page 277 concentrated above « 250 km depth and decreases rapidly within the depth interval of 250 to 350 km depth and is unresolvable at 400 km depth (Montagner and Tanimoto, 1991). While more restrictive schemes are available for averaging material properties such as Hashin-Shrikman bounds, Bina and Helffrich (1992) demonstrate that while the Hashin-Shrikman method gives tighter bounds than the V R H method, the averages for both are identical. 3.17 Results The adiabatic geotherm used in the calculations of Kg and Vp is shown in figure 3.12 along with the starting geotherm originally adopted in the modeling procedure. The predicted pyrolite density profile is shown in figure 3.13 along with other upper mantle density profiles such as akl35 (Kennett et al., 1995), and akl35-Q and akl35-F (Montagner and Kennett, 1996) that combine free-oscillation seismological data with the body wave travel based model akl 35. In deriving the akl 35-Q model, the density structure of the akl 35 model was varied to satisfy the free-oscillation constraints, while in the akl 35-F model, both density and the Vs and Vp velocity profiles of the akl 35 model were varied. I also plot two density profiles determined from high resolution regional studies that incorporate ScS, multi-bounce S-wave, and surface wave seismological data (AU3, Gaherty and Jordan, 1995; PAS, Gaherty et al., 1996). The calculated pyrolite density profile is that calculated earlier in modeling density and bulk sound velocity profiles and I show it for completeness because density is used directly in calculating the Kg and Vp velocity profiles discussed next. Figure 3.14 shows the predicted VS velocity profiles for the individual minerals which comprise the pyrolite model evaluated here. Also plotted is the V R H profile for the Chapter 3, page 278 bulk assemblage together with the akl35 velocity profile. In figure 3.15 the calculated V R H average profile is compared against the estimated standard deviation and maximum deviation of the seismological mean as calculated by Ita (1992). Figure 3.16 shows the related predicted compression velocity profiles for the same individual minerals, while figure 3.17 compares the V R H average against the seismological mean as calculated by Ita (1992). The mean and their error represent statistical averages of 34 published Vp and 32 Vs profiles (Chinnery and Toksoz, 1967; Hales et al., 1968; Herrin, 1968; Fairborn, 1969; Hales and Roberts, 1970; Buchbinder, 1971; Randall, 1971; Robinson and Kovach, 1972; Wright and Cleary, 1972; Wiggins et a l , 1973; Gilbert and Dziewonski, 1975; Hart, 1975; Kind and Muller, 1975; Dey-Sarkar and Wiggins, 1976; Hart et al., 1976; King and Calcagnile, 1976; Fukao, 1977; Burdick and Helmberger, 1978; Sungupta and Julian, 1978; McMechan, 1979; 1981; Uhrhammer, 1979; Given and Helmberger, 1980; Hales et a l , 1980; Burdick, 1981; Dziewonski and Anderson, 1981; Vinnik and Ryaboy, 1981; Fukao et al., 1982; Nakada and Hashizume, 1983; Grand and Helmberger, 1984a; b; Walck, 1984; 1985; Lyon-Caen, 1986; Lerner-Lam and Jordan, 1987; Paulssen, 1987; Grad, 1988; Graves and Helmberger, 1988; Montagner and Anderson, 1989; Lefevre and Helmberger, 1989; Bowman and Kennett, 1990; Dost, 1990; Kennett and Engdahl, 1991). These profiles are from studies that postdate 1974, under the belief that after this time researchers attempted to account for the affects of attenuation and thus, the profiles are largely free of systematic bias that arises from unmodeled attenuation. Ita and Stixrude (1992; 1993) combined the mean and standard deviation of the Vp and Vg profiles to obtain, through formal propagation of errors, the mean and standard deviation of V® via the expression F 0 = yjvf--%vj. Chapter 3, page 279 The calculated Vs profile in figure 3.15 gives a fair fit to the seismic mean in the upper mantle, but falls within the maximum bounds. The calculated profile is significantly faster than the mean at 100 km depth, the top of the modeling region, but because the velocity gradient is much steeper than the seismic mean, the misfit between the two decreases with increasing depth so that at the 410 km discontinuity, the seismic mean and the calculated profile are in good agreement. In the uppermost transition zone (410-520 km), the calculated pyrolite model is in excellent agreement with the mean, but a t « 520 km depth, the calculated Vs profile takes on a much steeper velocity gradient with the effect that calculated profile progressively cuts across the expected mean profile with increasing depth. At the base of the transition zone, the predicted velocity jump of the 660 km discontinuity is only about 1/2 the full width inferred from the seismic mean. Below the sharp 660 km discontinuity, the calculated Vs profile exhibits a gentle velocity gradient down to 730 km depth whereupon the velocity profile abruptly steepens to the velocity profile of the lower mantle (I postpone discussion of the lower mantle velocity profiles to chapter 4 and 5). While the mean of the seismic models possesses a shallow gradient below 660 km, the gradient within it is much steeper than the pyrolite model and extends to greater depth («750 km) than the pyrolite model ((«730 km). In contrast to the Vg, the calculated Vp profile in figure 3.17 gives a much better fit to the seismic mean in the upper mantle with the calculated profile nearly coinciding with the average profile with a velocity gradient that is comparable to the mean, but offset to slightly faster velocities. In the uppermost transition zone, the match between calculated and the seismic mean is good, but with the calculated profile exhibiting a shallow velocity gradient such that the calculated profile trends to faster velocities with depth down to « 520 km. At Chapter 3, page 280 this depth, the calculated Vp profile exhibits a change in velocity gradient to a steeper slope such that calculated profile cuts across the seismic mean and intersects the 660 km discontinuity at a slower velocity than the mean. The predicted velocity jump across the 660 km is significantly reduced compared to that of the seismic mean profile but still falls with the means maximum bounds. Of note is that the jump in Vp across the 660 km seismic discontinuity is not equal to that exhibited in the profile (compare figure 3.15 and 3.17) being substantially smaller (AVs = 6.39%; AVp = 3.13%). Below 660 km depth the calculated Vp profile exhibits a shallow velocity gradient to 730 km whereupon the gradient steepens abruptly to the lower mantle profile (I postpone discussion of the lower mantle velocity profiles to chapter 4 and 5). In figure 3.18 and 3.19 the calculated V$ and Vp velocity profiles are compared with recently proposed global average seismic models MD89ps, iasp89 (Kennett, 1991), iasp91 (Kennett and Engdahl, 1991), akl35 (Kennett, Engdahl, and Buland, 1995), and akl35-F (Montagner and Kennett, 1996). MD89ps, iasp89, iasp91 are all constructed to satisfy summary P and S-wave travel times over an epicentral distance of 30°, but differ in the magnitude of the velocity jumps at 210, 410, and 660 km depth and the velocity gradients between these discontinuities. Inspection of these figures reveals that there exists a surprising amount of variance in the velocity gradients for even modern "globally average" models -apparently the strong upper mantle and transition zone seismic heterogeneity (Nolet et al., 1994) may be satisfied by a diverse class of "globally averaged" models. I note that the seismic models are parameterized by a series of radial layers in the upper mantle separated by distinct discontinuities with the velocities within each layer represented by a linear gradient in velocity. For the iasp91, akl35, and akl35-F models, the major discontinuities Chapter 3, page 281 are placed at 210 km, 410 km, and 660 km depth, with breaks in velocity gradient allowed at 760 km. Thus, the discrepancy between the calculated pyrolite velocity profiles and the seismic models in the middle of the transition zone (the absence of the abrupt change in velocity gradient at « 520 km depth that is prominent in the pyrolite model) reflects the parameterization of the seismic models which do not allow for a discontinuity, nor a change in gradient at this depth. The shear wave studies by Shearer (1990, 1991, 1996), Shearer and Masters (1992), Flanagan and Shearer (1997), Revenaugh and Jordan (1991b), and Revenaugh and Sipkin (1994) document that a small seismic discontinuity a t « 520 km is a global feature. Although none of the globally averaged seismic models have yet to be parameterized to allow this feature to be expressed, the regional continental (AU3) and oceanic (PA5) seismic models of Gaherty and Jordan (1995) and Gaherty et al. (1996) respectively, have incorporated the ScS reverberation data of Revenaugh and Jordan (1991b; see below for more details) which yields precise estimates on mantle layering. This data set, in conjunction with multi-bounce shear body waves and surface waves were used to construct self consistent, path-averaged radial models of density, Vs, and Vp. Furthermore, these regional models were constructed with a 520 km discontinuity included in the initial velocity profile which was iteratively optimized to satisfy the seismic observations. The velocity profiles for AU3 and PA5 are shown in figure 3.20 and 3.21 together with the pyrolite mineral physics profiles. Of note here is the close similarity between the velocity profile and gradient for the continental AU3 upper mantle (250-410 km) and the pyrolite model in terms of Vs and Vp (and conversely, the distinct difference between the associated velocity profiles of the oceanic PA5 upper mantle (170-410 km) and the pyrolite Chapter 3, page 282 model). Gaherty et a l , (1996) interpret this difference between AU3 and PA5 to reflect the affects of water on the velocity profiles with the oceanic upper mantle "wetter" than the sub-continental upper mantle. The effect of a small amounts of partial melt, likely to be a silicate melt rather than actual water, is to decrease seismic velocities compared to a "dry" mantle with shear velocity being affected more than compression velocity. If their interpretation is valid, then the similarity between A U3 and the pyrolite model is to be expected since the mineral physics model is entirely "dry". In the transition zone, both of the regional seismic models show distinct changes in velocity gradient at the « 520 km depth, with the oceanic model PAS velocity profiles exhibiting the most similarity to the mineral physics model. This is encouraging, since the purely oceanic model is likely to be free of complications due to continental crust or lithosphere, which may contaminate the surface waves and the multi-bounce shear waves used in constructing both AU3 and PA5. Thus, the excellent agreement between the PAS transition zone velocity profiles and the predicted pyrolite profiles lends credence to the pyrolite Vs and Vp velocity profiles in the transition zone. Previous mineral physics interpretations (e.g. Duffy and Anderson, 1989) had used the relatively shallow velocity gradient in transition zone region of the P R E M global seismic models, which it should be noted, does not incorporate a 520 seismic discontinuity, to argue that a pyrolite composition may be ruled out since it was incapable of satisfying the gradients there. However, it would appear that the global seismic models are deficient in by not explicitly incorporating the 520 km discontinuity. The parameterization used in constructing the seismic models, where a linear velocity gradient is assumed between the 410 and 660 km discontinuities, would have averaged the shallow gradient in the upper part of the transition zone (410-520) and the steep Chapter 3, page 283 gradient in the lower part (520-660) of the transition zone to produce a final "mean" velocity model that would be difficult to explain in terms of the P-to y-olivine phase change that occurs in the middle of the transition zone. The transition zone shear and compression velocity gradients are plotted for both the pyrolite mineral physics model and a number of global and regional seismic models. These figures highlight the difference between the velocity gradients of the seismic models which do not explicitly have a 520 km seismic discontinuity and the pyrolite mineral physics model. In the upper half of the transition zone (410-520 km depth), the pyrolite model lies on the low side of the general field of the global models (yellow highlighted area), whereas in the lower half (520-660 km depth), the pyrolite model is clearly in conflict with these models. In contrast, there is very good agreement between the pyrolite model and the PA5 seismic model for both Vs and Vp gradients. A last point to consider is the variability in the velocity gradients exhibited by A U3 and PAS. Kennett (1991) has argued that due to the large degree of small scale (<300 km wavelength) seismic heterogeneity in the upper mantle and transition zone, it is not prudent to relay heavily on velocity gradients as a robust criteria to distinguish between particular compositional models as Duffy and Anderson (1989) and Ridgen et al. (1991; 1992) have. Indeed, i f I use just the seismic model PA5 as reference with which to judge the pyrolite model, the significant difference in the upper mantle shear velocity gradient would lead us to reject the "dry" pyrolite model for this region of the mantle, but accept it as a viable compositional model for the transition zone. Alternatively, i f the Vp profile and the associated velocity gradients are utilized then the pyrolite model gives an excellent fit to the PA5 seismic model (see figure 3.21). Chapter 3, page 284 To summarize, I find that in terms of the transition zone velocity gradient, the pyrolite model predicts gradients that are consistent with high resolution, regional seismic velocity profiles and in addition, correctly account for the change in gradient observed in the latest oceanic, high resolution regional models across the 520 km discontinuity. Previous mineral physics studies which relied on global seismic models that lacked an explicit 520 km seismic discontinuity (e.g. PREM) have erroneously concluded that isochemical compositional models are deficient in matching the transition zone velocity gradients. 3.18 A Mutually consistent olivine content from the 410 km seismic discontinuity; a check of (dp/dT)^olm"e Previous studies that focused on fitting the 410 km S-wave velocity jump predicted a significantly lower olivine content that i f the P-wave, bulk sound velocity, or density jumps had been considered instead (Bina, 1993). Since it is accepted that the relatively abrupt velocity and density increases at 410 km depth reflect the a - to p-olivine phase transition in an isochemical mantle, then the magnitude of the jumps may be used with extrapolated laboratory properties to place constraints on the olivine content in the mantle (e.g. Bina and Wood, 1986). Bina (1993) notes that while it is commonly claimed that it is the different values for the unmeasured temperature and pressure derivatives of the shear modulus for P-olivine phase, or the different equations of state, that are responsible for the wide range in olivine content inferred for the upper mantle (for example Duffy and Anderson (1989) argue for 40 vol% while Bina and Wood (1987) support 66 vol%), it is instead, the particular choice of which type of velocity (or density) was used as the discriminant for olivine Chapter 3, page 285 content. For instance, he notes that while Duffy and Anderson (1989) prefer an olivine content of 40%, this figure actually corresponds to the lower limit based on using the Vp seismic jump in as a discriminant: the seismic velocity increase ranges from 3.9% to 5.1 %, which predict an olivine content of 40-53 vol. %. In contrast, i f the jump in Vs is used as a discriminant then the olivine content that matches the observed jump of 4.6 % is only 35 voP/o. Thus, significant variation in the estimated olivine content can simply arise from the particular choice of the seismic functional at the 410 km discontinuity. Bina (1993) used the predicted laboratory properties for alpha and beta olivine published from three representative studies (Duffy and Anderson, 1989; Weidner, 1986; and Bina and Wood, 1987) to estimate the predicted change in all of the properties (density, Vs, Vp, V^) across the 410 km discontinuity via: P _ a y P _ y a P a V9a s vsa ' v,,a for the a - to p-olivine phase transition at the inferred T and P conditions of the 410 km discontinuity (13 GPa and 1700 K). Then representative parameter increases estimated from seismology were then divided by these laboratory estimates (for pure olivine phases only) to obtain an estimate of the olivine content: Vs olivine%= \ s { : , polivine % - \ p [ : * I . T , o_>R ^experiment ' f I Experiment [AVS pj [AP ) F 0 olivine% = \ ° { : , VP olivine% = \ F [ : w I «-vR ^experiment ' ' / „_vR \expenment Chapter 3, page 286 In the above ratios, the top entry represents the jump across the 410 from seismological models, while the bottom entry represents the jump across the 410 from the predicted alpha and beta olivine properties from the mineral physics model. Note that the mineral physics estimate is only concerned with the alpha and beta olivine properties and ignores the properties of any of the other mineral phases that may be stable at this depth. Table 3.9 lists the calculated increases from the mineral physics estimates compiled by Bina (1993), his own estimate, and lastly, the estimate from this study. Table 3.10 lists the calculated increase from some of the global and regional seismological models discussed in this chapter. Figure 3.24 re-plots the results of Bina (1993) when the seismological jumps were divided by the mineral physics predictions. Table 3.9. Parameter increases across the a-olivine to P-olivine phase transition at the 410 km seismic discontinuity. The top four rows are taken from Bina (1993). Model Ap<^ p A ^ r p A F ; r p Bina & Wood (1987) 5.9% 9.3% 6.6% 7.6% Weidner, 1986 6.1% 10.2% 6.9% 8.2% Duffy & Anderson, 1989 5.8% 12.7% 7.5% 9.7% Bina, 1993 6.7% 8.9% 9.6% 9.3% This study 7.3% 6.7% 7.1% 7.1% Table 3.10. Seismological estimates for the parameter increases across the 410 km seismic discontinuity. The top row is the representative inference utilized by Bina (1993). Model (Apa~"p ) s e i s m o ' ° B y (AF a~ > ' p Y'smol°sy ( A J / a _ > p y e i s m o l o s y ( A F a ^ p ) s e i s m o l o g y Bina, 1993 3.9 % 4.6% 5.1% 4.9% (1066B) (SNA & TNA) (GCA & S25) P R E M 5.085 % 3.571 % 1.971 % 2.584 % C R E M O 3.818% 0.557 % 1.309% 1.014% iasp91 - 3.660% 4.106% 3.654% akl35 5.883 % 4.312% 3.235 % 3.654% akl35-F 7.730 % 1.938 % 2.426 % 2.243 % pac91 - 2.669 % 3.756% 3.333 % PA5 3.631 % 4.132% 4.158% 4.148% AU3 3.072 % 5.625 % 4.339 % 4.842 % Chapter 3, page 287 The composition of the olivine and P-olivine phases are usually taken as constant across the phase change and equal to that used when modeling the full mineral assemblage (Mg 0 8 9 Fe 0 u ) 2 Si0 4 ) . Recently, Irifune and Isshiki (1998) have documented experimentally that assuming a constant iron content for the olivine and P-olivine phases across the 410 km discontinuity may not be valid. Their poly-mineralic experiments indicate that olivine becomes progressively more Mg rich with increasing depth and reaches a Mg content of roughly 0.92 immediately above the 410 km discontinuity. This is in contrast to the Mg content of the P-olivine immediately below the 410 which has a Mg content of 0.89. These effects may lead to a narrower transition width and a decrease in the calculated seismic jump (see Bina, 1998). However, in the calculations presented here, I do not incorporate the additional complexity of variable iron content for the upper mantle minerals; the very good agreement between the mineral physics model and the purely oceanic PA5 model indicates that variable iron content is not required to reconcile mineral physics and seismological inferences. If each mineral physics study were internally consistent and the seismological jumps accurate, then a particular mineral physics model should give the same predicted olivine content irrespective of the seismic data functional used. Inspection of figure 3.24 clearly reveals this is not the case, with widely varying olivine contents being inferred from each of the seismic functions for the different mineral physics studies. Also plotted is a recent estimate from Duffy et al., (1995) which assumes that the (dp/dr) P "'"'"c =(c3p/5r)" "'"""'and predicts an olivine content of (27%-38%) depending on Chapter 3, page 288 the particular seismic functional used. While these estimates are not strictly comparable to the other curves because Duffy et al., (1995) assume different values for the seismic jumps ( „ . ii \ seismo log y I n \ .veiwwolog v *VS ) = 4 - 3 % ; ( A ^ ^ p ) = 4.5% vs. jumps of 4.6% and 4.9%, respectively by Bina (1993)), their inferred values illustrate the severe discrepancy between conclusions drawn from modeling Vs and Vp velocity at only a single point in the mantle (in this case, the 410 seismic discontinuity) as compared to our results illustrated in the profiles above and with the conclusions drawn earlier from modeling density and bulk sound velocity profiles that cover the whole mantle. Bina and Silver (1990) and Bina (1993) note that of the four seismic parameters (jumps in density, Vs, Vp, V0), the jump in bulk sound velocity across the 410 km discontinuity should provide the best estimate on the olivine content of the mantle since V0 is dependent upon bulk modulus and density (V^ = yJKs/p ), while J^and Vp are dependent upon both the bulk and shear modulus and density (Vs = ->/p/p and Vp = i](Ks +%p)/p). While density is dependent upon bulk modulus, it suffers from being constrained only by free-oscillation data which averages information globally and has poor depth resolution. Finally, because seismic attenuation studies have concluded that most attenuation occurs via shear rather than bulk dissipation (e.g. Durek and Ekstrom, 1995; 1996), the seismic jump in shear velocity provides the least robust estimate of composition (assuming that attenuation effects are the largest source of error in constraining the absolute velocities on either side of the 410 km discontinuity). Thus, using the seismic jump in F 0 to obtain an estimate of olivine content, Bina (1993) then turned to the seismic Vsand Vp and by forward modeling the mineral physics Chapter 3, page 289 jumps in Vs and Vp iteratively adjusted the value for the unmeasured temperature derivative of the shear modulus for the p-olivine phase until a mutually consistent estimate for the olivine content emerged. This curve is shown in figure 3.24 (see line labeled Bina (1993)) and represents an olivine content of « 52 % for a value of the P-olivine temperature derivative of |dp/<3rj = -0.022 GPa/K. This inferred value for [d\ijdT^ is relatively high (it is significantly greater than that of a-olivine (|(3p/dT^ j = -0.014 GPa/K) and just below that of MgO ((Sp/dr) = -0.024 GPa/K), one of the highest measured values for a mantle silicate) and is higher than that inferred by Isaak (1992) via empirical thermodynamic approximations (-0.0165 GPa), and the value measured by Li et al. (1996) and adopted here (-0.017 GPa). Because the elastic data for the other required parameters (bulk modulus, and its temperature and pressure derivatives) adopted by Bina (1993) differ from this study, I also min era/ calculated the predicted jumps in the various seismic functions ((^AVSa^ j^ '"" 5 etc.) to determine if such a high value for (dp/dr)5 is indeed demanded to obtain a mutually consistent estimate of the olivine content which is consistent with a pyrolite mantle. I am using the measured value of Li et al., (1996), which is significantly below the estimate of Bina (1993). However, unlike Bina (1993), in the comparison here I combine the mineral physics jumps with seismological jumps where all of the seismic parameters are taken from the same model source. For example, the globally averaged models iasp91 (Kennett, and Engdahl, 1991), akl35 (Kennett, Engdahl, and Buland, 1995), PREM (Dziewonski and Anderson, 1981), and Chapter 3, page 290 CREMO (Montagner and Anderson, 1989a) and the regional models pac91 (Kennett, 1992), AU3 (Gaherty and Jordan, 1995) and PA5 (Gaherty et al., 1996) represent internally consistent seismic models that provide density and Vs and Vp velocity profiles. In contrast, Bina (1993) estimated the jump in Vs from the average jumps in the regional Vs models SNA and TNA (both from Grand and Helmberger, 1984), while the seismological jump in Vp was determined from averaging the jumps in the regional Vp models GCA (Gulf of California; Walck (1984)) and S25 (Canadian shield; Lefevre and Helmberger (1989)). Finally, the density jump was taken from model 1066B (Gilbert and Dziewonski, 1975). When I divide these recent global and regional seismic models by the jumps predicted from the pyrolite mineral physics model I obtain significantly different estimates of olivine content than that inferred by Bina (1993) with systematic differences exhibited between iasp91 and akl 35 on one hand and PREM and CREMO on the other (see table 3.11). The estimated olivine content when the either iasp91 and akl35 seismic models are used is not mutually consistent with values ranging from 80.44 vol% for p, 63.56 vol % for Vs, 51.40 vol. % for Vp, and to 45.12 vol. % for V®. Of note is that the predicted olivine contents determined from the Vs jump agrees well with experimental estimates for the pyrolite mantle (62 vol%; Irifune (1987)). In contrast, the estimated olivine content when either PREM or CREMO is used as the seismic model show much greater variance with the two models giving widely different predicted olivine contents for Vs and Vp jumps (see figure 3.25). Surprisingly, the CREMO model gives very low, and mutually inconsistent values for the olivine content of 8 to 18 vol% which conflicts with petrologic conclusions drawn from it (Montagner and Anderson, 1989) that favoured a 40% olivine content for the upper mantle (e.g. Duffy and Anderson, 1989) composition. That the low values are not due Chapter 3, page 291 to the particular thermoelastic parameters adopted in this study is demonstrated when I divide the seismic jumps of CREMO by the mineral physics jumps determined by Duffy and Anderson (1989) - the resulting olivine estimates (labeled CREMO/Duffy & Anderson, 1989 in figure 3.25) all fall below our estimates, and are even lower than any of the olivine contents proposed for the various mutations of piclogite (Bass and Anderson, 1984; Anderson and Bass, 1984; 1986; Duffy and Anderson, 1989). Table 3.11. Predicted olivine content from the velocity and density increases at the 410 km seismic discontinuity. Upper Mantle Olivine Content seismic model Ap A F 0 mineral physics model Bina & Wood, 1987 66 49 77 64 Weidner, 1986 64 45 74 60 Duffy & Anderson, 1989 67 36 68 51 B i n a , 1993 58 51 53 53 Duffy etal., 1995 - 38 27 32 PREM/this study 69.52 27.48 52.65 36.35 CREMO/this study 52.20 18.26 8.22 14.26 iasp91/this study - 46.95 60.54 51.40 akl 35/this study 80.44 45.12 63.56 51.40 akl 35-F/this study 105.67 33.83 28.57 31.55 pac91/this study - 52.38 39.35 46.88 /M5 / th is s t u d y 49.64 57.98 60.91 58.34 AU3/this study 42.00 60.52 82.92 68.11 modified akl35/this s t u d y - 62.29 63.56 61.97 CREMO/Duffy & Anderson, 1989 65.84 . 17.46 4.39 10.46 Of the two regional models considered here, the oceanic regional model PA5 gives self-consistent results which are in good agreement with the adopted olivine content of a Chapter 3, page 292 pyrolite mantle. This is in sharp contrast with the continental model AU3 which gives inconsistent estimates of the olivine content but nevertheless, does exhibit a similar pattern in terms of predicted olivine content to the global models akl35 and iasp91. Shearer (1996) has argued that relatively large crustal effects are imposed on S-wave waveforms for multi-bounce body waves which have continental bounce points as compared to those which have oceanic bounce points. This effect reflects the much more variable thickness and composition of continental crust as compared to the uniform thickness and composition of oceanic crust. Thus, the large contrast between PAS and AU3 likely reflects potential "contamination" of the AU3 radial velocity profiles from unaccounted continental effects. Alternatively, the large difference in the velocity models may reflect actual differences between the two regions which reflect strong lateral heterogeneity within the upper mantle. Lastly, it should be noted that both PAS and AU3 were constructed using only shear wave data - the density and Vp profiles in these models were simply scaled from the Vs profile during development of the models. Hence, while the density and Vp profiles in these two regional models are self-consistent internally, neither profile are strongly constrained by direct seismological observations along the particular seismic corridors. Finally, it is interesting to note that only a decrease of 0.065 km/sec in the P-wave velocity above the 410 km seismic discontinuity for either the iasp91 or akl3S global reference models, as illustrated in figure 3.26, will change the calculated olivine contents to being largely self-consistent at A F 0 « AVs~ AVp « 62% (see figure 3.27 and entry "modified akl35" in table 3.11). Thus, relatively trivial perturbations to only one part of one of the latest global reference seismic models will result in calculated mutually consistent olivine contents that agree with a pyrolite mineralogy. Such a relatively modest perturbation Chapter 3, page 293 to this portion of akl35 is permitted by the constraints (travel time data) used in constructing it (Kennett, personal communication). Alternatively decreasing the S-wave velocity by -0.019 km/sec below the 410 km seismic discontinuity for the akl35 model will result in largely self-consistent olivine contents of A F 0 « AVs& AVp « 51.5 vol%. Of the two possibilities, the observation that the PA5 A V$ gives a relatively high olivine content (« 58 vol%) argues in favour of adjusting the P-wave profile, since for this particular regional model, a large and diverse set of shear wave seismic observations were used to constrain the shear wave profile. Consequently, of all of the upper mantle seismic velocity profiles considered here, it can be argued that this particular profile is the most robust. What is encouraging from the exercise of comparing mineral physics to seismological jumps is that the value adopted in this study for the temperature derivative of the p-olivine phase ((d\x/dT)p = -0.017 GPa/K), when combined with the high resolution, regional seismic model PA5, results in mutually consistent olivine contents in good agreement with that expected for a pyrolite bulk composition. Consequently, the conclusion of Bina (1993) that a much higher value for the temperature derivative (-0.022 GPa/K) is required to obtain mutually consistent estimates of the olivine content is not supported, nor is the claim that a low value, similar to that for a-olivine phase, supports an olivine content consistent with piclogite mineralogy (40 vol%; Duffy and Anderson, 1989; Duffy et al., 1995). 3.19 Reflection properties of mantle discontinuities A n important test of the calculated pyrolite Vp and Vs profiles is provided by a comparison of reflection coefficients computed for the 410 km, 520 km and 660 km phase Chapter 3, page 294 transitions in the pyrolite model with those inferred from seismic observations. A n early study by Lees et a l , (1983) modeled P-wave reflection coefficients for their calculated density and Vp profiles (see figure 3.28). However, the mineral physics data was so sparse that many assumptions were made in generating the calculated Vp velocity profile (e.g. experimentally measured values for the shear moduli were not used; p was estimated by assuming all phases had a Poisson's ratio equivalent to P R E M and this, combined with the minerals adiabatic bulk moduli, Ks, allowed an estimate for the unknown shear modulus to be made via the relationship : p = 3 ^ s ( l - 2rj)/2(l + a)) - the resultant profiles are very poor fits to the seismic observations. They concluded that a uniform compositional model could not account for the Vp reflection properties of the mantle and argued that the 660 km seismic discontinuity represented a chemical boundary. Since their study, a great deal of new experimental thermoelastic data has been obtained and since the accepted values for the bulk moduli for the p-and y-olivine phases are significantly different than those adopted by Lees et al., (1983), the conclusions drawn from this study must be re-examined. Below I calculate the shear and compressional reflection properties of the pyrolite Vs-and Vp velocity profiles focusing first on the S-wave reflectivity, since the most recent seismic observations exist for this property, and then turning to consideration of the P-wave reflectivity. 3.20 V s reflectivity: ScSreflection coefficients Revenaugh and Jordan (1987; 1989) introduced a new method for investigating mantle discontinuities that is insensitive to velocity gradients in the mantle and utilizes SH-Chapter 3, page 295 polarized waves that reflect off the underside of the Earth's surface and the core-mantle boundary and bounce back and forth through the mantle many times as they traverse from the earthquake source to a particular seismometer (termed ScS waves, see figure 3.29 for a schematic diagram of ray paths). During propagation from source to receiver, these near vertical waves may also be reflected off internal mantle discontinuities, giving rise to a complex series of reverberations which when analyzed, allow information on the depth and velocity increase across the internal mantle discontinuities (for a detailed explanation of the technique see Revenaugh and Jordan (1991a)). For the purposes here I am interested in the ability of ScS reverberations to provide observational constraints on the near-vertical incidence reflection coefficients of the upper mantle and transition zone discontinuities via: R ( z ) = / s ( z + 5z) -Is(z-8z) °^ Is(z + bz) +Is(z-dz) ZMoho < Z < ZCMB where Is (z) = p(z) Vs (z) is the impedance at a depth z for SH polarized shear waves, z M o h o and z C M B are the depths of the moho and core-mantle boundary, respectively, and 8z is a depth scale determined by the seismic wavelength (X0 = 2n Vs/a>0)where co0 is the center frequency of the band pass. Revenaugh and Jordan (1991b) note that for a center frequency of 25 mHz, the wavelength in the transition zone is « 150 km. They go on to show that the reflection coefficient of a discontinuity decreases as the width of a seismic discontinuity, 5z, increases relative to the seismic wavelength, but that i f the discontinuity width is less than «30 km, the apparent reflection coefficient will underestimate the actual value by less than 20 %. Since most estimates for the widths of the upper mantle and transition zone seismic Chapter 3, page 296 discontinuities are thinner than 30 km, the apparent ScS reflectivity estimates (e.g. i?0(410)) will be robust. Revenaugh and Jordan (1991) note the inferred reflectivity profile is modeled by trial-and-error fitting of theoretical reflectivity profiles to the seismic profile - the theoretical profiles are generated from simple layered models where the depth and reflection coefficients of a small set of discrete discontinuities are superimposed on a reference density and shear velocity model (they use a modified P R E M as the reference model where the 220 km seismic discontinuity has been stripped away). In their technique strong velocity gradients which may be distributed over the transition widths are ignored in forward modeling the theoretical reflectivity profiles. Lastly, Revenaugh and Jordan (1991b, c) note that the reported depths and reflectivity values depend slightly upon the validity of the reference seismic model they use. Of interest here is that it is straightforward to calculate the shear wave impedance, Is (z) = p(z) Vs (z), and hence, estimate the ScS reflectivity, i?0(z) for the seismic discontinuities in the pyrolite model (density and Vs velocity profiles) and compare this against the seismic estimates determined by Revenaugh and Jordan (1991a, b, c) and Revenaugh and Sipkin (1994a) for corridors located in the Western Pacific and Asia. In calculating the reflection coefficients for the pyrolite model, I first smooth the density and velocity profiles by simply fitting 2nd order polynomials to the upper mantle (100-380) and lower most transition zone legs (520-660 km) and a linear equation to the upper most transition zone (415-465 km). This is shown in figure 3.30 and the coefficients of the equations are given in table 3.12. The functions facilitates extrapolating the velocity and density profiles to the mean depths Chapter 3, page 297 Table 3.12 Coefficients of the constants used in the polynomial fits to the predicted Vs and Vp velocity profiles. depth interval Vs profile 100-380 km FS = a + bD + cD 2 a b c 4.34338 0.00125899 -2.24346 xlO"7 415-465 km Vs = e + dD e d 4.28931 0.00177796 520-660 km FS=a + bD+cD2 a b c 4.76666 0.00127725 -3.20879 xlO"7 ^profile 100-380 km Vp = a + bD+cD2 a b c 7.6536 0.00303378 -3.09624 xlO"7 415-465 km Vp =e + dD e d 7.69362 0.00372844 520-660 km Vp = a + bD+cD2 a b c 8.19115 0.00360915 -1.05641 xlO"6 density 100-380 km p = a + bD+cD2 a b c 3.25813 0.000786425 1.40333 xlO"7 415-465 km p = e + dD e d 3.3295 0.00103239 520-660 km p = g + hD g h 3.44417 0.000894698 of the upper mantle and transition zone seismic discontinuities (410 km, 520 km, and 660 km) and I stress that fitting the above functions does not shift the velocity profiles to higher or lower values. I also show the smoothed velocity profiles in figure 3.31 which compares the velocity profiles to the global average reference seismic models MD89ps, iasp89, iasp91, and akl35. I note that the major affect of smoothing is to "iron out" the shallow velocity Chapter 3, page 298 gradient from 460 km to 520 km that reflected the broad equilibrium width of the p-to y-olivine phase transition that exists in the Ita and Stixrude (1992; 1993) pyrolite mantle. Effectively, this phase transition has been squeezed down to zero width and located at 520 km depth. The net effect of smoothing the profiles, in terms of calculating reflection coefficients, is to simplify the pyrolite velocity and density profiles into a simple layered model that contains discrete discontinuities. In calculating the shear wave reflectivity, I need only the density and Vs velocity profiles and for the upper mantle and transition zone theses are shown in figure 3.32 together with the related profiles of akl35, PA5, a regional oceanic upper mantle velocity and density model representative of the velocity structure beneath old (125 Ma), SW portions of the Pacific plate, and SSFIT1 (Shearer, 1996), a slightly modified iasp91 shear wave velocity model. While I have already remarked on the similarities and differences between the calculated pyrolite model and these seismic models, it is clear from this figure that the smoothed pyrolite profiles provide an excellent representation of the velocity and density profiles of the transition zone as inferred by these seismic models. The calculated shear wave reflectivity for an assumed transition width 8 of 4 km is shown in figure 3.33 along with the individual reflectivity values determined by Revenaugh and Jordan (1991c) and Revenaugh and Sipkin (1994a). At the 410 km discontinuity, the smoothed density and velocity profiles combine to predicts a value of R£yr"'"e (410) = 0.043 in excellent with the preferred composite value of R0 (410) = 0.046 ± 0.010. Likewise at the 520 km discontinuity the smoothed pyrolite model predicts a value of RPyr°'"e(520) = 0.020 which is slightly more than the seismic composite value of RQ (520) = 0.014±0.004. Finally, Chapter 3, page 299 at the 660 km discontinuity, the pyrolite model predicts a value of R£ywlile (660) = 0.0575, again slightly below the preferred value of Revenaugh and Jordan (1991b) of i? 0 (660) = 0.072±0.010. However, I note the average of the reported data (in table 1 of Revenaugh and Jordan, 1991c and table 2 of Revenaugh and Sipkin, 1994a) is less than their preferred value with an arithmetic mean of R0 (660) = 0.059±0.010. Unlike the value advocated by Revenaugh and Jordan (1991b), this value is nearly indistinguishable from that of the pyrolite model. A l l of the predicted values increase i f the assumed transition width is 10 km, rather than 4 km, and this is shown in figure 3.34. Now the predicted normal incidence shear wave reflectivity is indistinguishable from the seismic observations. Lastly, I note that the smoothed model cannot predict the sparse, positive reflection coefficients observed at « 750 km depth - the shallow gradient in the pyrolite model predicts a negative change in shear wave reflectivity. However, I note that the seismic models originally used in trial-and-error fitting of the reflectivity profiles are simple models with discrete velocity and density jumps and hence, it is not clear how a relatively wide zone with a shallow velocity gradient such as that between 660-730 km would influence the estimates of reflectivity using the methodology used here. In contrast, Stixrude (1997) has calculated frequency dependent estimates of the shear wave reflectivity for the garnet to perovskite phase transition, the reaction responsible for the high gradient zone from 660 to 730 km depth. He also incorporated the effects of a non-linear yield of the high pressure phase across the phase transition in his calculations. He found that the non-linearity caused the effective width of the phase transition to narrow from Chapter 3, page 300 the full width, such that the calculated shear wave reflection coefficient is in excellent agreement with the ScS reverberation observations of Revenaugh and Jordan (1991b). 3.21 F P reflectivity While much recent attention has been focused on the sharpness of the 410 km and 660 km discontinuities from reflected short period (0.8 - 2.0 sec) P-waves (e.g., Benz and Vidale, 1993; Vidale, et al., 1995; Neele, 1996), there is less information on the magnitude of the velocity jumps required to produce the seismic observations. Inspection of figure 3.35 reveals that the smoothed pyrolite Vp profile provides an excellent match to the various seismic models. The predicted velocity jump across the 410 km discontinuity is AVp - 4.30 %, in good agreement with the globally averaged velocity models akl35 and iasp91 (AVp = 3.65 %), but somewhat less than that inferred in the regional "410 reflector" model of Vidale et al. (1995; AVp= 5.3 %). This regional model was constructed to explain near-critical reflections off the 410 km discontinuity from nuclear explosions at the Nevada test site and recorded in the Pacific Northwest (Vidale et al., 1995). It is not clear i f the discrepancy between the "410 reflector" model and the pyrolite model is significant or not, since the absolute velocity in the calculated pyrolite model is slightly faster than the "410 reflector" model above 410 km depth, but in excellent agreement below this depth. Furthermore, while the Vidale et al. (1995) velocity profile has a steeper velocity gradient than the pyrolite model from 200 to 410 km, the average velocity over this interval for the two models is nearly the same. Consequently, a possible trade off between the magnitude of the velocity jump in the "410 reflector" model and the 200-410 km interval Chapter 3, page 301 absolute velocity profile may permit the pyrolite model to equally satisfy the seismic observations for this particular seismic study. Also shown in figure 3.35 is an estimate for the velocity jump across the 410 km discontinuity by Neele (1996) to explain short-period (1 Hz) P-wave reflections off the 410 km in the Gulf of California. Neele (1996) determined the velocity directly below the 410 km to be 9.40 km/s while directly above the velocity is 8.85 km/s giving a velocity jump of 6 ±2 %. A velocity of 8.85 km/s agrees very well with the pyrolite model, but the predicted jump in Vp for the pyrolite mineral physics model (4.30 %) only just satisfies the lower most error bound given by Neele (1996). Descending to the 660 km discontinuity (there are no seismic observations on the Vp reflectivity of the 520 km discontinuity) it is clear that the pyrolite model predicts a significantly smaller velocity jump across the 660 km than the global reference velocity models - this feature is in no way due to smoothing the lowermost portion of the transition zone. The predicted jump across the pyrolite mantle is only AVp = 3.13 %, much less than the globally averaged velocity models akl35, iasp91 (AVp = 5.78 %), or P R E M (AVp = 4.77 %). However, the predicted pyrolite AVp is very similar to the seismic AVp in EK1, a modified iasp91 Vp model proposed by Estabrook and Kind (1996). They noted from a large (>20,000) global data set of stacked long-period seismograms that there was a complete absence of underside reflections off the 660 km seismic discontinuity for the P P phase (see figure 3.36 for simple ray paths for these phases), in contrast to what is predicted for the iasp91 velocity model (see figure 3.37). The top panel in this figure shows the stacked observations, the middle panel shows the prediction resulting from the iasp91 model, while the bottom panel illustrates, in simplified form, the expected position of the various mantle Chapter 3, page 302 reflectors. Note that while the iasp91 model predicts an underside reflection P 6 6 0 P (middle), it is missing in the observed global stack (top). Estabrook and Kind (1996) noted that the excellent shear wave reflectivity of the 660 km discontinuity (e.g. Revenaugh and Jordan, 1991b) when considered together with their results demanded that any adjustments to the iasp91 model must concentrate on reducing only the Vp velocity jump in iasp91 to satisfy the reflectivity observations. Their final model, labeled EK1 in figure 3.38 and 3.35 has a jump of only AVp = 2.5 %, which compares very well to that in the pyrolite model (AVp= 3.13). While the velocity profile of EK1 is significantly different from both iasp91 and the pyrolite model in the immediate area of the 660 km discontinuity, with the inferred velocity gradients directly above and below the 660 km discontinuity at odds with both seismic and mineral physics models, it should be stressed that this difference is not significant from the point of view of the reflection properties of near incident seismic energy. The sole rational of the adjustments in the P-wave velocity profile which result in EK1 is to reproduce the predicted P-wave reflectivity and not to match waveforms. To satisfy the waveforms it is anticipated that much greater attention to the velocity gradients of the proposed EK1 profile would be needed. For example, the variable velocity gradients in the regional oceanic seismic model PA5 (Gaherty et al., 1996) reflect the fact that this particular model was constructed to satisfy many SH and SV waveforms, in addition to other S-wave seismic observations. The PA5 shear wave velocity profile is significantly different from that of pac91 (Kennett, 1992; see figure 3.40), a regional oceanic model constructed to give better agreement between travel times for purely oceanic earthquakes as compared to travel times predicted from the global reference model Chapter 3, page 303 iasp91, which was constructed with a "continental-style" upper mantle velocity structure (Kennett and Engdahl, 1991). A n indication of the similar Vp reflectivity of the pyrolite mineral physics model and EK1 is provided by calculating normal-incidence Vp reflectivity as was done for shear waves. This is shown in figure 3.41 where the predicted reflectivity for the smoothed pyrolite model, iasp91 and EK1 are compared. As noted above, the pyrolite model has a slightly higher Vp velocity jump than EK1, but this is offset by the lower pyrolite density jumps such that the calculated reflection coefficient of the pyrolite model is only slightly less than £ £ 7 . Lees et al., (1983) used a ratio of the amplitudes of the precursor phase P'660P', an underside reflection off the 660 km seismic discontinuity (see figure 3.42), to that of the PT' phase via: P'660 P'/P'P' to infer the Vp reflectivity of the 660 km seismic discontinuity. From reported values for the P'660 P'/P'P' amplitude ratio, which range from 0.1 to 0.2, they estimated the Vp reflection coefficient should range from R = 0.07 to 0.13 (see figure 3.43). They noted however that these values for the reflection coefficient are anomalously high; the highest value calculated for PREM, assuming a sharp discontinuity at 660 km depth is R = 0.07, and thus the higher values inferred from seismology are problematical. Nevertheless, they estimated the reflection coefficient from a number of simple mineralogical models obtaining value of less than 0.005% and concluded that the 660 km reflectivity is not consistent with a phase transition and that a chemical change must occur at this discontinuity. However, I note that a recent seismological study that recorded unambiguous P'660P' and PT' phases collected from a wide 700 station array (Benz and Vidale, 1993) noted that calculating the ratio of the relative amplitudes between P'660P' and PT' phases was Chapter 3, page 304 uncertain since the appropriate attenuation model from 660 km depth to the Earth's surface in the area of PT' bounce points is poorly known (the PP' phase is reflected off the Earth's surface, whereas the P'660P' phase is reflected off the 660 km discontinuity, hence, the PT' phase travels a longer path than the P'mP' phase and the extra loss of seismic energy, manifested in a decrease in amplitude, must be accounted for. Thus, use of an incorrect attenuation model will introduce errors into the amplitude of the P'P'phase, and hence, error into the P ' 6 6 0 P ' / P ' P ' amplitude ratio). That the values of P ' 6 6 0 P'/P'P'amplitude ratios are indeed incorrectly estimated, and hence, the required 660 Vp reflectivity overestimated, is indicated by the results of Estabrook and Kind (1996). As noted above they found that the Vp velocity jump in iasp91 (which is less than PREM) had to be significantly reduced to explain the absence of PP precursors. Lees et al., (1983) inferred a seismic Vp reflection coefficient that ranges from R = 0.07 to 0.13, significantly greater than that of EK1 (R « 0.045), akl35 (R « 0.067) and the pyrolite mineral physics model (R « 0.035; see figure 3.43). Recently, X u et al. (1998) studied the 410 and 660 Vp reflectivity using precursors to the P'P'df seismic phase. This phase does not suffer the problems associated with precursors to PP'ao, the phase used by Lees et al. (1983), in that P'P'df does not occur near a caustic, hence making it relatively more straightforward to estimate the high-frequency reflection coefficient. They stacked signals (>600) recorded across the California Seismic Network for a single earthquake located in the Tonga subduction zone and were able to recover clear reflections off the 410 and 660 km discontinuities. The derived reflection coefficients are 2.2% and 5.0 % for the 410 and 660 respectively and are plotted in figure 3.41. Inspection of this figure clearly shows excellent agreement between their 660 km Vp Chapter 3, page 305 reflection coefficient and that inferred by Estabrook and Kind (1996) and that calculated here for the pyrolite mineral physics model. 3.22 Discussion The results obtained here for predicted Vs and Vp velocity profiles demonstrate that a pyrolite mantle provides an excellent fit to the seismic observations of the upper mantle and transition zone. This conclusion is in complete agreement with the results obtained by comparing calculated density and bulk sound velocity profiles to the associated seismic observations. The value estimated here for the unmeasured shear modulus temperature derivative of the y-olivine shear moduli is both mineralogically plausible, and consistent with thermodynamic approximations (e.g. Isaak, 1992) that also give excellent predictions for the measured parameters for a-and (3-olivine. Table 3.7, discussed earlier, compares the elastic data used for the olivine phases in this and other studies. It is evident from this table that the recent acquisition of experimental measurements of the temperature and pressure dependence of the bulk and shear moduli have significantly reduced the number of unknown parameters for the olivine phases. A direct consequence is that because I have not had to relay upon mineral systematics as heavily as previous modeling studies, the conclusions drawn here are on much firmer basis than any of the early work. Unlike previous studies (e.g. Duffy and Anderson, 1989; Weidner, 1986) I first constrained the mineralogy and the temperature structure of the mantle, via modeling of density and bulk sound velocity profiles, which allowed these properties to remain fixed in modeling Vs and Vp velocity profiles. This approach significantly reduces the number of Chapter 3, page 306 variables with which to consider during modeling of Vs and Vp and focuses attention on the shear modulus and its related temperature and pressure derivatives. I concentrated only on predicting Vs and Vp velocity profiles for the pyrolite model, since I determined that it, and not piclogite, satisfies the more stringent constraints provided by p and V0 where all the required elastic data is measured. While the pyrolite bulk composition is not unique, and it is likely that other suitable bulk compositions can be found that also fit the p and V0 constraints, I adopted pyrolite as a successful compositional model and focus on the question of whether or not a pyrolite mantle can satisfy the seismic Vs and Vp constraints. I find that the predicted Vs and Vp velocity profiles agree very well in absolute value and in terms of the velocity gradient with seismic profiles derived from both regional and global studies. Notably, the most recent oceanic, regional model (PA5) which incorporates a 520 km seismic discontinuity and allows independent velocity gradients above and below this discontinuity is the seismic model which shows the best agreement with the predicted pyrolite velocity profiles. Prior studies that stressed the velocity gradients as a strong criteria in discriminating between plausible compositional models in the transition zone used seismic models that do not include the 520 km seismic discontinuity and hence have a constant velocity gradient across the full extent of the transition zone. Therefore, while these prior studies erroneously concluded that isochemical models fail to satisfy the seismic velocity gradient, they were using seismic profiles which possessed an "averaged" transition zone velocity gradient which did not distinguish between potentially different gradients above and below this discontinuity. Thus, the discrepancy found in these early studies between the gradients in the seismic and mineral physics models actually reflected larger shortcomings in the seismic model than the mineral physics models. Chapter 3, page 307 The seismological properties of the 410 km discontinuity may be compared to extrapolated experimental properties for the a - and (3-olivine phases to place constraints on the olivine content of the mantle. I found that for the experimentally measured value for the temperature derivative of the p-olivine shear modulus, the pyrolite model predicts mutually consistent values for the olivine content for V$ and Vp when the seismic jumps for the high resolution, regional, oceanic model PA5 is used. Furthermore, the predicted olivine content (59 vol%) is in good agreement with the experimentally determined olivine content (62 vol%; Irifune, 1987) for a pyrolite mantle. I point out that using the 410 km discontinuity to place constraints on the olivine content assumes that the mantle above and below the phase transition is isochemical. If the conclusions of Duffy and Anderson (1989) and Duffy et al. (1995), who argue for a piclogite composition (40 vol. % olivine), were correct, then there must exist a global chemical boundary and related thermal boundary layer, somewhere below the deepest depth extent of the continental roots (« 250-300 km; Grand 1994, Nolet et al., 1994), yet above the 410 km seismic discontinuity. Since no seismic evidence exists for such a global discontinuity within this depth interval, those who advocate a piclogite model must claim that such a boundary is seismically invisible. A major difficulty with such a hypothesis is that all of the thermoelastic properties for the upper mantle mineral phases are presently measured, and thus, one may not appeal to an unmeasured property to explain such an invisible boundary. If one were to entertain such a hypothesis one must also address the problem of mixing entrained mantle of the shallow upper mantle by subducting lithosphere with the chemically distinct, transition zone mantle. Because subducting oceanic lithosphere is unambiguously seismically imaged from the Earth's surface down to 660 km depth (e.g. Lay, Chapter 3, page 308 1994) and at least for some subduction zones, down to the core-mantle boundary at 2891 km (Grand et al., 1997; van der Hilst et al., 1997). It is difficult to imagine how a piclogite mantle, from 410 to 660 km depth (and potentially deeper), has escaped wholesale mixing with the overlying pyrolite mantle during Earth's history (recall that the chemical layering invoked is inferred to reflect relict layering that was created by freezing a global magma ocean that existed in the Earth's earliest history). Numerical and tank models demonstrate that subducting slabs should entrain a significant volume of the adjacent mantle during descent through the mantle (Griffiths and Turner, 1988). Thus, the observation of slab penetration to at least the 660 km discontinuity makes it a near certainty that the upper mantle and transition zone is being actively mixed and stirred by subducting oceanic lithosphere. Such problems concerning mixing or invisible chemical or thermal boundary layers do not plague the isochemical pyrolite model. The calculation of shear wave reflectivity demonstrates that the pyrolite model is also capable of satisfying velocity contrasts at the 520 and 660 km discontinuities, in addition to matching the velocity jumps across at 410 km depth. A n unexpected result from calculating both the S- and P-wave reflectivity was the predicted low P-wave reflectivity at the 660 km discontinuity. Estabrook and Kind (1996) had invoked the piclogite (low olivine content) model to explain the small jump in Vp across 660 km discontinuity. In contrast, I find that the different reflectivity between S and P-waves at 660 km depth is a natural product of the pyrolite mantle; there is no need to invoke a change in chemistry across this discontinuity to satisfy the reflectivity observations - an isochemical pyrolite mantle satisfies both sets of observations. Chapter 3, page 309 While I have concentrated on comparing the predicted pyrolite Vs and Vp profiles to seismic observations, the next step in testing these models would be to use them directly in seismic studies. That is, to adopt the pyrolite profiles as the starting model in any inversion scheme and then determine how the profile must be adjusted to satisfy the seismic observations. For example, it would be interesting to determine how much the pyrolite models must be perturbed to satisfy the seismic constraints that were used to generate the high resolution seismic models AU3 and PA5 (Gaherty and Jordan, 1995; Gaherty et al., 1996). While not discussed here, the pyrolite model has been extended to include anisotropy in the shallow upper mantle and the presence of small amounts of silicate melt to facilitate comparison with these two seismic models (Calderwood, 1997) and the effects of attenuation (Calderwood, 1998). These features should allow a more complete comparison between the predicted pyrolite velocity profiles with the seismic models. Another area where the pyrolite profiles could be directly tested by seismic constraints is in the transition zone at the 520 km discontinuity. Figure 3.32 plots the smoothed velocity profiles together with the shear wave model SSFIT1 which is an S-wave model constructed to fit the global oceanic reflectivity of the 520 km based on stacked seismograms that show precursors to double bounce (termed "SS") shear body waves (Shearer, 1996). These precursors are underside reflections off the upper mantle discontinuities and Shearer (1996) focused on the reflectivity and velocity gradients around the 520 km discontinuity by using only seismograms with oceanic SS bounce points (to minimize the effect of continental crustal reverberations in the seismograms). He found from simple forward modeling that the SS precursor data require slight modifications to the iasp91 global reference seismic model such that a small 520 velocity discontinuity must be Chapter 3, page 310 inserted and a steeper velocity gradient introduced immediately below the 660 km phase transition down to 727 km depth. In addition, the velocity contrasts across the 410 (AVs = 3.37%) and 660 km (AVg = 4.95%) discontinuities are slightly reduced compared to iasp91(AVg]0 =4.10%; AV£60 =6.25%). SSFIT1 is parameterized in terms of velocity discontinuities separated by linear velocity gradients, and thus to introduce the 520 km discontinuity, the transition zone velocity profile of iasp91 was simply broken at 519 km and the velocity profile above and below shifted slightly to accommodate this discontinuity. However, the velocity gradients above and below the discontinuity were kept the same as that of the starting model iasp91. Shearer (1996) stresses that this model is designed to be as simple as possible and notes that many other models may achieve fits to the seismic observations that are better than SSFIT1. Of interest, is that Shearer (1996) specifically notes that improvements in fit could be made by adjusting the velocity gradients above and below the 520 km discontinuity independently - unfortunately, these velocity models are not presented. Nevertheless, it would prove instructive to adopt the pyrolite shear wave profile to determine i f such velocity gradients are indeed allowed by the SS waveform observations. By constructing a mineral physics which satisfies a number of diverse seismic observations (discontinuity reflectivity at the 410, 520, and 660 km discontinuities, velocity gradients across the upper mantle and transition zone), one may be able to place tighter constraints on the values for the pressure and temperature derivatives for the y-olivine shear moduli than what can be achieved by simple visual comparison between the seismic and mineral physics profiles. Chapter 3, page 311 3.23 Conclusions The purpose of this research is to determine i f calculated profiles of Vs and Vp, for a pyrolite composition that utilized an self-consistent adiabatic geotherm, can successfully match the seismologic observations across the upper mantle and transition zone. The rational for focusing only on the pyrolite model is that by using a "viable" compositional model and its self-consistent adiabatic geotherm, I may concentrate on the unmeasured value of the shear modulus temperature derivative of y-olivine which is required to obtain a match between the predicted and observed Vs and Vp profiles. I initially estimate a value for the temperature derivative using the empirical relationships proposed by Isaak (1992) and Anderson (1988) and then adjust this to optimize the fit to the seismic profiles. I check the resulting set of temperature and pressure derivatives to ensure that the inferred of comparing the shape and velocity gradient of the predicted Vs and Vp profiles to observed profiles, the predicted profiles are also used to calculate a number of seismic properties, such as S- and P-wave reflectivity, that also test the viability of the pyrolite Vs and Vv profiles. In contrast to previous studies, I obtain an excellent match throughout the upper mantle and transition zone with a uniform pyrolite composition without requiring any thermal or chemical boundaries in the upper mantle or transition zone. Specifically, the magnitude of the seismic jumps at the 410, 520, and 660 km discontinuities as inferred from a recent high resolution, regional oceanic seismic model give mutually consistent estimates ( A F 0 « AVs ~ AVp) of the olivine content (59 vol%) which is in good agreement with that of a pyrolite mineralogy (62 vol%). Furthermore, a relatively trivial modification to the P-wave Y-olivine is "mineralogically plausible". Lastly, in addition to the traditional criteria Chapter 3, page 312 velocity structure in the current global reference seismic model akl35 directly above the 410 km discontinuity, results in this seismic model giving mutually consistent estimates of the olivine content of A F 0 « AVs~ AVp « 62 vol%. These results are in agreement with the conclusions drawn from the previous chapter that involved modeling only density and bulk sound velocity profiles throughout the mantle. In terms of the velocity gradients in the transition zone, I find that the pyrolite mineral physics model predicts velocity gradients which are in good agreement to that inferred from PA5, a recent regional oceanic seismic model which was constructed such that the velocity gradients above and below the 520 km discontinuity were free to vary. Significantly, this seismic model predicts that the velocity gradient decreases across the 520 km discontinuity, a feature also found in the pyrolite mineral physics model. I conclude that previous studies which asserted that isochemical models were ruled out on the basis of the misfit between predicted mineral physics velocity gradients and inferred gradients from seismic models which did not incorporate a 520 km discontinuity are incorrect. Seismic models which do not incorporate a 520 km discontinuity and do not allow the velocity gradient to vary above and below this feature will lead to erroneous conclusions since the velocity gradient from 410 to 660 km depth in such models will be averaged value that is unlikely to reflect the true velocity gradient in either the 410 to 520 km or 520 to 660 km depth intervals. The predicted reflectivity of the pyrolite mineral physics model gives excellent agreement with independent seismic S- and P-wave inferences of the near-normal incident reflectivity of the 410, 520, and 660 km discontinuities. Notably, the isochemical pyrolite model predicts significantly different values for the magnitude of the S- and P-wave jumps Chapter 3, page 313 across the 660 km discontinuity, a feature which has not been documented in previous mineral physics studies. Nevertheless, this feature results in predicted S-and P-wave reflectivity at the 660 km discontinuity which is in excellent agreement with the latest seismic observations (e.g. Revenaugh and Jordan, 1991b; Revenaugh and Sipkin, 1994a; Estabrook and Kind, 1996). The results presented here do not support the early conclusions of Lees et al (1983) that the seismic P-wave reflectivity at the 660 km discontinuity demands a chemical boundary at this depth. Although not considered in detail here, the high velocity gradient from 660 to 730 km depth is also consistent with ScS reverberation when frequency and non-linear phase change properties are accounted for (Stixrude, 1997). Hence, the weak reflections immediately below the 660 km discontinuity are not a feature which is in conflict with an isochemical interpretation of the transition zone. 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C u C u T J T J co co o o CO P 0" o~ PP RP ct ct Cu' ol 3 3 ft ft V O V O V O V O —] o v vo 00 VO o K J o © 1— 1— CO vo vo t r *o vo a Ov Os O -C.OQ s a c * C u » CO p _ OV 1 + Ov 1+ O J K J 00 Ov 1+ H • CO CO ^1 vo L/i o o © © I—1 OJ K J C/3 9 ^ T3 P P O T J H c r n> O J CD 2 . -4^ n o P 3 H P CD q & s o T l CD o CD ~CD ^3 Cu CD CD CD Cu P c CO CD Cu CO co B Cu O tr T3 CD 13 P CfQ CD O J VO P CO m m m m c e 3 3 ro ft C L C L ft ft c c CO co 3 3 rt ft B" B> ft a. ex C L ft ft cf> c c 3 P p ^ ~ ~ 3 CfQ era CfQ ft P " 6j O O P mm'— m m m e c v : P P S -I I ft o 3 n P era P P 3> ft a c C L > 3 C L ft -1 O 3 SO OO SO cr c B C L ft' on < P ft H *—»• OO 00 Cu © O o GO <-»-9-V J 3$ p P a H o n X xs CD 3 P co O & 3 TS p oo' o 13 oo O o p o Jo CD ~CD CD "5= CD CD CD CD CD Cu a P S3 oo CD CL 3' Er S3 CL rt o re 3 O cr rt P CTQ CO O J o n o Chapter 3, page 351 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 V o l u m e % P y r o l i t e Figure 3.1 Volume percentage of the mantle minerals present in the pyrolite model as a function of depth. Figure redrawn from Ita and Stixrude (1992). Chapter 3 , page 3 5 2 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Fe content of Betta Olivine Figure 3 . 2 . Inferred linear relationship of the shear modulus for betta-olivine as a function of Fe content. Chapter 3, page 353 1580 cr 1570 GO. B o 1560 1550 GO I CD 5 1540 O > ^ 1 5 3 0 u ' H l 5 2 0 ^ I P Equation: Y= 61.0121 *X+ 1514.41 1 Data sources: Ohtani et al, 1991 Sinogeikin et al, 1996 (AGU abstract) Sinogeikin et al, (1997) Pacalo & Weidner (1997) Yagi et al, 1992 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Fe content of Majorite 1.0 Figure 3.3. Inferred linear relationship of unit cell volume for Majorite as a function of Fe content Chapter 3 , page 3 5 4 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 F e c o n t e n t M a j o r i t e Figure 3 .4 . Inferred linear relationship of the adiabatic bulk modulus for Majorite as a function of Fe content. Chapter 3, page 355 0.00 0.20 0.40 0.60 0.80 1.00 F e - c o n t e n t o f M a j o r i t e Figure 3.5 Inferred linear relationship of the shear modulus for Majorite as a function of Fe content. Chapter 3, page 356 a o 1 O > 134 132 -130 -128 -126 -124 -122 F-120 118 I-116 P T I 1 I 1 I 1 I 1 I ' I ' I ' I ' I Fit 1: Linear, Y=B*X+A Equation: Y= 19.5738 *X + 114.01. Hazen et al, 1994b 114f^ Pacalo & Weidner, 1997 112 P-*" • I • I • 1 • I • I • 1 • I 110 I • I i 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 a m o u n t o f C a i n M a j o r i t e 1.0 Figure 3.6 Inferred linear relationship of the molar volume for Ca bearing Majorite as a function of Ca content. 3.55 Chapter 3, page 357 I 1 I 1 I ' I ' I 1 I 1 I 1 I 1 I 3.54 -3.53 -.3.52' 3.51 h '3.50 cn a o 5 g3.49 p ^ 3 . 4 8 3.47 3.46 3.45 Pacalo & Weidner (1997) Hazen et al, 1994a Fit 1: Linear, Y=B*X+A Equation: Y = -0.0489799 * X + 3.522 T i • i • i • i • i • i • i • i • i % 6 i—^ E CO IO 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 a m o u n t o f C a i n M a j o r i t e Figure 3.7 Inferred linear relationship of density for Ca bearing Majorite as a function of Ca content. Chapter 3, page 358 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 a m o u n t o f C a i n m a j o r i t e Figure 3.8 Inferred linear relationship of isothermal bulk moduli for Ca bearing Majorite as a function of Ca content. Chapter 3, page 359 0.00 0.50 1.00 1.50 2.00 2.50 3.00 Figure 3.9 Plot of (d n ld\ )p versus (dp/dP)T for measured compounds with the previous inferred values for betta-olivine and the recently reported experimental values. Abbreviations are; DA89, Duffy and Anderson (1989); DLA88, Anderson (1988); 187, Irifune (1987); W86, Weidner (1986); BW87, Bina and Wood (1987). Chapter 3, page 360 -0.040 -0.035 -0.030 O H O -0.025 C O C O -0.020 -0.015 -0.010 -0.005 0.000 y - olivine I M I | I I I I | I I I I | I M I | I I I I | I I I I Ridgen etal. (1991, 1992)~ • LiF Ti202 preferred value of the pressure^^^ derivative *TiC>2 y - olivine this stu / initial estimate from jGp~ 6 5 + Isaak (1992) v x |_ method ABW87 MgO Z *SrTiOL P~olivine W86t - initial estimate % ZJsaak (1992)^iiethod % # •ADLA88 187 WayaiiteForsterite • i i i t i i i 1 • ' • I ' i ' ' i ' ' ' ' i i i ' ' t cn co I O) CO i 0.00 0.50 1.00 1.50 (dix/d?) 2.00 2.50 3.00 Figure 3.10 Plot of (d u /AT )p versus (5 u Id ?)r for measured compounds with the previous inferred values for gamma-olivine. Abbreviations are; DA89, Duffy and Anderson (1989); DLA88, Anderson (1988); 187, Irifune (1987); W86, Weidner (1986); BW87, Bina and Wood (1987). Figure 3.11. Fourth order fit to the experimental shear moduli as a function of pressure (Abramson et al., 1997). 0 Mid-Ocean Ridge mantle potential temperature 1330 -1350 C (= 1605-1625 K) Chapter 3, page 362 ioo h-200 \ -300 400 8^00 Q 600 700 800 900 I 1 I 1 I T I 1 I 1 I ' I ' I ' I ' Ita & Stixrude (1992; 1993) Ito & Katsura, 1989 (assumed a constant adiabatic gradient) Pyrolite adiabatic geotherm P + 60F ATphase— change + 38.1 K +35 K + 23.6 K Y - > M g - P v + M w - 65 K 30.2 K -1 experimentally bracketed 660 transition temperature (1900 ± 1 0 from a C 0 2 laser D A G study (Boe & Chopelas, \992) Ita & Stixrude (1993) best fit lower mantle geotheYm J I I I I I L_J l _ J I I I I L Pyrolite LM geotherm J I L 1 1200 1400 1600 1800 2000 2200 T e m p e r a t u r e ( K ) Figure 3.12 The calculated pyrolite adiabatic geotherm for the upper mantle, transition zone, and the upper part of the lower mantle. ak±35 900 3.00 3.20 3.40 3.60 3.80 4.00 4.20 d e n s i t y ( g / c m 3 ) 4.40 4.60 Figure 3.13 The adopted bulk density of pyrolite as a function of depth compared to the global reference models akl35-Q and akl35-F density profiles (Montagner and Kennett, 1996) and the high resolution regional models AU3 and PA5 (Gaherty and Jordan, 1995; Gaherty et al., 1996). Chapter 3, page 364 3.00 4.00 5.00 6.00 S - w a v e v e l o c i t y ( k m / s e c ) Figure 3.14 The predicted shear wave velocity profiles for the individual minerals which comprise the Pyrolite composition. Also shown is the VRH average together with the akl35 profile. Chapter 3, page 365 S w a v e V e l o c i t y ( k m / s e c ) Figure 3.15. The predicted bulk shear wave velocity profile of pyrolite as a function of depth. The mean (greem), standard deviation (shaded), and maximum deviation (light blue) of the published seismic velocities as calculated by Ita (1992) are also plotted. 6.00 7.00 8.00 9.00 10.00 11.00 12.00 P - w a v e v e l o c i t y ( k m / s e c ) Figure 3.16 The predicted compression wave velocity for the individual minerals which comprise the pyrolite composition. Also shown is the VRH average profile for Pyrolite together with the akl 35 reference profile. 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 P W a v e V e l o c i t y ( k m / s e c ) Figure 3.17. The predicted bulk compression wave velocity profile of pyrolite as a function of depth. The mean (green), standard deviation (shaded), and maximum deviation (It blue) of the published seismic velocities as calculated by Ita (1992) are also plotted. 0 100 200 300 400 &500 Q 600 700 800 900 Chapter 3, page 368 I- I I I I I I I I I I I I I I I I I I I I I I I ak!35-F iasp89 Pyrolite iasp91 \HJS9ps fc ' ' ' I 1 • i i i i i i I i i ' ' ' ' 4.0 4.5 5.0 5.5 6.0 6.5 S w a v e V e l o c i t y ( k m / s e c ) Figure 3.18 The predicted bulk S-wave velocity profile of pyrolite as a function of depth compared to the proposed global reference seismic models iasp89 (Kennett, 1991), MD89ps (Kennett, 1991), iasp91 (Kennett and Engdahl, 1991), akl35 (Kennett et al., 1995), ak!35-F (Montagner and Kennett, 1996), and the seismic mean of Ita (1992). Figure 3.19 The predicted bulk P-wave velocity profile of pyrolite as a function of depth compared to the proposed global reference seismic models iasp89 (Kennett, 1991), MD89ps (Kennett, 1991), iasp91 (Kennett and Engdahl, 1991), akl35 (Kennett et al., 1995), akl35-F (Montagner and Kennett, 1996), and the seismic mean of Ita (1992). Chapter 3, page 3JQ 0 L I I I I | I I I I | I I I I | I I I I | I I I I -| T T T 100 200 300 ^ 4 0 0 &500 Q 600 700 800 900 E_ PAS AU3 - -- V -1 i— Illllll 4 Pyrolite \\ <^AU3 11 a 111111111 — \ — - I ' l l 1 i i i i 1 i t i i 1 i i i i 1 i i 1111 Iiiiiii 4.0 4.5 5.0 5.5 6.0 6.5 S w a v e V e l o c i t y ( k m / s e c ) Figure 3.20 The predicted bulk S-wave velocity profile as a function of depth compared to the high resolution regional seismic models AU3 (Gaherty and Jordan, 1995) and PA5 (Gaherty et al., 1996). 3 7 Op 100 200 300 400 & 5 0 0 Q 600 700 800 E-900 Chapter 3, page 37 / 1 F T AU3 -Pyrolite ^ iiiiii Illlllllllll PA5— — ^ — t_L 1 i I • I tr CL 3 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 P w a v e V e l o c i t y ( k m / s e c ) Figure 3.21 The predicted bulk P-wave velocity profile as a function of depth compared to the high resolution regional seismic models AU3 (Gaherty and Jordan, 1995) and PA5 (Gaherty et al., 1996). 1 Chapter 3 , page 3 7 ^ 400 500 Q 600 700 1 1 1 1 1 1 1 1 1 I 1 1 1 1 1 1 1 1 1 I 1 1 1 1 1 i 1 1 1 I 1 1 1 1 1 1 1 1 i PA5 1 \wc91 lSP6 1 c 5U a *5 •5 ft iasp89 ,iasp9V SNA \AU3 eakJ35-F —PREM CREMO •MD89ps PAS I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 1 I I I I I I I I t N "D J J s 0.0000 0.0010 0.0020 0.0030 0.0040 V s v e l o c i t y G r a d i e n t ( k m / s e c / k m ) Figure 3. 22 Comparison of seismic S-wave velocity gradients through the transition zone (410 - 660 km depth) to the predicted Pyrolite velocity gradient. Note the good agreement between the Pyrolite model and the purely oceanic, high resolution regional seismic model PA5 (Gaherty et al., 1996). Both PA5 and AU3 (Gaherty & Jordan, 1995) are the only seismic models which explicitly include a 520 km seismic discontinuity and allow the velocity gradients above and below to differ; all the remaining models treat the transition zone as homogenous. Chapter 3, page 373 400 500 O H Q 600 1111111111111111 i 11111111111 i 1111 i 1111111111111111111111111 iasp89 PyrSlite mineral p^hysics pac91j PA5 PA2 ak!35-F 1 "3 9a PAS A13 EU2 CJK cwMa P R E M H MD89p4 II III I l l l l l I M i l I I l l I II I III l l I II l l l l l l l l III I M i l l l l l l I II I I t CD •o > TJ O 700 0.0000 0.0010 0.0020 0.0030 0.0040 0.0050 0.0060 V p v e l o c i t y g r a d i e n t ( l o n / s e c / k m ) Figure 3.23 Comparison of seismic P-wave velocity gradients through the transition zone (410 - 660 km depth) to the predicted Pyrolite velocity gradient. Again there is good agreement between the oceanic, high resolution, regional seismic model PA5 and the mineral physics model. Only PA5 and the mixed oceanic-continental AU3 seismic models include a 520 km seismic discontinuity and allow the velocity gradients above and below to vary independently; all the remaining models assume that the transition zone is homogeneous. Chapter 3, page 374 Figure 3.24 Predicted olivine content (volume percent) from the 410 km seismic discontinuity jumps in density, bulk sound velocity, S-wave, and P-wave velocity (after Bina, 1993). Horizontal lines indicate the expected olivine content for the pyrolite (Ringwood, 1975, 1991; Irifune, 1987) and piclogite compositional models (Bass and Anderson, 1984; Anderson and Bass, 1984; Anderson and Bass, 1986; Duffy and Anderson, 1989). Chapter 3, page 375 a . a , 2 0 10 0 * — A & B 8 4 (22% olivine) " — • B & A 8 4 a (16% o l i v i n e )-— — 1 1 *3 4 ? ,0 s 4 ' 4 to Figure 3.25 Predicted olivine content (volume percent) from the 410 km seismic discontinuity jumps in density, bulk sound velocity. S-wave. and P-wave velocity using pyrolite mineral physics model together with the akl35, iasp91, AU3, PA5. P R E M or C R E M O seismic models. Chapter 3, page 376 b 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 d 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 P w a v e V e l o c i t y ( k m / s e c ) Figure 3.26 The predicted pyrolite P-wave velocity profile compared to the high resolution, oceanic regional seismic models PA5 (Gaherty et al., 1996) and the original akl 35 model (Kennett et al., 1995) and the modified version discussed in the text which results in consistent estimates for the olivine content across the 410 km discontinuity. Chapter 3, page 377 100 90 h 70 h 5 = I 50 Irifune, 1987 (62%) todified iasp 91 modified akl3S o r—I S ^ 40 cu a, CD I 30 20 10 0 D & A 8 9 (40% olivine) -A & B 8 6 (30% olivine) A & B 8 4 (22% olivine)" — B&A84a (16% olivine) — I 1 O) a f t Figure 3.27 Predicted olivine content (volume percent) from the 410 km seismic discontinuity jumps in density, bulk sound velocity, S-wave, and P-wave velocity using the modified akl 35 and iasp91 seismic models where the P-wave velocity directly above the 410 km discontinuity was decreased such that the prediced olivine content was self-consistent. Note that by only adjusting the P-wave jump of the seismic model, both the P and bulk sound velocity predictions are affected (but the S-wave prediction remains unaltered). Chapter 3, page 378 8.00 9.00 10.00 11.0O 1- 2 0 3- 4 0 3- 6 0 3- 8 0 4 0 0 4 - 2 0 4 - 4 0 4 - 6 0 VP ( k m / s e c ) d e n s i t y ( g / c m 3 ) Figure 3.28 Comparison of the predicted density and Vp velocity profiles to that calculated by Lees etal. (1983). Chapter 3, page 3 7 9 S660 4SScS 2 ScSS660 +SScS ScS 2S669+S t CO CN, Figure 3.29 Schematic ray paths for the ScS family of reverberations. The top three diagrams represent topside reflections from the 660 km discontinuity that constructively interfere to produce an observable arrival. The bottom two diagrams are similiar, but represent underside reflections off the 660 km discontinuity. Figure from Revenaugh and Jordan (1989). Chapter 3, page 380 D e p t h k m Figure 3.30 Smoothed density, S- and P-wave velocity profiles as a function of depth. 200 300 400 600 700 800 900 Chapter 3, page 381 I ' I 1 I iasp89 Smoothed Pyrolite profiles MD89ps akl 35 iasp91 iasp89 MD89ps q ukl3r-• iasp9l — yi \* — — IIIIMIIIIIII 1. 1 . 1 . 1 . 1 . ME 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 V e l o c i t y ( k m / s e c ) Figure 3.31 Smoothed S- and P-wave velocity profiles as a function of depth compared to profiles from global reference seismic models. 0 50 100 150 200 250 ^ 3 0 0 ^ 4 0 0 Q?450 Q 500 550 600 650 700 750 800 T T Chapter 3, page 382 1 PA5 (Gaherty, Jordan & Gee, 1996f~^ ^ V /,(*+5*)+ discontinuity transition width = 5z id — U IT^ iasp91 lit ^smoothed Pyrolite 1SFIT1 (Shearer, 1990, — 111111 1 111111 • 1 1 1 111111 3.00 4.00 5.00 6.00 7.00 smoothed S-wave velocity and density profiles Figure 3.32 Smoothed density and S-wave velocity profiles as a function of depth compared to PA5, a high resolution regional model for old (»120 Ma) Pacific oceanic upper mantle (Gaherty et al., 1996). Also shown is the transition zone S-wave model SSFIT1 of Shearer (1996). 0 Chapter 3, page 383 100 200 300 4^400 OH Q 500 EF 600 700 E T T T 3 smoothed Pyrolite profiles transition width, 8 z = 4 km. mean, Western Pacific + China q PA5 Revenaugh & Jordan 1991 suggested value PAS (cross) mean of total seismic data 800 i i 0.00 0.02 0.04 0.06 0.08 0.10 0.12 normal-incidence shear wave Reflectivity Figure 3.33 Predicted normal-incidence shear wave reflectivity as a function of depth for an adopted transition width of 4 km. Note the effect of increasing the transition width is to increase the predicted S-wave reflectivity. 0 Chapter 3, page 384 c—r 100 200 300 ^ 4 0 0 O H Q 500 600 700 800 T T i — • smoothed Pyrolite profiles transition width, 8 z = 10 km. mean, Western Pacific + China PA5 Revenaugh & Jordan 1991 suggested value PA5 (cross) mean of total seismic data l i 1 i 0.00 0.02 0.04 0.06 0.08 0.10 0.12 normal-incidence shear wave Reflectivity Figure 3.34 Predicted normal-incidence shear wave reflectivity as a function of depth for an adopted transition width of 10 km. Chapter 3, page 385 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 V p ( k m / s e c ) Figure 3.35 Predicted P-wave velocity profile as a function of depth. Also shown for comparison are velocity profiles inferred from seismic data (Vidale et al., 1995; Neele, 1996; Estabrook and Kind, 1996; Gaherty et al., 1996) Chapter 3, page 386 PP bouncepoints Figure 3.36 Schematic ray paths for the PP waves and the underside precursors P410P and P660P. There exist equivalent S-wave paths (figure from Shearer, 1996). Chapter 3, page 387 t 01 CO. Figure 3.37 Predicted and observed stacked and normalized travel times as a function of epicentral distance (Estabrook and Kind, 1996). The top panel (A) is the observed stack of 20,000 digital seismograms normalized to the PP phase, the thick, horizontal solid red-blue-red tricolour band located at 0 second time. The end points for the expected trace of the P660P precursor phase are marked by the solid black triangles (see also bottom panel (C)). The middle panel (B) illustrates the calculated stacked and normalized travel times as a function of epicentral distance when seismic events are traced through the iasp91 global reference seismic model. Note that iasp91 predicts an observable P660P precursor phase, which is not seen in the compilation of seismic observations in panel A . Chapter 3, page 388 Percent P P amplitude Distance (degrees) Distance (degrees) .o r--Figure 3.38 P-wave velocity models E K l (solid line) and iasp91 (dotted line). Figure from Estabrook and Kind (1996). See also figure 3.29 where E K l is plotted against the smoothed pyrolite mineral physics model. Chapter 3, page 390 S-wave Velocity (km/sec) Figure 3.39 A comparison of the upper mantle, shear wave velocity profile for the oceanic regional model pac91 (Kennett, 1992), PA5 (Gaherty et al., 1996), iasp91 (Kennett et al., 1991), the forerunner of pac91, and the smoothed pyrolite mineral physics model. 0 Chapter 3, page 391 i=—r 100 200 300 4^400 O H Q 500 600 700 800 T smoothed Mineral Physics profiles transition width, fyz = 4 km Pyrolite iasp91, EK1 Xu et al, 1998 Pyrolite Xu et al, 1998 1 i iasp9l 1 T 1—• 1 1 E 0.00 0.02 0.04 0.06 0.08 0.10 0.12 n o r m a l - i n c i d e n c e V p r e f l e c t i v i t y Figure 3.40 Predicted normal-incidence P-wave reflectivity for the pyrolite mineral physics model versus that of EK1 (Estabrook and Kind, 1996), and iasp91 (Kennett and Engdahl, 1991). Note that PREM is not drawn. Chapter 3, page 392 Figure 3.41 Schematic ray paths for the P'660P' and P'P' waves through the Earth together with a schematic waveform illustrating the different amplitudes of the two phases. Figure from Lees et al., (1983). 0.15 | 0.14 j ^ 0.13 I § 0 . 1 2 0.11 W i o o 0 0.09 § 0 . 0 8 O 0 . 75H0.06 P^O.05 § 0 . 0 4 ^ 0 . 0 3 Chapter 3, page 393 ~i 1 1 r——i 1 1 1——l 1 r Seismic estimates x>f the 660 reflection coefficient from observations from amplitude ratios ofP'P' and P'660P' cited by Lees, Bukowinski and Jeanloz (1983) RVp-(A,), W a v e l e n g t h o f i n c i d e n t vp r a y ( k m ) 2TC2 ^ ( / ^ ( r 1 - 1 ) ) I = p V p L sinh ( j - ^ f c - 1 ) ) # ( t r + i ) ) transition zone thickness (km), here assumed = 4 km and the constant 4 is arbitarily increased to maximize the reflection coefficient. Figure 3.42 Predicted 660 km P-wave reflection coefficient as a function of wavelength of incident VP for the pyrolite mineral physics model, EK1, akl 3 5, and PREM compared to the range of calculated 660 VP reflection coefficients discussed by Lees et al. (1983). Note that Lees et al. suspected that the reported seismic values were overestimated and hence adopted a value of » 0.05 rather than the range of 0.07-0.13. Chapter 4, page 394 Chapter 4 Constrained Adiabatic Decompression of a Pyrolite Lower Mantle and constraints on (du./d7^for Mg-perovskite from u.0 and Poisson's ratio (a). Chapter 4, page 395 4.1 Abstract The zero pressure properties (p0, K$0, , Ho) of the lower mantle are commonly obtained by adiabatic decompression, in which an equation of state is fit by least squares to the seismic properties of a reference Earth model. These properties are then compared to plausible compositions, in which the zero pressure mineral properties of the mixture are extrapolated to high temperature, to place constraints on the composition of the lower mantle. However, as noted by Bukowinski and Wolf (1990), adiabatic decompression may lead to biased estimates of the lower mantle properties i f unconstrained fits to seismic model are used. They recommended that by applying apriori constraints on the equation of state that the bias could be eliminated or reduced, and hence, fixed the density, p 0 in the equation of state to values determined for trial mantle compositions. From comparing predicted and observed profiles of density and bulk sound velocity, I have demonstrated that a uniform pyrolite composition provides an excellent fit along an adiabatic geotherm that is consistent with independent temperature estimates of the shallow mantle from decompression melt studies (Tp = 1334°C). Thus, apriori, pyrolite is known to fit the density and bulk moduli throughout the lower mantle. However, an interpretation of the decompressed shear modulus of the lower mantle, p.0 has been the avoided because the shear modulus temperature derivative (|3|j,/9rj ) of Mg-perovskite, the mineral that dominates the composition of the lower mantle, is unmeasured, in contrast to magnesiowustite. To obtain an estimate for|dp./d!rj , constrained adiabatic decompression is applied to the lower mantle region of the P R E M seismic model by assuming that pyrolite is the lower mantle composition. Hence, the density, p0, and bulk modulus, Kso terms in the 4th order equation of state fit are fixed to the high temperature values for a simplified pyrolite composition comprising only Mg-perovskite and magnesiowustite. This results in a new estimate for p.0, which in turn, is used to constrain the parameter (do/dT\ via the relationship: < p decompressed r=1607K ^0 lower mantle ^0 Pyrolite mix where the simplified pyrolite composition is given by: T=1607K / „ \ 7-=1607K »0Pyro,„e m,X = 84 W / % + 16v 0/% ^ V I VRH mix with the predicted high temperature values for the shear moduli of Mg-perovskite and magnesiowustite calculated via: Mg-Pv r=1607K _ Pv re/ 1 - 1 ^ P v 1 -^ m i K = pv^f + ( 5 | a / 5 7 ^ " ( 1 6 0 7 o K - 2 9 8 o K ) Chapter 4, page 396 / / \ Mg-l'v _ decompressed Because the parameter ^dp/9Tj^ is the sole unknown, the new estimate of \^Q,omr m a n l k for ( / \ Mg-l'v d\i/8Tj by determining the value decompressed 7'= 1607 K necessary to satisfy the equality \i0hwer m m l l e = p 0 / , I 'yrolile mix Mg-l'v ( I \ Mg-I'v d\i/dTj = -0.0224 GPa/K, a value that is not abnormal relative to lower mantle silicates. Another avenue of determining ( I \ Mg-l'v \d\jLldTj is to compare Poisson's ratio (a), calculated via: 3-2H 0/J:S 0) (6 + 2n0/tfS0) ' Using Kso and \xn from constrained adiabatic decompression results in a value of a = 0.2439; to match this value by correcting the room temperature and pressure properties of a simplified n I 1 \ Mg-l'v pyrolite to 1607 K and room pressure, constrains (dp/d7j = -0.0224 GPa/K. Thus, conclusions drawn by Poirier (1987) and Weidner and Zhao (1992) that to rationalize the calculated Poisson's ratio with the decompressed lower mantle value required either a high iron content in the lower mantle or an unusually high temperature derivative of the Mg-perovskite shear modulus, are not supported by this study. Chapter 4, page 397 4.2 Introduction There are two ways of comparing elastic data for minerals with seismological observations. The first technique extrapolates known mineral properties to the high temperatures and pressures of the mantle and compares them directly to seismological observations. For example, in chapter two I tested two compositional models by comparing predicted density and bulk sound velocity profiles to the equivalent seismic profiles in P R E M (Dziewonski and Anderson, 1981) and akl35 (Kennett et al., 1995). The second method, followed here, is to adiabatically decompress the seismological observations (density p, compression velocity Vp, and shear velocity Vs) for a given region of the mantle to the Earth's surface and then compare these properties to modeled compositions (Anderson, 1968; Anderson and Jordan, 1970; Davies and Dziewonski, 1975; Anderson, 1977; Sawamoto, 1977; Butler and Anderson, 1978; Stacey et al., 1981; Liu, 1982; Jackson, 1983; Jeanloz and Thompson, 1983; Bass and Anderson, 1984; Ito et al., 1984; Anderson and Bass, 1986; Knittle et al., 1986; Jeanloz and Knittle, 1986; Poirier, 1987; Bukowinski and Wolf, 1990; Stacey, 1996). One weakness of this technique is that the decompressed properties correspond to "hot" values at an unknown high temperature, but at ambient pressure. If independent evedence can be used to demonstrate that the whole mantle is isochemical and lies along the same adiabatic geotherm, then the temperature of the "hot" decompressed properties simply corresponds to the mantle potential temperature. Because the mantle potential temperature of the upper mantle is well constrained by decompression melt studies on mid-ocean ridge basalts, this means that the temperature of the decompressed lower mantle properties is also well known. Thus, in comparing potential bulk compositions against the decpressed properties, one simply has to correct up the Chapter 4, page 398 room temperature properties of the required minerals to the M O R B mantle potential temperature. However, i f the lower mantle has a different bulk composition from the overlying upper mantle and transition zone, and therefore, lies along a hotter adiabatic geotherm than the upper mantle, then the temperature of the decompressed lower mantle properties is very poorly constrained. Decompression is accomplished by fitting an equation of state to the seismic models to estimate the zero pressure values. This technique has been commonly used with the goal of placing constraints on the composition and thermal state of the decompressed region with most studies focusing on the lower mantle (Jackson, 1983). For this region, the spherically averaged seismic profiles are well known and exhibit little variation (unlike the upper mantle and transition zone) and recent 1 dimensional reference seismic models (e.g. P R E M , iasp91, akl35) have differed little over the lower mantle. In addition, the seismic profiles are smooth and without any seismic discontinuities, implying that there is little inhomogeneity or deviations from an adiabatic temperature gradient. While an adiabatic gradient cannot apply completely across the lower mantle, since at the base of the mantle there exists a large temperature jump between the liquid iron-alloy outer core («4000 ±200 °K; Boehler, 1996) and solid, silicate mantle (« 2475 °K; Calderwood, 1996), the bulk of the lower mantle is considered adiabatic to first order. While some researchers have argued there might exist slight systematic non-adiabatic affects (e.g. Heinz and Jeanloz, 1982; Shankland and Brown, 1985; Stacey, 1996), the deviation in the inhomogeneity parameter r\ is slight for P R E M (but not for earlier reference seismic models (e.g. P E M (Dziewonski et al., 1975; 1066B (Gilbert and Dziewonski, 1975); see figure 1 of Shankland and Brown, 1985). The inhomogeneity parameter is defined as: Chapter 4, page 399 O dp T 1 = pgdr where O is the seismic parameter and defined as: and p is density, g is the acceleration of gravity, and (dp/dr)is the radial derivative of density. As noted by Jeanloz and Knittle (1986), the inhomogeneity parameter is simply the ratio of the average adiabatic bulk modulus to the effective bulk modulus (K£) given by the pressure-density derivative in the Earth, where Kg is defined as: dp dp giving: r\-KE In P R E M , r) is very close to 1 (« 0.975 to 1.01) across the lower mantle, and indeed, Dziewonski and Anderson (1981, p. 310) noted that small deviations from 1 are likely an artifact of the polynomial representation used to parameterize the seismic model as a function of radius. Thus, I make the assumption, as have previous studies, that the lower mantle is homogeneous and adiabatic, and consequently, suitable to adiabatic decompression. In interpreting the seismic properties (p, Ks, v)^^mantle0^ the decompressed lower mantle, which are at some unknown high temperature (7^,), but at P = 0, it is common practice to compare these properties against the laboratory properties of Mg-perovskite and magnesiowustite, the two major mineral phases that comprise the lower mantle. To ensure that Chapter 4, page 400 the comparison is done under the same physical conditions the room temperature (298°K) properties must be corrected up to a high temperature (71,) inferred to equal the unknown high temperature, Tp of the decompressed lower mantle. This highlights the major drawback of the decompression technique - it provides no information on the actual temperature which corresponds to the "hot" adiabatically decompressed properties. Thus, there is considerable uncertainty in correcting up the room temperature laboratory properties, since it is unclear as to how hot the adiabatically decompressed lower mantle actually is. In this study I utilize the results of the previous chapters which demonstrate that the properties of a uniform pyrolite bulk composition, calculated along an adiabatic geotherm, provides an excellent match to the seismic properties. Thus, I adopt the mantle potential temperature of the pyrolite adiabatic geotherm as the "hot" temperature of the decompressed lower mantle. This temperature correction is done using the following expressions for molar volume, density, adiabatic bulk and shear moduli: pv V0(T,) = V0(T298K)Qxp 1 ja(T)dT .298 P"Po(T7) = M fdK^ ^KS0(T,) = KS0(T2gs) + ^ - (r7 -298) pv ^0(r?) = ^ 0 ( r 2 9 8 )+^J (r?-298) where Vo is the molar volume (cm3/mole), a(7) is the coefficient of thermal expansion(°K"'), M is the molecular mass (grams/mole), (dKs/dT)p is the temperature derivative (GPa/K) of the adiabatic bulk modulus Ks (GPa), and (3 ja/d T) p is the temperature derivative (GPa/K) of the Chapter 4, page 401 shear modulus, p (GPa). Next, the properties of these two minerals are mixed in the appropriate amounts for a pyrolite or piclogite model to obtain a set of "hot" properties (p 0, Kso, \La)"°iralorymixwhich are then compared to their equivalent "hot" decompressed lower mantle properties,(p0, Kso, P 0)"l„ r a n, f e-Because both the composition (silica and iron content) and the "true" high temperature, Tp of the decompressed lower mantle are unknown, comparisons of this type are non-unique with trade offs existing between composition and temperature (Jackson, 1983; Jeanloz and Thompson, 1983). In addition, early studies also faced the problem that the thermoelastic properties of Mg-perovskite were also uncertain (e.g. thermal expansion coefficient (a); temperature derivative of the bulk moduli, [d Ks /dT) p) or unmeasured (e.g. shear modulus, p; temperature derivatives of the shear (d p/d T} p). In spite of these difficulties, certain constraints could be placed on the composition of the lower mantle. For example, assuming that the lower mantle has the same composition of the upper mantle, then a temperature estimate somewhere along an upper mantle adiabatic geotherm could be used to predict the temperature at the top of the lower mantle at 660 km depth. This temperature point could then be used to anchor an extrapolation back up to the surface to obtain an estimate of Tp. With an estimate of Tp it is now possible to correct up the room temperature phases and compare the hot mixture to the hot decompressed lower mantle properties. Because the shear modulus (p) for Mg-perovskite was unknown until only recently (Yeganeh-Haeri, et al., 1989a, b; Yeganeh-Haeri, 1994) and its related temperature derivative still unmeasured, few previous studies considered this property. Likewise, because the temperature derivative of the Chapter 4, page 402 bulk modulus (dKs/dT)p was, until only recently, poorly known, utilizing the bulk modulus was precluded for quantitative analysis. This left density as the major property to discriminate between possible changes in composition between the upper and lower mantle because experimental measurements for the thermal expansion coefficient for Mg-perovskite were available (e.g. Knittle et al., 1986). Jeanloz and Knittle (1986) found that a pyrolite composition could only match the decompressed lower mantle density if the high temperature used to correct the room temperature properties was less than <1400 ± 100°K (1100°C), a temperature that was significantly less than their inferred lower mantle potential temperature of Tp = 1720 ± 260°K (1422°C). This discrepancy between the calculated hot density for a pyrolite composition and the density of the decompressed lower mantle was interpreted as evidence that an upper mantle composition is not applicable to the lower mantle with the suggestion that the lower mantle may be enriched in iron and/or silica, relative to the upper mantle. Unfortunately, to go farther and define how much iron (and/or silica) enrichment there is for the lower mantle suffered from uncertainty on the appropriate value to use for the lower mantle potential temperature. For the situation where the lower mantle bulk composition differed from the overlying upper mantle, a thermal boundary layer must exist at the chemical boundary separating the two layers. The thermal boundary layer will offset the lower mantle geotherm to significantly higher temperatures than the temperature at the base of the upper mantle geotherm, but unfortunately, there are few constraints on exactly the magnitude of the offset. Because the value for the high temperature used to correct the laboratory properties will trade off against a change in composition (i.e., iron or silica content), the uncertainty in the appropriate value for the Chapter 4, page 403 mantle potential temperature for a chemically distinct lower mantle precluded making quantitative estimates on the required change in chemistry. Inspite of this shortcoming, on the basis of the discrepancy in predicted and decompressed density, the conclusion that the lower mantle composition differed from the upper mantle was considered robust (Jeanloz and Knittle, 1986; 1989). A n additional point of uncertainty, noted by Bukowinski and Wolf (1990), was the choice of the equation of state used to fit the seismic properties of the lower mantle. They noted that previous studies had derived values for the decompressed density and bulk modulus that differed by 1% and 35% respectively, a variance which suggested systematic errors or bias may have occurred. They found that fits to the P R E M with a 3rd order equation of state were likely to underestimate the decompressed density; Because of trade offs with the decompressed bulk modulus during least squares fitting of the equation of state, errors in the bulk modulus were also introduced. Expanding the number of terms to a 4th order equation of state reduced the bias introduced by decompressing the seismic observations. In a further attempt to eliminate the problems introduced by extrapolating the seismic models to the Earth's surface, they introduced the concept of "constrained" fits to the seismic observations. Previous studies had simply fit an equation of state (via least squares) to the seismic observations to obtain the decompressed estimates. In contrast, Bukowinski and Wolf (1990) argued that mineralogical constraints should be introduced during the fit to seismic model by fixing the decompressed density and bulk moduli to the predicted high temperature values for a particular compositional model. Then the resulting fit to the seismic model is compared to 3rd and 4th order unconstrained fits to the same seismic model and trial compositions that plot near the 3rd order unconstrained fit are rejected as viable candidates. In contrast, compositions which plot near the 4th order unconstrained fit are Chapter 4, page 404 deemed plausible and its related pressure derivative and inferred decompressed temperature were then evaluated for plausibility against likely values for the particular assemblage. Nevertheless, this approach suffered from similar problems that plagued earlier ones; namely, the thermoelastic data for the major mineral phase, Mg-perovskite was incomplete, and the surface temperature of the decompressed lower mantle was poorly constrained. While I have noted the pitfalls faced by studies that employ adiabatic decompression, one significant advantage of this technique is that the pressure derivatives of both the bulk (dKs/dP)Tand shear modulus (d[x/dP) are not required, since having decompressed the lower mantle, the difference between the laboratory measurements and the seismic observations are solely due to temperature. For our purposes, this is an important advantage since for the M g -perovskite phase both the temperature and pressure derivatives of the shear moduli are unmeasured. Recall that to calculate Vs and Vp velocity, a high temperature and pressure estimate for the shear modulus is required (e.g. VS(T,P) = ^ J[i(T,P)/p(T,P) and VP(T,P) = J!(K(T,P)+%ii(T,P))/p(T,P) ) and that with both (d\i/dP)T and (du/d7/ ) unmeasured for Mg-perovskite, it w i l l prove difficult to calculate reliable profiles of P- or S-velocity. While one could attempt to find a suitable pair of values for (d \i/d P) and (d\i/dT)p for Mg-perovskite that would result in predicted velocity profiles that fit the seismic models, the predicted profiles would not be robust, since a particular choice for (d [i/d P) w i l l trade off against (d \x/d f) . This situation would be similar to that encountered in other studies that attempted to model upper mantle Vs and Vp profiles; the trade off between the unmeasured Chapter 4, page 405 temperature and pressure derivatives for the (3- and y-olivine phases resulted in a wide range of estimates for the olivine content of the upper mantle. In this study, I adopt a different goal than that of previous studies that have used adiabatic decompression; instead of placing constraints on composition and temperature, I turn around and assume that the pyrolite composition and its associated adiabatic geotherm is, in indeed, the composition and temperature structure of the lower mantle. Consequently, in making this assumption, I am adopting a mineralogy that has been successfully tested previously via calculated p and V& profiles, and thus, is expected to also fit the decompressed properties of the lower mantle. Furthermore, from this previous study there is a tight constraint on the temperature of the decompressed lower mantle; in modeling p and Vo profiles a self-consistent adiabatic geotherm was also calculated throughout the whole mantle and it was found that the seismic p and V® profiles could be fit along a lower mantle adiabatic geotherm concordant with that of the upper mantle. Thus, for a pyrolite composition, the surface temperature of the adiabatically decompressed lower mantle is simply the upper mantle potential temperature. Obviously, by adopting the pyrolite composition and its related geotherm, it is not possible to place constraints on lower mantle composition. Instead, in this study, the focus is solely only placing constraints on the unmeasured Mg-perovskite temperature derivative of the shear modulus [|<9p/drj ], via the technique of adiabatic decompression. By adopting the pyrolite model I am assuming that the whole mantle is isochemical and lies along a single, concordant adiabatic geotherm. This is a safe assumption in light of the results of chapter 2 where predicted whole mantle profiles of density and bulk sound velocity were compared against the seismic profiles. Thus, the room temperature pyrolite density, bulk and shear moduli, when Chapter 4, page 406 corrected to the high surface temperature of the decompressed lower mantle, must equal the corresponding values obtained via adiabatic decompression of the lower mantle seismic properties: decompressed 7'=1334C ^0 lower mantle P 0 Pyrolite mix decompressed 7*=1334C SO lower mantle SO Pyrolite mix decompressed 7'=1334C ^0 lower mantle r^Q Pyrolite mix * In the above expressions, the left hand side of the equality represents the values obtained by adiabatic decompression, while the right hand side represents a simplified pyrolite mineralogy of only Mg-perovskite and magnesiowustite. Of the three expressions, the first two, in terms of laboratory properties, are well known - indeed it would not be possible to confidently adopt the pyrolite model, if I could not predict the high temperature density and bulk moduli for Mg-perovskite and magnesiowustite - this allowed the calculation of predicted profiles of density and bulk sound velocity. The last expression, involving the shear modulus, is the focus here. The thermoelastic properties of magnesiowustite are well known from experimental study, so that relative to Mg-perovskite, this mineral may be considered "known" with experimental values available for the temperature derivatives [(d[i/8T)p and (dKT/dT)p] of both the shear and bulk moduli of periclase (Isaak et al., 1989) and wiistite (Bonczar and Graham, 1982; Jackson et al., 1991) and for a magnesiowustite with a composition of (Mgo.6,Fe0.4)0 (Fei et al., 1992). In contrast, for Mg-perovskite, the set of temperature derivatives is incomplete; the temperature derivative for the bulk modulus, (dKr/8T) has been measured (e.g. Mao et al., 1991; Wang et al., 1994; Funamori et al., 1996), but not for the shear modulus, Chapter 4, page 407 [d\i/df)p. Thus, in correcting the room temperature values up to Tp to compare with the estimates obtained via adiabatic decompression, one may confidently extrapolate density (p) and bulk moduli (Ks), but not the shear moduli (u) for Mg-perovskite. On the other hand, for magnesiowustite, all three properties may be corrected up to high temperature. Therefore, since the shear moduli temperature derivative for Mg-perovskite is the sole unknown in comparing the decompressed lower mantle and the laboratory properties, I can exploit this situation, and simply solve for the necessary value to obtain the equality. Therefore, the purpose of this research is to obtain an estimate for (Sp./ST')^ by decompressed comparing the constrained adiabatic decompressed value of \i0lower manlh obtained from the P R E M 7"=1334C seismic model to the related property u . 0 p / / < e m t e estimated for a simplified, high temperature pyrolite mineralogy. Once a constrained estimate for (d[i/dT)p is available, then one may shift the focus to obtaining a value for pressure derivative of the shear modulus, {d\x/dP)T, and therefore, calculate lower mantle shear and compression velocity profiles. I first adopt the approach of Bukowinski and Wolf (1990) and calculate new estimates for (p,^s,\^)tZlZaniied v * a constrained adiabatic decompression. This is required since Bukowinski and Wolf (1990) only focused on density and bulk moduli and did not consider the shear moduli in their study (this reflected that fact that the room temperature and pressure value for the shear modulus (\iref) of Mg-perovskite had only just been measured (e.g. Yeganeh-Haeri et a l , 1989a, b). Indeed, because these early experimental values differ considerably from the current recommended experimental values (Yeganeh-Haeri, 1994), attempting to utilize the early values Chapter 4, page 408 would have lead to confusion, since the density and bulk moduli may not have been consistent with results based on the shear moduli. ( \ decompressed p, Ks, p by applying / lower mantle adiabatic decompression to the lower mantle seismic model P R E M , I do not adopt these values since they did not constrain the fit of the 4th order equation of state to the P R E M seismic model. ( \ decompressed p, Ks, p derived from fitting the pressure-/ lower mantle velocity P R E M observations, do not agree with the same parameters derived independently from fitting the pressure-density P R E M observations. In addition, subsequent experimental analysis of Mg-perovskite has demonstrated that the value for the coefficient of thermal expansion determined by Knittle et al., (1986) is in error, likely due to breakdown of the Mg-perovskite during heating in the diamond anvil cell (Ross and Hazen, 1989; Hi l l and Jackson, 1990; Wang et al., 1994; Funamori et al., 1996). Thus, in calculating the high temperature properties of the simplified pyrolite mixture, the thermoelastic data utilized here for Mg-perovskite differs from that used by both Bukowinski and Wolf (1990) and Jeanloz and Knittle (1986). Nevertheless, I utilize the Jeanloz and Knittle (1986) equations, but adopt the philosophy of Bukowinski and Wolf (1990) and constrain the high temperature values for density and bulk moduli used in fitting the equations to the P R E M to the values for a pyrolite composition at Tp = 1334°C. Interestingly, the calculated pyrolite p 0 estimated here is indistinguishable from the p 0 determined for an unconstrained 4th order fit obtained earlier by Bukowinski and Wolf (1990). Chapter 4, page 409 decompressed The resulting new value for \x0lower manlle differs significantly from that obtained earlier by decompressed Jeanloz and Knittle (1986). I also combine p 0 w m a n , k w i m m e b u l k moduli and calculate the Poisson's ratio (a) of the decompressed lower mantle via the expression: ( 3 - 2 p / £ s ) rj = - '-(6 + 2 p / ^ s ) ' Previous studies had used a comparison between an inferred lower mantle value for a and a calculated one from mineral physics to argue that either the lower mantle composition was enriched with iron or that there existed an unusual temperature affect on the shear modulus (Poirier, 1987, Weidner and Zhao, 1992). decompressed 7*=1334C I find that to satisfy the equality | i 0 t e r w f c = ( i 0 ^ , that the shear moduli temperature derivative for Mg-perovskite must be (d\x/dT)p= -0.0224 GPa/K. This value, although higher than most silicates, still falls within the observed range of experimentally determined values for mantle silicates and indicates, and is contrary to earlier suggestions (e.g. Poirier, 1987; Yeganeh-Haeri et a l , 1989a; Weidner and Zhao, 1992) that Mg-perovskite takes on an abnormal temperature dependence for its shear properties to rationalize a uniform pyrolite mantle composition with the seismological observations of the lower mantle. To demonstrate that this is indeed the case, I need to calculate predicted Vs and Vp profiles that may be compared directly to the seismic observations. This is undertaken in the following chapter. 4.3 Methods Chapter 4, page 410 4.4 4th order Finite Strain equations Although Bukowinski and Wolf (1990) used 4th order Birch-Murnaghan finite strain equations and apriori estimates for p 0 and K$n to obtain constrained fits to the P R E M seismic model, they did not consider the shear moduli, \i0 or any of its associated terms that are also determined by a 4th order fit (e.g. |du/<9PJ , ^ s o u./8P2 j ). Since |J.0 is the focus here, I re-analyze P R E M within the framework of constrained decompression using 4th order finite strain equations (Davies and Dziewonski, 1975; Jeanloz and Knittle, 1986): P = 3f (1 + 2 / ) 5 / 2 KSO(\ - n0]f + T C 0 2 / 2 ) Pv2 = (l+2ff2 K S O (Ko-Kf+K2f2) p F s 2 = ( l + 2 / ) % 0 ( l - a 0 1 / + G 0 2 / 2 ) where P is pressure, Vp and Vs are compression and shear velocities, respectively, and fis defined as: t=x-2 f \ 212, 1 with density given by p and the zero pressure value by p0. The coefficients in the expression for pressure and velocity are defined by: n°2=2 K, so dK, so y. DP + I dP J dK, s o T \ \ d P j T J + • 143 Chapter 4, page 411 A,0 0 -1+ 4_Po 3 K so A. 0 1-5 ^02 — , 1+ 4 P-c 3 KSL o j 8K so BP JT 4 +-I 3 Kso rd2K5S BP7 4K so JT dp2 + f f d K A N UJVso JT dP JT 4 +— 3 8P - 4 JT J KdPJrJ 35 3 K so J a 0 1 = 5 -3 CT°2=2 d p 0 Po U P J r A:. 50 K so a p 2 + a A: 50 dP - 4 35 9 As explained by Jeanloz and Knittle (1986) the difficulty in applying these equations to the mantle is that the zero pressure decompressed density p 0 is unknown, and therefore the parameter / cannot be calculated at each depth where the seismic reference model is tabulated. Recall that the goal is to determine values for the decompressed lower mantle / \Hol I \ H u l [Po> Kso> H - o ) / o „ , „ f e w h i c h c a n b e compared with ^p0, K s o , ^ 0 ] ^ . Jeanloz (1981) first outlined how to solve the above equations to obtain these parameters. I follow this approach, as detailed in a later study by Jeanloz and Knittle (1986). The parameter fis re-normalized to an arbitrary reference density, p* giving: g = 1 ( v / 3 _p_ vp J -1 Introducing the parameter, the length ratio, P = ^ p* /p0) •> the parameter/is now expressed as Chapter 4, page 412 ' n ~ 2 i which is substituted back into the equations relating P, pVf, and pVJ with / After some rearranging, P, pV2,, and pK s 2 are related to new parameters Gn, G x and G n , which are expressed as polynomials in g: l ( l + 2g) 5/2 p^, 2 G x s , *" ' = ax +Ks + cxg2 I \ 5 / 2 1+2* P ^ 2 = a„ + 6„# + c„,e 2 ( 1 + 2 « ) The coefficients in the above polynomials are defined as: so ' p 2 - l ^ V J l + ^L ( l -p - ) + ^ ( l - P ' ) J SO i + n o i ( i - p ' ) + 2 ^ ( i _ p ' ) SO *oi +• 02 371 02 SO ^ ^ ' - P 1 ) + T-( ,- p 1)' ' SO ^ 0 1 + x 0 2 ( l - p2 ) 02 Chapter 4, page 413 CT01 + a 0 2 (i-e')] C C T = P9 ^ 0 CT02 As explained by Jeanloz and Knittle (1986), the normalized pressure, Gn and moduli Gx and GCT and g can be determined as a function of depth from the seismic reference models. To optimize convergence I adjust the normalized density (p*) to obtain the best fit of the functions of GK, Gx, and Ga to the seismological data for the P R E M lower mantle (771 - 2771 km) (Dziewonski and Anderson, 1981). Jeanloz and Knittle (1986) undertook 3rd and 4th order fits to P R E M via G„ to obtain unconstrained estimates for the decompressed values of p0, Kso, dP J and Kso ( d2K ^ u 2^S0 v dP1 j„. and I list the 4th order fit values in table 4.3 under "fit to pressure-density". In addition, they also undertook 3rd and 4th order fits to the normalized moduli Gx and Ga, to obtain independent estimates of Kso, rdKS0^ dP rd2KS0^ dP2 \dPj and K so \dP2j and I also list these 4th order values in table 4.3 under "fit to velocities". Of note is that these separate fits give different values for the parameters they have in common (e.g. compare the values for Kso, rdKs; dP J > Kso dP )„ ). Butler and Anderson (1978) point out that finite bulk and shear attenuation may have a sufficient affect on both seismic bulk modulus and shear modulus so that these estimates may not be directly comparable to laboratory results. However, recent 1 dimensional shear attenuation models (Durek and Ekstrom, 1996) demonstrate that shear Chapter 4, page 414 attenuation is most pronounced in the shallow most upper mantle (100-200 km) and decreases with increasing depth. In the lower mantle, the S-wave quality factor, Q$, is relatively high. Thus, I do not believe the discrepancy between the common values obtained via adiabatic decompression of the lower mantle P R E M reflects dispersion in the seismic velocities, but rather, reflects a bias that Bukowinski and Wolf (1990) discussed for unconstrained equation of state fits (I comment further on dispersion below). Thus, in the next section I re-determine new values from a 4th order fit to PREM, but within the framework of constrained adiabatic decompression. 4.5 Constrained Decompression Bukowinski and Wolf (1990) argued that one possible explanation for the variation in estimates of decompressed values for p0, Kso, V BP j and Kso 9 Ks 8P T v - ' " 7 1 J , was that the fits to the lower mantle seismic models suffered from trade offs between the parameters. Small adjustments in p 0 have a nonlinear affect on the remaining parameters and result in relatively large uncertainties in values for Kso and fBK \ 5 0 ' , They also noted that i f the fit was done with BP r a 3rd order equation of state, rather than a 4th order version, the estimated values for the decompressed parameters differed again. As an example, they fit both a 3rd and 4th order EOS to theoretical molecular dynamic equation of state data for Mg-perovskite that extended over the full depth range of the lower mantle. They fit the equations to the data and determined the decompressed values - in this case, the zero pressure values were already known, so they could assess the error introduced by extrapolating to zero pressure with the 3rd or 4th order expansions Chapter 4, page 415 of the equation of state. They found that the known zero pressure density was significantly overestimated by the 3rd order fit; the 4th order fit reduced this discrepancy, but did not completely remove it (figure 4.1). Figure 4.1 is a F versus/plot where F is Birch's normalized pressure given by; p F = [3/11 + 2 / ] where P is pressure, and fis defined as; 5/2 f = k ( p / P o ) 2 / 3 - l where p is density and p 0 is the zero pressure value. This plot highlights the discrepancy between the actual equation of state (labeled as 'actual isotherm' and denoted by the solid lines) and the theoretical least squares fit to the high pressure data (>20 GPa) using either a 3rd or 4th order equation. Lastly, note that as temperature increases (compare the 700°K to the 300°K curves) the discrepancy between the extrapolated and actual zero pressure values increases, thus implying that at the high temperatures expected for the decompressed mantle, there will exist a significant discrepancy, even for a 4th order extrapolation. Bukowinski and Wolf (1990) also undertook a finite strain fit to the lower mantle portion of P R E M . They concluded that the bias introduced by extrapolation to zero pressure may introduce a significant source of error in the estimated decompressed values of P R E M (figure 4.2). They note that the true F-f curve for the lower mantle will fall closer to the 4th order curve than the 3rd order curve, but without additional constraints, the precise position of the true curve above or below the 4th order curve is unknown. They argued that a simple way of addressing this uncertainty was to undertake "constrained decompression" where the fit to the seismic model is Chapter 4, page 416 constrained by the known zero-pressure properties of a particular compositional model. Effectively, this is making the assumption that the lower mantle seismic model is indeed the high temperature and pressure expression of a particular mineral assemblage along an adiabatic geotherm. By adopting a trial composition, the room temperature density p 0 0 and adiabatic bulk modulus, Ksoo a r e known, and the "hot" equivalents may be estimated assuming a plausible temperature. While Bukowinski and Wolf (1990) adopted this approach, they were still hindered by the fact that they did not know the mantle potential temperature of the decompressed lower mantle - they estimated approximate temperatures via comparison between the hot density of the trial composition (p) calculated via the relationship Kso \ p 0 j and the hot density of the trial composition calculated using the coefficient of thermal expansion (e.g. p = p r e / + oc | r -298°KJ) . An additional source of error is related to the Anderson-Gruneisen parameter, 5S. They admitted that while the value for os was measured for magnesiowustite, there were no experimental measurements for Mg-perovskite, and hence, they were forced to estimate this property via thermodynamic relationships. In this study I follow the philosophy of Bukowinski and Wolf (1990), but instead of evaluating a number of trial compositions, the focus here is solely on the pyrolite composition. While this bulk composition is not unique, I adopt it because independent modeling presented in chapter 2, of density and bulk sound velocity profiles has already demonstrated that pyrolite, (and not a chemically layered composition such as piclogite) can fit the seismic observations throughout the whole mantle along a concordant adiabatic geotherm. Furthermore, when the Chapter 4, page 417 adiabatic geotherm used in calculating the predicted p and profiles is extrapolated to the surface, the zero pressure temperature is consistent with independent estimates for the mantle potential temperature based on comparisons between the predicted and observed melt volume and composition at mid-ocean ridges (e.g. McKenzie and Bickle, 1988; McKenzie and O'Nions, 1991; White et al., 1992; Brown and White, 1994; White and McKenzie, 1995). Compilations of ocean crust thickness determined from marine geophysical surveys (Chen, 1992; White et al., 1992) have documented that ocean crust exhibits very little variation globally. This uniformity is interpreted in the context of theoretical models for decompression melting at mid-ocean ridges to indicate, that away from hotspots, the mantle potential temperature has little global variation (e.g. ± 30 °C , White et a l , 1992; ± 20 °C, Brown and White, 1994; ± 10 °C, Su et al., 1994). In terms of modeling the properties of the lower mantle via the approach of adiabatic decompression, the results from the study utilizing p and V0 are very important since they tightly constrain (e.g. 1334 ± 30 °C) the "unknown temperature" of the decompressed lower mantle, and they provide a mineral composition that is known apriori, to satisfy the seismological observations of the lower mantle. Thus, I fit the lower mantle seismic observations in P R E M with the values of density and adiabatic bulk moduli in the equation of state constrained by values for a "hot" pyrolite mineralogy that has been corrected from room temperature up to 1334°C. 4.6 Mineralogical model: simplified pyrolite model Inspite of the confidence in adopting the pyrolite compositional model as a successful mineralogical model of the lower mantle, I must make some simplifications to the mineralogy to Chapter 4, page 418 constrain the unmeasured value of the temperature derivative of the Mg-perovskite shear modulus, (<3p/<9 T) . The complete pyrolite mineralogy in the lower mantle is comprised of «75 vol% Mg-Fe-Al perovskite, «12 vol% Ca-perovskite, and «7 vol% magnesiowustite (Ita and Stixrude, 1992; 1993). While the temperature derivatives for both the bulk and shear moduli for magnesiowustite are experimentally measured, only the temperature derivatives for the bulk moduli of the two perovskites are known. Hence, to reduce the number of unknowns, I follow common practice (e.g. Poirier, 1987; Bina and Silver, 1990; Bukowinski and Wolf, 1990; Hemley et al., 1992; Stixrude et al., 1992; Zhao and Anderson, 1994) in assuming that the shear moduli properties of the Ca-perovskite phase are similar enough to Mg-perovksite that I may approximate the full pyrolite mineralogy by only Mg-perovskite and magnesiowustite. This simplification has often been invoked in previous studies of lower mantle mineralogy due, in part, to the small volume percent of the Ca-perovskite phase, but largely due to the lack of thermoelastic data for this phase. While well constrained values for some of the elastic properties of Ca-perovskite have recently been measured (e.g. Wang et al., 1996), the shear modulus and its temperature and pressure derivatives remain unmeasured. Thus, to reduce the number of unknowns in forward modeling the hot shear modulus of a pyrolite composition, I are forced to simplify the pyrolite mineralogy to a two phase mineral aggregate. As noted above, this has been common practice in earlier studies and hence, I adopt the pyrolite mineral volume percents given in Zhao and Anderson (1994). The goal of this study is to place constrains on the unmeasured for Mg-perovskite and this is done by determining the necessary value to obtain agreement between the decompressed shear moduli from the seismic model and the extrapolated laboratory mix via: Chapter 4, page 419 decompressed 7'=1334C / ,, ,„ , , „ M o , „ „ , f e = M o « „ „ = (^VOl% 1 + 1 6v 0/% ) WW/ mix where the term on the left represents the shear moduli estimate determined by constrained adiabatic decompression of the lower mantle P R E M seismic properties. The term on the right represents the equivalent simplified pyrolite mineralogy, which is a V R H averaged (Watt et al., 1976) mix of the individual high temperature shear moduli for perovskite (Pv) and magnesiowustite (Mw) calculated via: Pv,, 7=1334C _ Pv,,T=29S"K . Mo - Mo + \dTj Pv ( l 6 0 7 o K - 2 9 8 o K ) (note that 1607°K = 1334°C) and M > ™ C =0.86 M i ' °p .r i 3 3 4 C +0-14 '• wVo , l" U ; where magnesiowustite is an ideal mix of its pure end member phases periclase (MgO) and wiistite (FeO). The individual shear moduli for these minerals are determined via: MgO,, 7=1334C _ MgO,,T=29&"K , Mo _ Mo + 8T; MgO ( l607°K-298°K) FeO,,r=1334C _ FeO T=29&" K , Mo _ M-0 + \dTj ( l 607°K-298°K) . The important point to note is that the reference value of the periclase and wiistite shear modulus ( F e 0 \ i l = m ' K , MgCVo=298''K) and the related temperature derivative / / \MgO I , \FeO [^d(i/d7j , ^dyi/dTj ] are measured (Isaak et al., 1989; Sumino et al., 1980; Bonczar and Graham, 1982; see table 4.1); likewise, the reference value for the Mg-perovskite shear modulus Chapter 4, page 420 PvtlT=29&"K M-o ) is experimentally determined (Yeganeh-Haeri, 1994): this leaves the unmeasured temperature derivative of Mg-perovskite [[d\i/dT ] as the only unknown in the equality In this study the aluminum and Fe content in Mg-perovskite is accounted for by adopting the composition of Irifune (1994) and expressed in terms of unit cell volume via (O'Neil and Jeanloz 1994): F 0 ( A 3 ) = 162.59 + 5.86xF e S / 0 3 + 10 .70*^ For the average composition of Irifune (1994; X F E = 0.10; A1 2 0 3 = 0.10) this results in a molar volume for perovskite of 24.73 cmVmole, a value significantly greater than the molar volume of pure Mg-perovskite (V0 = 24.46 cmVmole). Within experimental uncertainties, the isothermal bulk moduli for Mg ] . J C Fe x Si0 3 perovskites for x = 0, 0.1, and 0.2 are indistinguishable, implying that iron substitution does not affect the compressibility (Mao et al., 1991). I assume this is equally valid for the addition of aluminum and thus adopt a room temperature isothermal bulk modulus for Mg-Fe-Al perovskite of KJQ = 261.5 GPa, a value that falls within accepted convention (e.g. Jeanloz and Hemley, 1994; KJQ = 263 ± 3 . 0 GPa), within the experimental uncertainty of the low temperature Brillouin spectroscopy results (Yeganeh-Haeri, 1994; Kso = 264.0 ± 5.0 GPa), and lastly, very near the "recommended" value from a recent re-evaluation of available thermoelastic data for Mg-perovskite (Jackson and Ridgen, 1996; KJQ = 262A GPa). The periclase and wustite molar volumes are experimentally measured and I combine the end member properties to predict that of magnesiowustite again adopting the Fe content determined by the synthesis experiments of Irifune (1994; X ? E = 0.14). The room temperature Hot Olow mantle Chapter 4, page 421 values for all of the properties used here for Mg-perovskite, periclase and wiistite are listed in table 4.1. Table 4.2 lists the coefficient of thermal expansion (a) used for the phases and the associated polynomial expression for a(7). Table 4.1. Tabulated values for measures properties Mg-perovskite, periclase, and wiistite. Properties Mg-perovskite ref MgO periclase ref FeO wiistite ref M(grams/mole) 103.6279 1 40.304 71.846 Vo (cmVmole) 24.731 1 11.242 5 12.25 6 p (g/cm3) 4.190 (4.031) 1 3.585 (3.388)a. 5.865 (5.722) KTO (GPa) 261.5 161.6(132.1) 5 154 6 KSO (GPa) (241.36) 163.93 (144.42) (134.57) I . dT , (GPa/K) -0.0295 2 -0.0320 -0.020 7 Y 1.50 3 1.52 5 1.63 9 p (GPa) 177.3 4 131.8(106.4) 5 46.4 (24.14) 6 dp (GPa/K) T -0.0224 -0.026 5 -0.017 8 1, O'Neill and Jeanloz, 1994 with Fe and A l contents from Irifune (1994); 2, Funamori et al., 1996; 3, O.L. Anderson et al., 1995;4; Yaganeh-Haeri (1994); 5, Isaak et al., 1989; 6, Jackson et al., 1990; 7, Bonczar and Graham, 1982; Fei et al., 1991; 8, Sumino et al., 1980; 9, Jeanloz and Ahrens, 1980. a Entries in brackets are the high temperature value - For Mg-perovskite and wiistite I first made the temperature correction of the isothermal bulk modulus to high temperature via KT = Kr+(dKT 18^^-29%) and then converted to the adiabatic equivalent via Ks = Kr | l + a y T j . For periclase, the high temperature experiments of Isaak et al., 1989 are tabulated for both Ks and ^ f r o m room temperature up to 1800°K. Chapter 4, page 422 Table 4.2. Values for the coefficient of thermal expansion used in the calculations. Mineral Formula thermal expansion coefficient a(7) = a 0 +a ,r+a 2 T - 2 a 0 a, Mg-perovskite1 M g S i 0 3 1.982 x IO"5 9.18 x IO 9 -0.474 periclase2 MgO 3.681 x 10"5 9.283 x IO"9 -0.7445 wiistite3 FeO 1.688 x IO"5 2.040 x IO"9 0.0190 1, Funamori et al., 996; 2, Fei, 1995; 3, Fei et a l , 1991 4.7 Correction from room temperature to T E As noted above I adopt 1334°C (1607°K) as the surface temperature of the adiabatically decompressed lower mantle and correct the reference room temperature (298°K) and pressure value of the isothermal bulk modulus to this temperature using the following relationship: rdKj dT , ( 1 6 0 7 ° ^ - 2 9 8 °/T) where KJO is the isothermal bulk modulus, (dKT/dT) is the isobaric temperature derivative of the isothermal bulk modulus, 1607°K is Tp, the surface temperature of decompressed lower mantle, and 298°K represents the reference state at room temperature. Next the hot isothermal bulk modulus is corrected to its adiabatic equivalent via the thermodynamic relationship: Kso=Kro (l + a(TP)yTP) where y is the Gruneisen parameter, and a(7p) is the coefficient of thermal expansion. In a similar fashion, the molar volume is corrected from room temperature and pressure v{Tref,Pref^ to 1607°K using the expression; 'l607 / % V(T, Pref ) = V(Tref, Pref ) exp J a T) dT V 298 V ' Chapter 4, page 423 where a(I) is the thermal expansion coefficient and is used to express the volume change of a mineral due to a temperature change (Fei, 1995). Commonly the thermal expansion coefficient is reported as a polynomial expression: a(r) = a 0 + a i r + a27'~2 where a 0 , a , , and a 2 are constants determined by fitting experimental data. Substituting the polynomial expression in the above expression for molar volume and integrating gives: V(T,Pref) = V(Tref,Pref)exp VL a a0(7-298) + ^ L ( r -298 2)-a 2(r"' -2981) where T= 1334°C in the above expression. Finally, the hot density is calculated via: P ( ^ / ) = M V(TP,Pref) where M i s the molar mass. The Voigt-Reuss-Hill averaging scheme (Watt et al., 1976) was used to determine volume averaged properties for the mineral assemblages. 4.8 Results Results for a constrained 4th order equation of state fit to P R E M are shown in figure 4.3 where normalized pressure, Gn and moduli Gx and G a are plotted as a function of depth, with p* = 0.1537. It is evident that the fit to the normalized velocities is poorer in the upper most region of the lower mantle. It is interesting to note that this region of the lower mantle is where the new seismic reference model akl35-F (Montagner and Kennett, 1996) differs the most from P R E M . Jeanloz and Knittle (1986) also noted a discrepancy between fits that involved just the pressure-density relationship and the fits that involved the pressure-velocities. They attributed this to the shortcomings in the P R E M model. Table 4.3 lists the various parameters obtained by the fit and Chapter 4, page 424 compares them against similar values obtained from previous unconstrained 4th order fits to P R E M by Bukowinski and Wolf (1990) and Jeanloz and Knittle (1986). Jeanloz and Knittle (1986) note that their results demonstrate that anelastic dispersion is not affecting the decompressed zero pressure properties of the lower mantle, since the adiabatic bulk modulus determined from the normalized pressure, GK (a low frequency value based on free-oscillations seismological constraints) is systematically higher than the value they obtained from the normalized moduli Gx and GCT, which are based on velocities (higher frequency values since the seismic data was predominantly body waves). They point out that attenuation-related dispersion of the moduli is predicted to have the opposite affect, such that the Kso derived from GK should be lower than Kso derived from Gx and GCT . o" >< rt- CD P rt rt- S3 p rt. Cu o O E3 ^ O CD i-b Cu ex, CD 13 Cu O rt-CD CO rt-3" CD T3 rt e CD a I-o ° N r+ cu >-d | s ^ ^ CD I — i c/T N O 3 oo 3. O N o V| c i CD O . 1 rt 3 3 cr CD cr o u O I— rt N 3 3" <T> 3 co CTQ ^ . Cu ^ CD co 3 cr co p rt Cu v< rt. * c l co trt C D o C u CD r? 3 co rt- rt-3" cr CO rt 3 CD Cu co CD to C o s 5 | —J CD e CD CD o O o O N —J o o N O - J CO CD CD • r t U> o 4^ CD CD •3 — i CD a xt P o to - J -rt 00 o o tO -rt - 0 - J o to -rt to -rt o o O N O N 00 Co CD CD" to bo H-t o to o CD "a "-i CD c ^ -rt 'to H-o -rt O N O 1^ 1 -rt Co o TJ CTQ Xi rt Cu CD O o Xt rt CD co co CD Cu v - I I I' rt ™ 3 ) to rt p 3 O ^ O N 21 O rt N S &> o g rt ro S ' <—-V '—' N O oo O N TJ 9 cr a ^ -rt 1>J rt c r a CD O o 3 Xt rt CD CO CD Cu Xt rt P 3 CD U J CD 3 '-i co % o 5- 3 CO o o 3 co rt-rt P rt a-° 3" rt-) CD ^ - N CU s -cr S o Cu rt CD rt & rt, rt C D * l-ti N O ° oo rt O N C T • — ' CD o CD rt 3 P CD* > co O O cr •§ rt-CD TS P era CD -rt to I-i o Chapter 4, page 427 The important value in table 4.3 for this study is the adiabatic decompressed value of the shear moduli, p 0. For the constrained fit to P R E M I obtain a value of p 0 = 139.32 GPa, significantly greater than that obtained previously by Jeanloz and Knittle, (1986; p 0 = 130.10 GPa) via an unconstrained 4th order equation of state fit to PREM. As noted by Jeanloz and Knittle (1986), a major difficulty in evaluating the decompressed values of the lower mantle is that there is no accepted way in estimating the uncertainty associated with the density or velocity values tabulated in the original P R E M model. They noted that since P R E M results from a non-unique and nonlinear inversion of seismological data there exists a tradeoff between depth resolution and absolute uncertainty in the tabulated values. Thus, the uncertainty values estimated by Bukowinski and Wolf (1990) are based on the uncertainties in the experimental values adopted in the constrained fits, and not in the P R E M model. In optimizing the constrained 4th order fits to P R E M I found that near p 0 = 139.32 GPa there existed other solutions where p 0 varied by up to 1 GPa greater than 139.32 GPa, and the other parameters (e-g. V dP Jr d % 0 . dP2 j \dP)n 5 2 p 0 ) varied around the values listed in table 4.3 It is important to stress that since the high temperature values for density and bulk moduli in the 4th order fit are fixed, the resulting decompressed value for p 0 directly reflects these values. If different values for p 0 and Kso w e r e used, I would naturally obtain a different estimate for p 0. Exactly how different is difficult to quantify since in this study I am not attempting to constrain the lower mantle composition by substituting various trial compositions and their associated p 0 and Kso m t o the constrained fits. Nevertheless, I have shown previously by comparing predicted profiles of density and bulk sound velocity to the seismic observations that pyrolite successfully satisfies the seismic models, whereas the piclogite model does not. Thus, while the Chapter 4, page 428 derived value for p 0 is directly affected by the p 0 and Kso values, I believe that only compositions that are "pyrolite-like" will satisfy all of the constraints. To determine, in a general way, the sensitivity of p 0 to our fixed input values, I fixed the high temperature values of p 0 and Kso to those for a 3 phase pyrolite where Ca-perovskite has been included (3.939 g/cm3 and 222.02 GPa); the resulting value for the decompressed shear moduli decreases slightly to p 0 = 138.63 GPa. Note, however, it is not possible to compare this decompressed shear moduli to a high temperature 3 phase pyrolite because, with the introduction of Ca-perovskite, there are now 3 unknowns (instead of one for the case of a simplified pyrolite) in correcting the room temperature shear moduli up to high temperature (e.g. C a P v p , 4.9 Discussion To equate the constrained adiabatically decompressed shear moduli to the high temperature value for a simplified pyrolite mixture, the value for the temperature derivative of / \Ca-l'v / I \ Mg-l'v dii/dT] , a n d ( d n / d 7 : ) ). Pv the Mg-perovskite shear modulus, adjusted in the following expression: decompressed T= 1607 K Mo lower mantle M 0 Pyrolite mix 7=1607 K 0 where the only unknown in the above equality is d[i/dT in the relationship: Pv,,T=\334C H-0 Pv,, T=298"K M-o + (5 p/S T) J v(l607°K - 298°K). Chapter 4, page 429 I find (d u / d r) ' V = -0.0224 GPa/K to satisfy the equality. This is illustrated i f figure 4.4 where the decompressed shear and bulk moduli are plotted along with the values calculated for a simplified pyrolite model. Also shown are the results of Jeanloz and Knittle (1986) where I have combined their calculated value for the decompressed shear moduli with both of the estimates for Kso obtained from either fitting the velocities or the density (the shear moduli correctly applies to the K$o determined from the velocities). In figure 4.5 the decompressed seismic parameter O, calculated via <t> = KsolPa is plotted against the decompressed Poisson's ratio a calculated via: _ ( 3 - 2 | i 0 / ^ 0 ) ( 6+2 - i 0 / * i 0 ) Poirier (1987) attempted to interpret the decompressed Poisson's ratio of the lower mantle to place constraints on the composition of this region. However, he visually extrapolated the lower mantle profile of Poisson's ratio, calculated with the seismic Vs and Vp velocities via: (VPIVs)-2 0 = — 2 (^M ) 2 -2 to the Earth's surface, rather than use finite strain equations. While he acknowledged that the resulting value was at some unknown high temperature, he claimed that it was permissible to neglect the variation of Poisson's ratio with temperature (this is equivalent to ignoring any temperature affects on either the bulk or shear moduli or assuming that they vary together as a function of temperature). Thus, he compared his high temperature decompressed estimate to laboratory properties at room temperature and pressure. Lastly, in calculating the Poisson's ratio for a simplified pyrolite or piclogite assemblage of Mg-perovskite and magnesiowustite, he was Chapter 4, page 430 forced to evaluate a wide range of parameter space because the room temperature and pressure value of the shear moduli, p for Mg-perovskite was, at that time, unmeasured. In spite of these difficulties he argued that the decompressed lower mantle Poisson's ratio at room temperature and pressure was about 0.24 ± 0.01 but he was unable to determine i f this value was consistent with a uniform or distinct chemical composition for the lower mantle. The first experimentally measured value of the Mg-perovskite shear modulus was reported by Yaganeh-Haeri et al. (1989a, b; Ks = 246.4 GPa, p = 183.5 GPa) and led them to suggest that to match the lower mantle seismic properties at 1071 km depth, Mg-perovskite must have an unusually high temperature derivative for the shear moduli of « -0.030 to -0.040 GPa/K (see figure 4.6 which plots (d\x/8T)p versus [dyi/dP)T. Note that for the inferred value for ( r3p /5P) r at 1071 km depth in the lower mantle, the corresponding values of (5 p /d f) to satisfy the trade off curves for pyrolite, chondrite, and perovskite models ranges from w -0.030 to -0.040 GPa/K), or that assuming that the shear modulus of Mg-perovskite is affected by iron substitution in a similar way to magnesiowustite, that the lower mantle must be substantially enriched in iron (Weidner and Zhao, 1992; figure 4.7). The later conclusion reflects the difficulty in decreasing the shear modulus from the rather high experimental value of 183.5 GPa down to one which, when combined with the bulk modulus, would give a Poisson's ratio that was in agreement with the inferred value of Poirier (1987) for the lower mantle. However, these early experimental values have been superseded by subsequent measurements where it was found that in the new single crystal experiments the crystals did not suffer from the insitu crystal twinning that had plagued the earlier studies. Yaganeh-Haeri (1994) report Ks = 264.0 ± 5.0 GPa, p = 177.3 ± 3.5 GPa, values that I adopt here, and which Chapter 4, page 431 result in a room temperature Poisson's ratio of 0.2238. Since I am solving for the value of temperature derivative of the shear modulus for Mg-perovskite that is necessary for agreement between the constrained decompressed lower mantle shear moduli and the high temperature simplified pyrolite mixture, I do not consider other factors, such as the affects of iron on the perovskite shear modulus. Nevertheless, I find that for a "normal" value for the temperature derivative (d = -0.0224 GPa/K, I can obtain a match without appealing to iron enrichment in the lower mantle (see figure 4.7). To emphasize that "normal" values for the temperature derivatives for Mg-perovskite can satisfy the lower mantle, figure 4.8 and 4.9 re-plot the calculated tradeoff curves for pyrolite, chondrite, and perovskite compositions from Yeganeh-Haeri et al. (1989a) with the results obtained in this study. Recall that these curves give the combinations of {dKs/dT^ and (dKjdPy^ (figure 4.8) and (du/d7/) and (dy /dp ) (figure 4.9) for the Mg-perovskite phase in these three compositions that are required to satisfy the seismological constraints at a single depth of 1071 km in the lower mantle. The iron content, expressed via Fe/(Fe + Mg), was assumed to be constant at 0.10, a normal value for a uniform composition and the geotherm was anchored to a surface temperature of 1400°C. Yeganeh-Haeri et al., (1989a, b) also plotted estimates for the pressure derivatives ({dKs/dP^ and | S u . / d P J ) at 1071 km depth that were derived from the P R E M model at this depth, and concluded, that while relatively "normal" values for the temperature derivative of the bulk moduli would allow a fit between the laboratory properties and the seismic properties (figure 4.8), this was not the case for the shear moduli (figure 4.9). However, I find that the constrained decompressed lower mantle bulk Chapter 4, page 432 moduli pressure derivative is 4.16, a value significantly greater than that inferred by Yeganeh-Haeri et al. (1989a, b; (dKs/d PJ = 3.60) - note that our value is not highly dependent upon the constrained input values I used in fitting the 4th order equation of state to P R E M . The unconstrained 4th order fits of Bukowinski and Wolf (1990) give {dKs/d PJ = 4.2, while that of Jeanloz and Knittle (1986) give 4.05 and 4.38). In addition, there are now experimental measurements for the temperature derivative of the Mg-perovskite bulk modulus (Mao et a l , 1991; Wang et al., 1994; Funamori et al., 1996; Utsumi et al., 1995) and these are plotted along with values adopted in the modeling studies of Duffy and Anderson (1989; (dKs/8T)p = -0.0310), Zhao and Anderson (1994; (dKs/8T)p = -0.0177 GPa/K), O.L. Anderson and Masuda (1994; (dKs/dT)p = -0.0134), and our previous work (Calderwood, 1996; (dKs/dT)p = -0.0175). I note that all of these theoretical studies have adopted values which plot within the uncertainty of the latest experimental values of Utsumi et al. (1995) and Funamori et al. (1996). Since these experiments were carried out at both high temperature and pressure, the resultant values are expected to be the most reliable estimates to date. Although the measured estimates for the temperature derivative (actually (dKT/8T)p is converted into (dKs/8T)p for plotting following the expression 26 in Sumino and Anderson (1984) - see footnote c of table 6.4 for this expression) are "high" relative to the field of "normal" values considered by Yeganeh-Haeri et al. (1989a, b), they are still consistent with a pyrolite composition, since the pressure derivative has shifted to a higher value. Also note that the calculated tradeoff curves of Yeganeh-Haeri et al. (1989b) for the 3 compositions should be re-calculated since they utilize the Yeganeh-Haeri (1989a) elastic properties for Mg-perovskite that have now been superseded Chapter 4, page 433 (Yeganeh-Haeri, 1994). Lastly, the large difference in the values for the pressure derivative at a depth of 1071 km and that for the entire lower mantle emphasize the arguments made by Zhao and Anderson (1994) that it is inappropriate to compare predicted and observed elastic properties at a single depth. Focusing on the temperature and pressure properties of the shear moduli (figure 4.9) note that the value of the pressure derivative |du/<3PJ for the lower mantle, determined by constrained decompression, is greater than the value inferred by Yeganeh-Haeri et al. (1989a, b) at a depth of 1071 km, although the difference is not as great as that found above for the bulk moduli. Also shown on figure 4.9 is the |<3u/<3rj estimate determined in this study for the Mg-perovskite (-0.0225 GPa/K) and two values that were adopted in previous modeling studies (Duffy and Anderson, 1989, (d\i/dT} = -0.0280 GPa/K; Zhao and Anderson, 1994; (du,/srj = -0.0336 GPa/K). Casual inspection of this figure would imply that the inferred values adopted by Duffy and Anderson (1989) and Zhao and Anderson (1994) are consistent with the intersection of the tradeoff curves for the 3 compositional models and the inferred lower mantle pressure derivative. However, I note again that the tradeoff curves are based on out-of-date elastic properties for Mg-perovskite, and hence, need to be re-calculated with the Yeganeh-Haeri (1994) values. That these tradeoff curves must shift is evident from our estimate which is determined assuming apriori a pyrolite composition when deriving the value of decompressed lower mantle shear moduli - the tradeoff curve for pyrolite should pass through the intersection of the decompressed lower mantle pressure derivative and this studies estimate Chapter 4, page 434 Lastly, I point out that the inferred temperature derivatives adopted by Duffy and Anderson (1989) and Zhao and Anderson (1994) are based on {DLA} parameters. Anderson (1988) notes that these dimensionless parameters are derived from mineral systematics based on a large data base of measured compounds, and allow the prediction of the temperature or pressure derivatives. Duffy and Anderson (1989) adopted the coefficient of thermal expansion of Knittle et al. (1986; cc(298°K) = 3.14 x IO"5 K"1), estimated the value of the shear modulus for Mg-perovskite, which was then unmeasured (p - 153 GPa), and then derived a value for S p / s r j via the {DLA} relationship: f ^ \ s x 1 ^ = — a p \ d T ) p Their tabulated value for(dp /a r) = -0.0280 GPa/K implies the {DLA} parameter {p}p = 5.8. In contrast, Zhao and Anderson (1994) arbitrarily adopted a high temperature, average value for the coefficient of thermal expansion of a(900°K) = 3.00 x 10"5 K"' rather than use either the full expression of the high experimental value of Mao et al. (1991) or the full expression of the low experimental value of Wang et al. (1991; 1994). Combining the Zhao and Anderson (1994) choice for a with their adopted Mg-perovskite shear modulus (175 GPa) and their tabulated {DLA} parameter {[i}p = 6.4, one obtains the estimate for [dp/dT^ = -0.0336 GPa/K. Note, however, the large change in the value of the {DLA} parameter {p}p used in these two studies (e.g. Duffy and Anderson, 1989 versus Zhao and Anderson, 1994) - Anderson (1988) gives the mean value for {p}p based on averaging reported experimental measurements for other perovskite compounds as 5.0 (table 2, p. 4692) and suggested that the uncertainty associated Chapter 4, page 435 with this value was ± 10%. However, later in table 7 (p. 4697), he listed 2 sets of predicted values for Mg-perovskite of {[i}p = 6.5 or {\x}p = 5.7. Unfortunately, it is not explained how these two sets of predicted values for the same mineral were determined, nor is it explained why both values fall outside the mean estimate derived from measured perovskite compounds. Consequently, it is unclear, i f either value in table 7 (or the value in table 2) of Anderson (1988) are to be favoured. Alternatively, I may derive a new estimate for {\i}p using our estimate for the temperature derivative [d\i/dTJ = -0.0224 GPa/K. Combining this with the measured Mg-perovskite shear modulus from Yeganeh-Haeri (1994; p = 177.3 GPa) and the coefficient of thermal expansion of Funamori et al. (1996; a(298°K) = 1.72 x 10"5 K"1) gives a predicted {DLA} parameter of {p}p = 7.4. By contrast, i f one were to adopt the various values estimated for the {DLA} parameter {ujp and combine them with the measured properties of Yeganeh-Haeri (1994) and Funamori et al. (1996), it is possible to predicted new estimates for the temperature derivatives for Mg-perovskite, that within the framework of the {DLA} parameters, no longer suffers the problems faced by Duffy and Anderson (1989) and Zhao and Anderson (1994), who were forced to estimate the input parameters (see table 4.4). Chapter 4, page 436 Table 4.4. Expected shear moduli temperature derivatives for the listed {DLA} parameter {p}P-{^}p reference adopted Mg-Pv (d p/a 7J predicted Mg-Pv (d yi/d 7J using measured p, and a 5.0 Anderson (1988) - -0.01526 GPa/K 5.7 Duffy & Anderson (1989) -0.0280 GPa/K -0.01771 GPa/K 6.4 Zhao & Anderson (1994) -0.0336 GPa/K. -0.01954 GPa/K. These predicted values for the temperature derivative of the Mg-perovskite shear modulus are significantly lower than the values that were actually adopted by Duffy and Anderson (1989) or Zhao and Anderson (1994). It is evident that from this exercise that, in spite of the claimed predictive properties of the {DLA} parameters, they do not appear to provide robust estimates. It is disconcerting that when experimentally measured values are substituted into the {DLA} relationship {p} ; J = — (d[i/dT\ , the result is an uncomfortably wide range of predicted values for |r3 p/r3 r j , none of which satisfy the equality used in this study, nor agree with the actual values adopted by the original authors. In summary, I find that it is possible to obtain a match between the decompressed shear moduli of the lower mantle with a simplified pyrolite mixture (figure 4.5) without appealing to either an unusually high temperature derivative for Mg-perovskite or a high iron content. 4.9 Conclusions Chapter 4, page 437 In this study I obtain a new estimate for the decompressed lower mantle shear moduli by undertaking constrained adiabatic decompression of the seismic model P R E M . I assumed apriori that the bulk lower mantle composition was a pyrolite composition based on conclusions drawn earlier from an independent mineral physics study that modeled density and bulk sound velocity profiles along an adiabatic geotherm and compared them to seismic observations throughout the whole mantle. Hence, I interpret the decompressed properties of the lower mantle in terms of a simplified pyrolite mineralogy that is comprised of only Mg-perovskite and magnesiowustite, ignoring any contribution from Ca-perovskite. By adopting the simplified pyrolite composition it is possible to estimate a value for the unmeasured temperature derivative of the Mg-perovskite shear moduli, | d u / d r j by assuming that the decompressed value must equal the high temperature simplified pyrolite via: decompressed 7*=1607K Mo lower mantle Mo Pyrolite I obtain = -0.0224 GPa/K, a value that is not abnormal with respect to other high pressure phases (e.g. the corresponding parameter for MgO, measured at high temperatures, is -0.0260 GPa/K (Isaak et al., 1989)). Thus, I contend that Mg-perovskite does not have an unusually large temperature dependence of the shear modulus, as had been suggested earlier (Yaganeh-Haeri et al. (1989a, b), nor is the lower mantle enriched in iron with respect to the bulk upper mantle (Weidner and Zhao, 1992). The estimate determined here also does not support the relatively large temperature dependence inferred using {DLA} parameters. However, it appears that at least for Mg-perovskite, the {DLA} parameters do not provide a robust framework within which to predict the temperature derivative of the shear moduli. Chapter 4, page 438 As I noted in the introduction, there are two ways of comparing elastic data for minerals to seismological observations and the approach taken in this study was to adiabatically decompress the lower mantle and interpret the zero pressure properties to obtain an estimate for Sp/ST'I . To fully exploit this parameter, it will be necessary to adopt the alternative technique and extrapolate a pyrolite mineralogy to the high temperature and pressure conditions of the lower mantle. In this case, I will have to estimate a value for the unmeasured pressure derivative of the shear moduli for Mg-perovksite, (dp/<3P) . Nevertheless, this is not an impossible task, because unlike previous studies (e.g. Zhao and Anderson, 1994), this pressure derivative is now the single unknown parameter in modeling the Vs and Vp velocity profiles for a simplified lower mantle pyrolite composition. Chapter 4, page 439 4.11 References Anderson, D. L. , 1968. Chemical inhomogeneity in the mantle. Earth and Planetary Science Letters, vol., 5, 89-94. Anderson, D.L., 1977. Composition of the mantle and core. Annual Reviews of Earth and Planetary Science, vol., 5, 89-94. Anderson, D.L., 1988. Temperature and Pressure Derivatives of Elastic Constants with application to the Mantle. Journal of Geophysical Research, vol., 93, 4688-4700. Anderson, D. L. , and Bass, J.D., 1986. Transition zone of the Earth's upper mantle. Nature, vol., 320, 321-328, 1986. Anderson, D. L. , and Jordan, T., 1970. The composition of the lower mantle. Physics of the Earth and Planetary Interiors, vol., 3, 23-35. 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An application of normal mode theory to the retrieval of structural parameters and source mechanisms from seismic spectra. Philosophical Transactions of the Royal Astronomical Society of London, vol., A278, 187-269. Heinz, D. L. , and Jeanloz, R., 1982. Inhomogeneity parameter of a homogeneous Earth. Nature, vol., 301, 138-139. Hi l l , R.J., and Jackson, I., 1990. The thermal Expansion of ScA10 3 - a silicate Perovskite Analogue. Physics and Chemistry of Minerals, vol., 17, 89-96. Ito, E., E. Takahashi, and Y . Matsui, 1984. The mineralogy and chemistry of the lower mantle: An implication of the ultrahigh-pressure phase relations in the system MgO-FeO-Si0 2 . Earth and Planetary Science Letters, vol., vol., 67, 238-248. Isaak, D.G., Anderson, O.L., and Goto, T., 1989. Measured Elastic moduli of single crystal MgO up to 1800 K. Physics and Chemistry of Minerals, vol., 16, 704-713. Irifune, T., 1994. Absence of an aluminous phase in the upper part of the Earth's lower Mantle. Nature, vol., 370, 131. Chapter 4, page 441 Jackson, I., 1983. Some geophysical constraints on the chemical composition of the Earth's lower mantle. Earth and Planetary Science Letters, vol., 62, 91-103. Jackson, I., Khanna, S.K., Revcolevschi, A. , and Berthon, J., 1990. Elasticity, shear-mode softening and high pressure polymorphism of wiistite (Fe;. xO). Journal of Geophysical Research, vol., 95, 21,671-21,685. Jeanloz, R., 1981. Finite Strain equation of state for high pressure phases. Geophysical Research Letters, vol., 8, 1219-1222. Jeanloz, R., and Ahrens, T.J., 1980. Equations of state of FeO and CaO. Geophysical Journal of the Royal Astronomical Society, vol., 62, 505-528. Jeanloz, R., and Thompson, A .B . , 1983. Phase transitions and mantle discontinuities. Reviews of Geophysics, vol., 21, 51-74. Jeanloz, R., and Knittle, E., 1986. Reduction of Mantle and Core Properties to a standard state by Adiabatic Decompression. IN: Advances in Physical Geochemistry, edited by S. Saxena, vol., 6 pp. 275-309. Springer Verlag, New York. Jeanloz, R., and Knittle, E., 1989. Density and composition of the Lower mantle. Philosophical Transactions of the Royal Society of London, vol., A328, 337-389. Knittle, E., Jeanloz, R., and Smith, G.L., 1986. Thermal expansion of silicate perovskite and stratification of the Earth's mantle. Nature, vol., 319, 214-216. Knittle, E., and Jeanloz, R., 1987. Synthesis and equation of state of (Mg,Fe)Si0 3 perovskite to over 100 gigapascals. Science, vol., 235, 668-670. Liu, L . G., 1982. Chemical inhomogeneity of the mantle: Geochemical considerations. Geophysical Research Letters, vol., 9, 124-126. McKenzie, D., and Bickle, M.J. , 1988. The volume and composition of melt generated by extension of the lithosphere. Journal of Petrology, vol., 29, 625-679. McKenzie, D., and O'Nions, R.K., 1991. Partial Melt Distributions from inversion of Rare Earth Element Concentrations. Journal of Petrology, vol., 32, 1021-1091. O'Neill , B. , and Jeanloz, R., 1994. MgSi03-FeSi0 3-Al 203 in the Earth's Lower mantle; Perovskite and garnet at 1200 km depth. Journal of Geophysical Research, vol., 99, 19,901-19,915. Poirier, J.P., 1987. On Poisson's ratio and composition of the Earth's lower mantle. Physics of the Earth and Planetary Interiors, vol., 46, 357-368. Chapter 4, page 442 Ross, N .L . , and Hazen, R .M. , 1989. Single crystal X-ray diffraction study of M g S i 0 3 perovskite from 77 to 400 K. Physics and Chemistry of Minerals, vol., 16, 415-420. Sawamoto, H. , 1977. Orthorhombic perovskite (Mg, Fe)Si0 3 and constitution of the lower mantle, in: Hish Pressure Research. Manghnani, M . H . and Akimoto, S.,(eds.), pp. 219-244, Academic, San Diego, California. Shankland, T. J., and Brown, J.M., 1985. Homogeneity and temperatures in the lower mantle. Physics of the Earth and Planetary Interiors, vol., 38, 51-58. Stacey, F.D., 1996. Thermoelasticity of (Mg,Fe)Si0 3 perovskite and a comparison with the lower mantle. Physics of the Earth and Planetary Interiors, vol., 98, 65-77. Stacey, F. D., Brennan, B.J., and Irvine, R.D. 1981. Finite strain theories and comparisons with seismological data. Geophysical Surveys, vol., 4, 189-232. Sumino, Y . , Kumazawa, M . , Nishizawa, O., and Plushkell, W., 1980. The elastic constants of single crystal Fe/_ xO, MnO, and CoO, and the elasticity of stoichiometric wiistite. Journal of the Physics of the Earth, vol., 28, 475-495. Su, W., Mutter, C.Z., Mutter, J .C , and Buck, W.R., 1994. Some theoretical predictions on the relationships among spreading rate, mantle temperature, and crustal thickness. Journal of Geophysical Research, vol., 99, 3215-3227. Weidner, D.J., and Zhao, Y. , 1992. Elasticity and equation of state of Perovskite: Implications for the Earth's Lower mantle. IN: Hish Pressure Research; Application to Earth and Planetary Sciences, Syono, Y. , and Manghnani, M.H. , (eds.) American Geophysical Union, Washington, D.C., pp. 191-196. White, R.S., McKenzie, D., and O'Nions, R.K., 1992. Oceanic crustal thickness from seismic measurements and rare earth element inversions. Journal of Geophysical Research, vol., 97, 19,683-19,715. White, R.S., and McKenzie, D., 1995. Mantle Plumes and flood basalts. Journal of Geophysical Research, vol., 100, 17,543-17,585. Yeganeh-Haeri, A . , 1994. Synthesis and re-investigation of the elastic properties of single crystal magnesium silicate perovskite. Physics of the Earth and Planetary Interiors, vol., 87,111-121. Yeganeh-Haeri, A . , Weidner, D.J., and Ito, E., 1989a. Elasticity of M g S i 0 3 in the Perovskite structure. Science, vol., 243, 787-789. Yeganeh-Haeri, A. , Weidner, D.J., and Ito, E., 1989b. Single crystal elastic modulus of magnesium metasilicate perovskite. IN: Perovskite: a structure of Great interest to Chapter 4, page 443 Geophysics and Material Science. Navrotsky, A. , and Weidner, D.J., (eds.) American Geophysical Union monograph, vol., 45, 13-35. Chapter 4, page 444 270 U w GO Q H 2 6 0 <D N 13 o a a 250 b 240 order actual isotherm Ird order extrapolation 700 K-\ 1 actual isotherm 1 i 1 0.00 0.02 0.04 0.06 0.08 s t r a i n f 0.10 0.12 Figure 4.1 Theoretical F-f equations of state for Mg-perovskite. The solid lines were calculated from molecular dynamic data complete to zero pressure where as the 3rd and 4th order finite strain fits were based on a least squares fit to data above 20 GPa and extrapolated to zero pressure. Note that increasing temperature increases the discrepancy between the extrapolated and actual curves. Figure re-drawn from Bukowinski and Wolf (1990). Figure 4.2 Theoretical F-f equation of state fits to the PREM lower mantle. Figure re-drawn from Bukowinski and Wolf (1990). Chapter 4, page 446 700 800 900 1000 1100 1200 1300 1400 ^1500 H1600 •5 1700 JM800 P 1900 2000 2100 2200 2300 2400 2500 2600 W- 3(1+2g) a n + b n 8 + cx 2700 i l l l l l l l l T T I I I I I I I I I I I I I I I I I 5 2 (\+2gf2 — <h+ kg + <hg2 (\+2gf2 Fixed Po = 3.981 g/cm3 = 225.62 GPa O = 56.67 solved for l l l l l K' = 4.16 KSK" = - 5.59 n = 139.44 GPa = 7.47 W = -3.31 a = 0.2437 a\+kg + c>Jg2 —\ J _ L ' ' ' i i i i i i I I i I I I I 0.0 1.0 2.0 3.0 Figure 4.3 Constrained 4th order equation of state fit to the lower mantle portion of PREM showing the normalized pressure GK, and moduli G^ and Q as a function of depth. Chapter 4, page 447 150 O ^ 1 4 5 3 O 140 (3 m 135 CO GO © | 1 3 0 O o 125 11111111111111111111111111111111111111111111 n 11111111 tconstrained! study I 4th order J&K86) J&K86) fit t Q b u l k modulus-density 4th order f" (fit to velocities) i 111111111111 I 11111 11111 190 200 210 220 230 240 decompressed adiabatic Bulk Modulus^ (GPa) u(T) = n (T) + (J^r)(T - 298) KsiJ) = K4T) + (J f^) (T - 298) Figure 4.4 Decompressed shear modulus (p) versus decompressed adiabatic bulk modulus (K$ ). 0.27 decompressed lower mantle T = 1334 C I A •B 0.26 E- V gO.25 13 <D 0.24 m d) ?-OH O 0.23 o 0.22 T T T Chapter 4, page 448 1 1 F—3 adjusting the shear moduli temperature derivative shifts the predicted point only vertically. f , , Mg-perovskite Ks= 263.5 GPa V = 177.3 GPa 0 R J = -0.0224 GPa / l3 Jrd order J&K86 4th order J&K86 Pyrolite olite 4th or a e r constraint 1 7 h is study ~ I • I • I • I • I • 1 • I • 1 • I t 56 57 58 59 60 50 51 52 53 54 55 d e c o m p r e s s e d S e i s m i c P a r a m e t e r O ( T ) ( k m 2 / s e c 2 ) a ( T ) = ( 3 - 2 u ( T ) / K ( T ) ) ^ } (6 + 2^(T)/Kj:T)) O(T) = J&CD P(T) m = MCFJ + (|*) (T - 298) y unknown variable adjusted until pyrolite falls within the parameter space of the decompressed PREM lower mantle. p(T) = p(Tre^ +ct(T-298) K ( T ) = K (T e f ) + ( | ^ ) (T - 298) Figure 4.5 Decompressed Poisson's ratio (a) versus decompressed Seismic parameter (O). Chapter 3, page 449 0.000 -0.010 M I I I I I I I I I I lower mantfe 1071 km 1 ^-0 .020 o W - 0 . 0 3 0 E-p c o ~ a 0 4 0 -0.050 E--0.060 E •0.070 i I i i i i I i i i i l i i i i -pyrolite chondrite H perovskite ' ' ' ' H c !0 CD <B >-0.50 1.00 1.50 2.00 2.50 3.00 ( d p / d P ) Figure 4.6 Trade off curves between(5 p /ST^and(3 u/dP ),for Mg perovskite in pyrolite, chondrite and pure perovskite lower mantle compositions. Chapter 4, page 450 0.26 c 0.10 0.20 Fe/(Fe + Mg) Figure 4.7 Calculated Poisson's ratio as a function of iron content for a pyrolite composition. Also plotted is the calculated Poisson's ratio determined from constrained adiabatic decompression of the lower mantle PREM seismic properties. Chapter 4, page 451 0.000 -0.010 pO.030 C O CO ^>0.040 -0.050 -0.060 i n — 1 — 1 — r - 1 "ir*constrained adiabatic. ^decompressed lower mag. tie adopted value "| Mg-perovskite * .pyrolite z chondrite i perovskite J L <u 3.00 3.50 4.00 (5K 5/ap) r 4.50 5.00 Figure 4.8 Trade off curves between ^K^dT^and (df^/dPl for Mg perovskite in pyrolite, chondrite and pure perovskite lower mantle compositions. Also plotted are recent inferred values for (c3K/5T)J based on converting experimental estimates of (dKT/ffY)P to their adiabatic eqivalenis. 1, Wang et al. (1994) average value; 2, Funamori et al. (1996) best fit; 3, Utsumi et al. (1995); 4, Mao et al. (1991) fit B; 5, Stixrude et al. (1992) as listed in O.L. Anderson (1997); 6, O.L. Anderson & Masuda (1994); 7, O.L. Anderson (1997); 8, Zhao and Anderson (1994); 9, Duffy and Anderson (1989). Chatper 4, page 452 0.000 -0.010 ^ -0.020 OH o ^-0.030 H CO co-0.040 -0.050 -0.060 -0.070 3 ~ T I i i i i | i i i lower mantle @ 1071 km 1 1 1 1 | 1 1 1 1 | 1 1 1 1 -^ constrained adiabatic z decompressed lower mantle z ^ Mg-perovskite ~ ft this study z zr 2 1 -| E l \ ^ i i 1 i i i i 1 i i i 1 \ -perovskite \ \ ^chondritez i i I i 1 i i i i W , i i l l — t o c CO o> CD 0.50 1.00 1.50 2.00 (SLl/aP) 2.50 3.00 Figure 4.9 Trade off curves between (dp / ST),, and (dp / dP)T for Mg perovskite in pyrolite, chondrite and pure perovskite lower mantle compositions. Also plotted are the inferred values for (d\i 13T )P adopted by 2, Duffy and Anderson (1989) and 1, Zhao and Anderson (1994) and that calculated in this study. Chapter 5, page 453 Chapter 5 Mineral Physics constraints on the Chemical Composition of the Earth's lower mantle from Vs and VP velocity profiles; a test of the Pyrolite model. Chapter 5, page 454 5.1 Abstract Recent studies comparing predicted Vs and Vp velocity profiles for various bulk chemical compositions to seismological models have concluded that the lower mantle is chemically distinct from the upper mantle and transition zone (Zhao and Anderson, 1994). This is in conflict with the results of modeling density and bulk sound velocity profiles: for these properties, for which all the required parameters are experimentally measured, it is found that the lower mantle predicted p and V® profiles for a uniform composition provide an excellent fit to the seismic observations along an adiabatic geotherm concordant to the upper mantle geotherm. In contrast, the predicted p and F 0 for a piclogite composition, calculated along a realistic hot lower mantle geotherm, cannot fit the seismic observations. To resolve the discrepancy between the conclusions based on Vs and VP velocity profiles versus those based on p and F 0 1 extend our modeling to include Vs and Vp . I calculate, using third-order Birch-Murnaghan finite strain theory, Vs and VP velocity profiles for a pyrolite bulk composition throughout the lower mantle along an adiabatic geotherm previously calculated from modeling p and V®. For consistency, all of the thermoelastic parameters used in modeling p and F 0 are treated as fixed parameters, leaving only the shear moduli temperature and pressure derivatives as unknowns. I estimate the temperature derivatives for the Mg-and Ca-perovskite shear moduli [|<9 p/srj ] via the high temperature approximation of Isaak (1992). Next, for Mg-perovskite, I cross-check this prediction against the value determined via constrained adiabatic decompression of the lower mantle seismic properties. The two predicted estimates are virtually identical, implying that the temperature derivative estimates are robust. Consequently, these are held fixed to their predicted values and not treated as adjustable parameters in fitting the seismic profiles. For the pressure derivative of the perovskite shear moduli S p / d P I assume that the Ca- and Mg-perovskites have similar values and initially adopt the calculated value of Patel et al. (1996) for Mg-perovskite, determined by molecular dynamics simulations, and then perturb it to optimized the fit between the predicted and observed Vs and VP velocity profiles. Thus, a single parameter is being adjusted to fit the lower mantle seismic properties. I rationalize this "tuning" because I know apriori, from modeling p and V0, that the pyrolite model can satisfy the lower mantle seismic observations along this adiabatic geotherm, and hence, must also satisfy the seismic Vs and Vp observations. I check the resulting set of shear moduli derivatives to determine if they are mineralogically plausible when compared to other perovskite compounds. I find that the predicted Vs and VP velocity profiles for a pyrolite mantle can fit the lower mantle akl35 seismic profiles to ± 0.2% uncertainty. Thus, together with the results of a previous study for the upper mantle and transition zone, I find a uniform composition can fit the whole mantle seismic Vs and Vp observations along a single adiabatic geotherm. In contrast, when I adopt a hot lower mantle geotherm (Glatzmaier and Schubert, 1993) and Chapter 5, page 455 model a piclogite composition, the predicted profiles fail to match the seismic constraints. Therefore, away from chemical and thermal boundary layers that characterize the surface and basal thermal and chemical boundary layers of the mantle, a pyrolite composition with its associated phase changes, satisfies all the seismic constraints. There is no need to invoke any thermal or compositional breaks within or between the upper or lower mantle. This conclusion supports the findings from the previous modeling of p and V0 profiles and argues strongly that the present day style of convection within the Earth is whole mantle convection. Chapter 5, page 456 5.2 Introduction In a recent study, Zhao and Anderson (1994) calculated p, Vs , and V,, profiles in the lower mantle for both a pyrolite and piclogite composition and compared these profiles to the P R E M reference seismic model. They modeled both compositions along a lower mantle adiabat that has a mantle potential temperature of 1500 °C, a value that is consistent with independent estimates for the temperature of hot spot magmatism (White and McKenzie, 1995), and hence, approximately 150°K hotter than the "normal" upper mantle geotherm. They concluded that either compositional model could satisfy the seismic observations, claiming that the experimental data were too imprecise to rule out either compositional model as viable compositional model for the lower mantle. The conclusion that either model can satisfy the seismic observations is in conflict with our results from modeling density and bulk sound velocity for the pyrolite and piclogite compositions presented in chapter 2. In calculating density and bulk sound velocity I compiled an up-to-date thermoelastic data base of measured properties and found that of the two compositions considered, only a pyrolite compositional model, calculated along a self-consistent adiabatic geotherm consistent with a "normal" mantle potential temperature of 1334°C, could satisfy the seismic constraints. In contrast, the piclogite composition, when calculated along a hot lower mantle geotherm, resulted in predicted p and V& profiles that significantly misfit the seismic observations with the result that this compositional model could be unambiguously rejected. Because all the required thermoelastic data to calculate predicted p and V® profiles are experimentally measured, unlike the situation for Vs and VP profiles where significant gaps still remain in the experimental data base, the conclusions Chapter 5, page 457 drawn from modeling p and profiles are more robust than that deduced from studies which focus on Vs and VP profiles. Nevertheless, because, Vs and Vp velocity, and not bulk sound velocity, is routinely measured by seismology, it is the shear and compression velocity profiles that are of greater interest in solid earth geophysics. To determine if the discrepancy between the results of Zhao and Anderson (1994) based on predicted Vs and Vp profiles, and our prior results based on p and F 0 profiles, is real or an artifact, the modeling is extended to predict lower mantle Vs and VP profiles. However, unlike Zhao and Anderson (1994) who only considered a simplified two-phase mixture of Mg-perovskite and magnesiowustite to model both pyrolite and piclogite, I use the complete lower mantle mineralogy by including Ca-perovskite. Furthermore, I use experimental values for the coefficient of thermal expansion and the isothermal Anderson-Gruneisen parameter for Mg-perovskite unlike Zhao and Anderson (1994), who arbitrarily selected hypothetical values for both the coefficient of thermal expansion a (T = 900 K) and the adiabatic Anderson-Griineisen parameter 8S. Since Mg-Perovskite comprises a significant volume (68-77 vol%) in either compositional models (see figure 5.1 and 5.2), the choice of elastic data for this mineral is crucial to accurately modeling lower mantle properties. Thus, it is uncertain i f both a pyrolite and piclogite can provide equally good fits to the lower mantle given that the particular thermoelastic data for Mg-perovskite adopted by Zhao and Anderson (1994) is not based on experimental measurements. In contrast to the assertion of Zhao and Anderson (1994) who claimed that there is no compelling reason to accept or reject the very high or low experimentally measured values for a and 8S, I believe there is sufficient experimental (Navrotsky, 1989; Ross and Hazen, 1989; Parise et al., 1990; Chapter 5, page 458 Funamori and Yagi, 1993; Wang et al., 1991; 1994; Morishima et al., 1994; Kato et al., 1995; Utsumi et al., 1995; Funamori et al., 1996, Chopelas, 1996; Gillet et al., 1996) and theoretical (Hill and Jackson, 1989; O.L. Anderson and Masuda, 1994; O.L. Anderson et a l , 1995; 1996; Jackson and Ridgen, 1996) evidence to warrant rejecting the reported high values for these parameters (Knittle et al., 1986; Mao et al., 1991). Recall that it was the use of new laboratory elastic data for Mg-and Ca-perovskites that allowed us to match pyrolite p , and in the lower mantle along a self-consistent geotherm that was concordant with the upper mantle geotherm, contrary to previous studies. In addition to the difference in elastic data, I do not pursue modeling that involves perturbing any of the properties in the thermoelastic data base used previously in modeling p and V0 because in this study, I wish to focus on the unmeasured shear moduli properties of the perovskite phases, specifically the temperature and pressure derivative of the shear moduli ({d[i/dT)p, and {d\i/dP)T) for Mg-and Ca-perovskite, and the effects these properties have on the predicted Vs and Vp profiles. Consequently, to limit the number of adjustable parameters, I fix all the thermoelastic parameters used in modeling p and V® (Kf, (dKT/8T)p, (dKT/8P)T, a(T), y, 87) at the values adopted earlier, and in addition, adopt without modification, the self consistent adiabatic geotherm calculated in modeling p and F 0 when modeling the pyrolite composition. By contrast, for the piclogite model, I do introduce a single degree of freedom when calculating the predicted Vs and Vp profiles by undertaking the calculations with a "hot" lower mantle geotherm that is consistent with independent estimates of the lower mantle temperature structure for a convectively layered lower mantle (Glatzmaier and Schubert, Chapter 5, page 459 1993). It is invalid to model a distinct chemical composition, such as piclogite, along the same lower mantle geotherm that is used for a uniform composition, as Zhao and Anderson (1994) have done. This reflects the fact that the boundary separating a chemically distinct lower mantle from the upper mantle, will also be the site of a large thermal boundary layer, over which the temperature structure between the two regions rapidly changes. A l l previous studies have concluded that the lower mantle, i f chemically distinct, must have a significantly hotter temperature structure with the estimates in the increase in the lower mantle geotherm ranging from + 500 K to 1,500 °K (Jeanloz and Richter, 1979; Schubert and Spohn, 1981; Glatzmaier and Schubert, 1993). I note that while the adopted geotherm of Zhao and Anderson (1994) is hotter than both the preferred upper mantle adiabatic geotherm determined by Ita and Stixrude (1992; 1993), and that determined by our density and bulk sound velocity modeling (Calderwood, 1996); their temperature structure is also inconsistent with modeling either a pyrolite or piclogite composition in the lower mantle. For a uniform pyrolite composition, the adiabatic geotherm in the lower mantle should be concordant with that of the upper mantle, which the adopted geotherm of Zhao and Anderson's (1994) is not. On the other hand, as I noted above, for a lower mantle composition which is chemically distinct from the overlying upper mantle, the appropriate lower mantle geotherm should be significantly hotter than their adopted geotherm, which again, theirs is not. In this study I take advantage of two improvements that allow a much more reliable estimate of Vs and Vp velocity profiles in the lower mantle. First, the modeling, presented in chapter 2, of density p and bulk sound velocity has demonstrated that the pyrolite composition best matches the observed seismic properties throughout the whole mantle Chapter 5, page 460 along a concordant adiabatic geotherm. Consequently, barring pathologic behaviour of the shear moduli, I assume that the same pyrolite composition must also satisfy the seismological Vs and VP constraints. Thus, I adopt a pyrolite mineralogy, the related thermoelastic parameters, and the associated self-consistent adiabatic geotherm for the lower mantle and treat these as "fixed" parameters in modeling the lower mantle Vs and Vp velocity profiles. This significantly reduces the number of free parameters by fixing the values for Kj, (dA" 7 . /d7/^, {dKr/dP^, a(T), y, dp , and Tadiabatic- Consequently, I ( I \ Mg- Pv dyL/dTj and / , \ Mg-Pv pressure y 8 uy 8 Pj derivatives of the Mg-perovskite shear moduli. ( / \ Mg-Pv 8\x/8Tj for Mg-perovskite via a comparison between a "hot", but room pressure, shear modulus of a simplified pyrolite composition and the decompressed shear modulus of the lower mantle determined via constrained adiabatic decompression of the seismic model P R E M . In that study, laboratory properties for Mg-perovskite and magnesiowustite were corrected up to the mantle potential temperature of 1334°C and compared to "hot", but decompressed lower / / \ Mg-Pv mantle properties, with the goal of estimating a value for yd \JL/8 TJ for Mg-perovskite. The "hot" laboratory properties of the simplified pyrolite were dependent upon temperature / I \ Mg-Pv only and the yd\i/dTj property of the simplified pyrolite was the only unknown in order to match the pyrolite model to a decompressed seismic model of the lower mantle: Chapter 5, page 461 decompressed 7'=1607K ^0 lower mantle ^0 Pyrolite mix ( i \ Mg-Pv dii/dTj .1 may use this estimate for | 5 p / d 7 j ^ to check the independent estimates, calculated here, using the high temperature approximation of Isaak (1992), for the shear moduli temperature derivatives of Ca and Mg-perovskite. Hence, as a result of these calculations, I may constrain these unmeasured properties prior to any modeling of the lower mantle Vs and V,, velocity profiles. The estimates for (d p/5 f) for the perovskite phases are, consequently, treated as fixed parameters and not adjusted during fitting of the seismic profiles. Thus, the only parameter I adjust in modeling and fitting the lower mantle seismic Vs and Vp velocity ( / \ Mg-Pv dii/dPj Lastly, in modeling the lower mantle velocities I start with a recent result from molecular dynamics simulations of Mg-perovskite that provides an estimate for ( 5 p / 5 P ) T , the experimentally unmeasured value of the pressure derivative, to calculate Vs and Vp profiles. I assume that both Ca- and Mg-perovskite phases have the same pressure derivative and this initial value for ( 5 p / 5 P ) T is then perturbed to optimize the fit between the predicted and observed velocity profiles. I check the final set of temperature and pressure derivatives to ensure they are mineralogically plausible. In modeling the piclogite composition, I follow previous studies (Zhao and Anderson, 1994) and use the same elastic data set in calculating the velocity profiles, but along a hot lower mantle geotherm. Chapter 5, page 462 Using the constrained estimate for the (5 p/5 T) of Mg-perovskite I conclude that a pyrolite mineralogy provides an excellent fit to the seismic Vs and Vp profiles along a self-consistent adiabatic geotherm using mineralogically plausible values for the unmeasured shear moduli temperature and pressure derivatives. This geotherm, unlike that adopted by Zhao and Anderson (1994), is concordant with an adiabatic geotherm calculated for the upper mantle and transition zone - thus there is no need to invoke a thermal or chemical boundary layer at the 660 km seismic discontinuity to satisfy Vs and Vp constraints. In contrast, a piclogite model, when calculated along a hot lower mantle geotherm, cannot fit the observed seismic velocities, and consequently, may be rejected as a viable composition model. 5.3 Methodology I calculate shear (Vs ) and compression ( Vp ) velocity profiles (where Vs = /^pTp and Vp = yj[K + %[i)/p) using third-order Birch-Murnaghan finite strain theory as discussed in detail by Bina and Helffrich (1992) and outlined briefly below. Re-analysis of exiting P-V-T data for Mg-perovskite by Jackson and Ridgen (1996) has resulted in estimates for some of the mixed derivatives (e.g. [d2 KT where this property is used in accounting for the affects of temperature on the pressure derivative of the isothermal bulk modulus via: compliment of mixed derivatives are still unavailable (i.e. no estimate is available for Jackson and Ridgen (1996) estimates in the Chapter 5, page 463 following calculations. Furthermore, I restrict the calculations to a third-order equation of state since the analysis of experimental data on the lower mantle phases have not required higher fourth-order terms. A third-order Birch-Murnaghan equation of state is commonly used in extrapolating laboratory properties to the high temperature and pressure conditions of the mantle and has been used by nearly all previous studies that involved modeling Vs and Vp velocity profiles (e.g., Duffy and Anderson, 1989; Gwanmesia et al., 1990; Ridgen et al., 1992; Bina, 1993; Duffy et al., 1995; Zhao and Anderson, 1994). First I discuss the thermoelastic properties used in the calculations and compare the values adopted here with those values inferred by Duffy and Anderson (1989) and Zhao and Anderson (1994). Next, the third-order Birch-Murnaghan finite strain equations are introduced and discussed, followed by the Results. 5.4 Experimental Data base The thermoelastic parameters and the respective data sources for the minerals are listed in Table 5.1, 5.2 and 5.3. Those parameters that were utilized in modeling density and bulk sound [Kp, (d KT / dT^ p,(d Kr / d P^, a(T), 8 r , y] are held fixed (tables 5.1 and 5.2) at the values used in this previous study of lower mantle density and bulk sound velocity. Consequently, the "new" elastic properties [p, {d\i/dTJ , |c9p/9PJ ] introduced to calculate Vs and Vp velocity are listed in table 5.3. Chapter 5, page 464 Table 5.1. Summary of elastic data used previously in modeling p and F 0 Mineral v0 Km (dKj/8P)T (dKj/dTfp Y Molar Volume (cm3/mole) Isothermal Bulk Modulus (GPa) KJQ pressure derivative temperature derivative (GPa/K) Gruneisen Parameter Anderson-Griineisen Parameter Mg-perovskite 24.731" 261.50b 3.99° -0.0295" 1.50e 5.001 Ca-perovskite 27.450g 232.00s 4.80 s -0.0330 s 1.70 h 4.65" magnesiowustite 11.390' 158.861 4.10 k -0.0270' 1.50 m 4.30" a, based on the Fe and Al content in Mg-perovskite from Irifune (1994) and expressed in the molar volume relationship of O'Niell and Jeanloz (1994); b, from Jeanloz and Hemley (1994) and Yeganeh-Haeri (1994); c, after Knittle et al. (1987) and Jeanloz and Hemley (1994); d, after Funamori et al. (1996); e, after O.L. Anderson et al., (1995; 1996) and Chopelas (1996);/ after O.L. Anderson et al., (1995; 1996) and Chopelas (1996); g, Wang et al., (1996); h, after Wang et al. (1996) and Wang and Weidner (1994); i, j , k, 1, m, n, . I utilize the most up-to-date data for the various parameters and kept within the reported experimental error stated by the respective authors. Following convention (e.g. Bina and Helffrich, 1992) the elastic properties of a phase are estimated by averaging on the mole fraction of the end member phases assuming ideal mixing (e.g. the bulk and shear moduli for (Mg 0 8 6Fe o 1 4 )0 are determined by 0.86 MgO + 0.14 FeO). Table 5.2. Constants in the polynomial expressions for the coefficient of thermal expansion. Mineral Formula coefficient of thermal expansion a(T) = a 0 + a i r + a 2 r -2 oc0 a. Mg-perovskite17 M g S i 0 3 1.982 x 10"5 0.818( ± 0.257) x IO'9 -0.4740 (±0.118) this study 1.982 x IO"5 0.918 x IO"9 -0.4740 Ca-perovskite18 CaSi0 3 3.06 x 10"5 magnesiowustite19 (Mg,Fe)0 3.768 x IO"5 7.404 x 10'9 -0.7446 17, Funamori et al., 1996, note I s ightly adjusted the coefficient oq within the stated experimenta errors by 0.100. This is shown in the row directly below; 18, Wang et al., 1996, I use the empirical relationship of O.L. Anderson et al., 1992 to extrapolate this value to high temperatures (their eq. # 31): ( a ( r ) / a 7 > e ) = l / [ l + a 7 . > e 8 7 ,(r-7^)], where 0 is the Debye temperature for Ca-perovskite (TQ = 1100 K), 5 j is the Anderson-Gruneisen parameter which for Ca-perovskite 8j = 4.65. O.L. Anderson et al. (1992) apply this to Mg-perovskite due to the paucity of high temperature thermal expansion data for that mineral; 19, Fei 1995. Chapter 5, page 465 5.5 Magnesiowustite (Mg 0 - 8 6 Fe a H )O There are a great number of ultrasonic, static compression, shock-wave, and theoretical studies of the thermoelastic properties of periclase (Isaak et al., 1989; Anderson and Zou, 1989; Isaak et al., 1990; Duffy and Ahrens, 1995; Inbar and Cohen, 1995; Duffy et al., 1995; Fiquet et al., 1996), and to a somewhat lesser degree, on wiistite (Jackson et al., 1990; Stolen and Gronvold, 1996; Mao et al., 1996), and magnesiowustites with varying iron content (Sumino et al., 1980; Jackson et al., 1978; Bonczar and Graham, 1982; Richet et al., 1989; Fei et al., 1992). Consequently, the required parameters for this mineral are well constrained such that reliable predictions of density and velocity at lower mantle conditions may be made. The adopted iron content used here [ (Mg 0 8 6 F e 0 1 4 ) 0 ] for magnesiowustite reflects the experimentally determined iron content from the observed iron partitioning between magnesiowustite and Mg-perovskite in a natural pyrolite bulk composition (Irifune, 1994). Richet et al. (1989) reported a study of the bulk modulus of (Mg,Fe)0 as a function of iron content by in situ x-ray diffraction and concluded that KJQ is only weakly dependent upon the iron content, especially for the relatively low iron contents considered here. The values for (Kj, [dKr/dT^, and {dKT/dP^ , 8 r , y) are from Fei et al., 1992, who analyzed P - V - T data for a magnesiowustite which has a greater iron content that that used here [ (Mg 0 6 0 Fe O.4o)0]- m spite ° f the difference in iron content, the derived value for (dKr/dT\ = -0.027+0.003 GPa/K, is very similar to the value experimentally measured p for pure M g O at lower mantle temperature Chapter 5, page 466 0.028±0.001 GPa/K, Isaak et a l , 1989). The adopted pressure derivatives of the shear modulus is taken from Bonczar and Graham (1982) where they studied the change in (a^/ar) and ( a p / a p ) as a function of iron content of magnesiowustite. Since this study did not experimentally analyze a specimen of composition [(Mg 0 8 6 Fe 0 , 4 )0], I interpolated between the reported results for [(Mg0 9 2Fe 0 , 2)0] and [(Mg0 7 2 5 Fe 0 2 7 5)0] (see figure 5.3). The adopted temperature derivative {dyi/df^ is taken from the high temperature rectangular parallelepiped resonance experiments of Isaak et al. (1989) on pure MgO, since this study recorded measurements across the temperature range of 300-1800°K, and hence, up to temperatures representative of the lower mantle. I assume that for the low iron content adopted here, that the appropriate value for [(Mg 0 8 6 Fe 0 1 4 )0] will not be significantly different. While it is evident that a complete set of thermoelastic data does not, at present, exist for [(Mg 0 8 6 Fe 0 I 4 )0] magnesiowustite, and hence, the thermoelastic parameters used here are a "composite" of measurements made on magnesiowustite and periclase, I consider, as have previous studies (Jackson, 1983; Zhao and Anderson, 1994), that the thermoelastic properties of magnesiowustite may be treated as "known". Consequently, I assume that the thermoelastic properties of this mineral as well constrained, at least with respect to Mg-and Ca-perovskite. 5.6 the Ca-Perovskite shear modulus The room temperature and pressure values for the bulk and shear moduli for Mg-perovskite are now known with confidence (Yeganeh-Haeri, 1994) and I use these values to Chapter 5, page 467 estimate the unmeasured shear modulus of Ca-perovskite from the empirical mineral systematic relationship used by Bass (1984) on perovskite analogue compounds: VP A / M = constant where M is the mean atomic weight (the molecular weight divided by the number of atoms in the molecule), and Vp is the compression velocity. Specifically, adopting the measured properties for pure Mg-perovskite ( M = 20.08, Ks = 261.5 GPa, p = 177.3, p = 4.108 g/cm3), the empirical relationship predicts a value for the constant of: JM= 49.333. I assume that the Mg-perovskite value for the empirical "constant" applies to Ca-perovskite, and use it to estimate the unmeasured shear modulus. Thus, for Ca-perovskite the measured properties are M = 23.23, Ks = 232 GPa, p = 4.231 g/cm3 (Wang et al., 1996), and result in a predicted shear modulus of p = 158.4 GPa. Alternatively, this value may be cross-checked by a prediction using the relationship advocated by Ita and Stixrude (1992; 1993): where, in this case, Vo and p are the molar volume and shear modulus of Ca-perovskite, and Voref ana" V-ref a r e the molar volume and shear modulus of Mg-perovskite. This simple relationship predicts p = 157.9 GPa, in excellent agreement with the previous estimate. I simply adopt a value very near the arithmetic average of the two predictions (p = 159.00 GPa). Note the estimate here is significantly greater than the value originally estimated by Bass (1984) and subsequently adopted by Duffy and Anderson (1989; p = 125 GPa). This VpyJM = l 1 Chapter 5, page 468 difference can be attributed to two factors. First, the density of Ca-perovskite is now well known (p = 4.231 g/cm3) and is significantly greater than the value adopted by Bass (1984; p = 4.13 g/cm3). Second, the measured properties (Ks, p, and p) of Mg-perovskite provide a complete reference silicate perovskite (as opposed to analogue perovskites) with which to base predictions on for the Ca-perovskite phase. 5.7 Mg-Fe-Perovskite As noted above, I adopt as fixed for this study all the properties used earlier in modeling p and V0 profiles in the lower mantle (V0, Kj, l^dKT/dTj ,{dKT/d PJ , a(7), 5 7 , y) and hence only introduce the shear modulus, and its temperature and pressure derivatives (p, |<9p/drj , {d\i/dP^ ). Nevertheless, I briefly justify the choice for the thermoelastic data for Mg-perovskite since these properties are critical in the final velocity profiles. The value for the coefficient of thermal expansion [a(7)] is central to discussions on whether or not the lower mantle is chemically distinct from the upper mantle and transition zone. Theoretical studies using the decompressed properties of the lower mantle (Jackson, 1983; Jeanloz and Thompson, 1983) noted that if the average value of the coefficient of thermal expansion of Mg-perovskite, taken over the temperature range of 298-1400 °C, was greater than 3.0 x 10"5 K"1, then the decompressed density of the lower mantle could not be matched simply by a "hot" mixture of Mg-perovskite and magnesiowustite with a bulk composition equal to the upper mantle. These studies noted that for a m e a n > 3.0 x 10"5, the Chapter 5, page 469 bulk composition must be enriched in iron and/or possibly silica, while i f it was below this value, then no change in chemical composition was required. The focus on density as the criteria in determining the chemical composition of the lower mantle reflected the lack of measured values for the temperature derivatives for the bulk and shear modulus. Because density is also used in calculating the shear and compression velocities, the experimentally measured value of the coefficient of thermal expansion for Mg-perovskite is central to questions on the composition of the lower mantle. Expansivity is determined via analysis of relative molar volume (V(T)/V29S) versus temperature (see figure 5.4). This figure shows calculated curves of the change in molar volume, normalized to its room temperature value, as a function of temperature generated via the Suzuki et al. (1979) equation (see below). These curves are typically fit to experimental data (see figure 5.5, for an example) and allow the variation of the coefficient of thermal expansion with temperature to be determined by taking the derivative of the best fit curve; the resulting curves of thermal expansion are presented in figure 5.6 (from O.L. Anderson and Masuda, 1994). The curves in figure 5.4 and 5.6 were generated with all of the required parameters in the Suzuki equation (V0, KJQ, [d KT/d PJ , 0 ) held fixed at the values listed in the figure except for the Gruneisen parameter (y), with the intention of focusing on this parameter and its affect on the calculated coefficient of thermal expansion. As noted by O.L. Anderson and Masuda (1994) there is general agreement now on the values for V0, KJQ, d KT Jd Pj , 0 for Mg-perovskite, but not for y, which led them to isolate its affects on the calculated thermal expansion coefficient. I return to discuss these parameters below, after Chapter 5, page 470 further discussion of the experimental constraints on the coefficient of thermal expansion for Mg-perovskite. As noted by Zhao and Anderson (1994) and others there exists a discrepancy between the coefficient of thermal expansion reported by Knittle et al. (1986) and Mao et al. (1991) on one hand and Wang et al. (1994) on the other (the Wang et al. values are also supported by experimental work by Navrotsky, 1989; Parise et al., 1990; Funamori and Yagi (1993); Utsumei et al., 1995; Funamori et al., 1996; Chopelas, 1996; Gillet et al., 1996). The inferred thermal expansitivity of Knittle et al., (1986) and Mao et al., (1991) as a function of temperature is shown in figure 5.7. The two curves of Mao et al. (1991) are derived from fitting their experimental P-V-T data alone and their data in combination with the previous zero pressure thermal expansion measurements. Specifically, they fit their data to an equation of state where the thermal contribution of the P-V-T data was calculated from; 8 r = -1 a Kr V dT J p where 87 is the isothermal Anderson-Gruneisen parameter and is assumed to be a constant at high temperatures above the Debye temperature. The coefficient of thermal expansion is expressed as: 1 a = — V where the coefficients in the polynomial expansion (a0, a,, and a2) represent the zero pressure state. Lastly, the temperature dependence of the isothermal bulk modulus was expressed as: rdK^ V dT j (r-298) Chapter 5, page 471 They optimize the coefficient of thermal expansion, a and | d Kr/8 rj simultaneously from their P-V-T data and also constrained the value of a at 400 °K to equal the estimate of Ross and Hazen (1989; a 4 0 0 ° K = 2.2 x 10"5 1/K). The least squares fit result in the thermal expansion curve labeled fit A in figure 5.7 and resulted in values of (s KT/d r) = -0.080±0.005 GPa/K and 87 = 7.5±1.0 for temperatures above 950°K. Alternatively, they also fit the Knittle et al. (1986) V-T data, fixing the 400 °K value of a to equal the value estimated by Ross and Hazen (1989). This results in the thermal expansion curve labeled fit B in figure 5.7 and dKT/dT} = -0.063 ± 0.005 GPa/K and 87 = 6.5 ± 1.0 above 950 K. They note there exists a correlation between a and Sj 1 such that a high value for the room temperature thermal expansion coefficient at zero pressure requires a high value for 87 to satisfy the experimental data. Of note is that the values for a, , and dp derived by Mao et al. (1991) are very high (in comparison to subsequent analysis of Mg-perovskite and other mantle silicates). The Mao et al., (1991) data set was subsequently used by Hemley et al., (1992), Stixrude et al. (1992), Ita and Stixtrude (1992; 1993) in modeling lower mantle density and bulk sound velocity, and in part, used by Zhao and Anderson (1994) in modeling density and V$ and Vp. In a subsequent experimental study, Wang et al., (1994) noted that their Fe bearing Mg-perovskite samples [Mg 0 9 Fe 0 ,)Si0 3] exhibited irreversible behavior on heating whereas the pure Mg end member was reversible to « 400°K. This bears on the Mao et al. (1991) study since their data set included iron bearing perovskites with compositions of [Mg 0 9 Fe 0 1 )SiO 3 ] and [Mg 0 8 Fe 0 2 )SiO 3 ] . Wang et al. (1994) also note that the thermal Chapter 5, page 472 expansion coefficient determined by Ross and Hazen (1989), and subsequently used by Mao et al. (1991) as a 400°K constraint on ct(7), is not a robust value because the single high temperature point (381°K) that was used in calculating the value of 2.2 x 10"5 K/ ' is from a measurement where the perovskite crystal became twinned, and hence, began to break down. Wang et al., (1994) found that their low temperature (77-400 °K) mean thermal expansion for Mg-perovskite (1.6 x 10"5 K"1) agreed with that of Ross and Hazen (1989) over the temperature interval 77- 298 °K (1.5 x 10"5 K"1), whereas inclusion of the 381°K point elevated the latter's average up to 2.2 x 10"5 K _ l . The observation by Wang et al. (1994) that Mg-perovskite samples exhibit irreversible behavior on heating above « 400 °K is also relevant to the Knittle et al., (1986) data set, since their preferred value for the coefficient of thermal expansion is based on fitting only the high temperature (T = 450-850 °K ) subset of their total data set. Hi l l and Jackson (1989) had earlier re-analyzed the Knittle et al. (1986) data set using the Gruneisen theory of thermal expansion as formulated by Suzuki et al. (1979), as did Knittle et al., (1986), but with the addition of constraints on the bulk modulus and Debye temperature from the single crystal elasticity measurements of Yeganeh-Haeri et al. (1989). The form for the Suzuki equation is: where V0K is the molar volume and the subscript zero represents ambient conditions, V(T) is l-4kE the molar volume at the experimental temperature where Chapter 5, page 473 ( d KT/d P is the pressure derivative of the isothermal bulk modulus, KJQ is the isothermal bulk modulus, y0 is the Gruneisen parameter, and E is the thermal energy which is a function of (T/0) and commonly approximated by (Hill and Jackson, 1990; equation 3): and 0 is the Debye temperature, which may be estimated by its acoustic approximation calculated from the density, and shear and compression velocities via (O.L. Anderson 1995, where the constant 251.2 embodies the terms h/k\9 N A / 4nj where h is Planck's constant, k is Boltzmann's constant, and NA is Avogadro's number, M is the mean atomic weight (the molecular weight divided by the number of atoms in the formula), p is the density, and Vs and Vp represent shear and compression velocities respectively. Knittle et al. (1986) had originally fit their molar volume data to obtain values for the Gruneisen parameter, Debye temperature, the pressure derivative, and the zero temperature molar volume of Mg-perovskite and gave two sets of parameters representing a best fit to the full temperature range (298-840 °K) and a fit to just the high temperature data (450-840 °K), which they favoured (see table 5.3 below). Their high temperature fit resulted in an average thermal expansion coefficient over this temperature range of 4.0 xlO"5 K"' and a room temperature value of 3.14 x xlO"5 K"1 (the resulting curve of expansivity versus temperature is shown in figure 5.4 while the corresponding curve of the coefficient of thermal expansion as p . 2 4 ) : -1-1/3 Chapter 5, page 474 a function of temperature, taken from O.L. Anderson and Masuda (1994), is plotted in figure 5.6 and 5.7). In re-analyzing the Knittle et al. (1986) data set, Hi l l and Jackson (1989) constrained the values for the isothermal bulk modulus (KJO = 246 ± 5 GPa) and Debye temperature (0 = 1094 K) from the elasticity data of Yeganeh-Haeri et al. (1989), fixed d Kr/d p) = 5.0, and then solved for the Gruneisen parameter (y0) in the Suzuki equation. They found it was impossible to fit the entire V-T data set with a single value for the Gruneisen parameter y0; either the lower temperature subset (<350°C) was fit well by y0 = 1.20 with the high temperature data being underestimated (a fit which also satisfied the low temperature Ross and Hazen (1989) data); or the high temperature subset was fit, but without satisfying the lower temperature data. Consequently, they argued that the expansitivity of Mg-perovskite was not well experimentally well constrained, based on the Knittle et al. (1986) data, and speculated that the results might be invalid because the measurements were collected under conditions where Mg-perovskite exists in a metastable state. In contrast to the concerns expressed by Hil l and Jackson (1989), the high value determined by Knittle et al. (1986) appeared to receive support from the results of the Mao et al. (1991) study, which as noted above, also determined very high values for the coefficient of thermal expansion. Nevertheless, subsequent experimental (Parise et al. (1990), Wang et al. (1991; 1994), Funamori and Yagi (1993); Utsumi et al., 1995; Funamori et al., (1996); Navrotsky (1989); Chopelas (1996); Gillet et al. (1996)) and theoretical (Anderson and Masuda; 1994; O.L. Anderson, 1995; 1996) studies do not supported such high values (see figure 5.7). Specifically, the careful experimental study of Wang et al. (1994) where unit cell measurements were made both on the increasing temperature and decreasing Chapter 5, page 475 temperature legs of the heating cycles have demonstrated clearly that suspicions of Hi l l and Jackson (1989) concerning the stability of Mg-perovskite outside its stability field is justified and that the very high oc(7) values reported by Knittle et al., (1986), based on measurements at temperatures where Wang et al. (1994) observed irreversible behavior, are not likely to be valid. Likewise, the Mao et al., (1991) data set may also likely to suffer the same problems. For instance, of the 17 experimental runs listed in their table 2, where the run temperature for the iron bearing sample [Mg 0 9 Fe 0 i)Si0 3 ] exceeded room temperature, there is only a single run below 400°K, the temperature at which Wang et al. (1994) found Mg-perovskite began to transform into amorphous phases. Thus, the temperature dependence of the thermal expansion coefficient in the Mao et al. (1991) experiments is largely based on measurements where the temperature would have caused Mg-perovskite to decompose. Recently, a relatively new method has been applied to determining the thermal expansion of Mg-perovskite that does not suffer from the problems of irreversible behavior documented in the above studies. Chopelas (1996) and Gillet et a l , (1996) analyzed Mg-perovskite via Raman vibrational spectroscopy as a function of pressure. Chopelas (1996) notes that a, y, and oj1 may all be constrained from measurements of vibrational spectra as a function of pressure. The Gruneisen parameter may be approximated by the weighted average of the mode Gruneisen parameters, while the high pressure measurements, in conjunction with statistical mechanics, allow the pressure dependence of Cp and entropy 5" to be determined. In turn, the pressure dependence of entropy allows an accurate estimate of thermal expansivity, since a thermodynamic Maxwell's relation links a change in entropy as a function of pressure to the change in volume as a function of temperature via: Chapter 5, page 476 rdV^ dT) Because the coefficient of thermal expansion is defined as: a = V dT) it is straightforward to calculate thermal expansion by multiplying the change in entropy with pressure by the molar volume at those conditions. Of specific note, is that the entropy measurements as a function of pressure, determined via Raman spectroscopy, are made at room temperature and do not involve heating the mineral sample, as do the above experimental techniques. Consequently, the problem of mineral decomposition and meta-stability do not exist for this technique. In addition, the vibrational frequencies are measured with uncertainties to < ± 0.3% and the observed change in vibrational frequency with increasing pressure (for P up to 65 GPa) is greater than or equal 30%, which results in well determined estimates of the change in entropy with pressure [d s/d p) , and hence, thermal expansion. Lastly, the isothermal Anderson-Gruneisen parameter may be accurately estimated by analysis of the resulting values of the coefficient of thermal expansion at high pressure. As noted by Chopelas (1996) the Gruneisen parameter determined via Raman spectroscopy is calculated by the weighted average of mode Gruneisen parameters via: d In co, dlnV y = Chapter 5, page 477 where Q is the Einstein heat capacity of mode i, and (5 In co ;/5 \nV)T'is the mode Gruneisen parameter, where ©j is the vibrational frequency for the mode and V is the volume. The calculated Raman Gruneisen parameter y is usually slightly less than or equal to the thermal Gruneisen parameter y estimated via its thermodynamic definition: a K a V < V = y y Chopelas (1996) calculated y =1.43 which implies y = 1.45-1.50. From the density of states (also known as the frequency distribution function), g(co), she determined the heat capacity at constant volume Cy , which is then converted to its equivalent at constant pressure (Cp), via C,.= C K ( l + ay7'). This, in turn, allows the entropy to be calculated via: T r S= p^dT. o T By obtaining Raman vibrational spectra at successively higher pressure, the heat capacity and entropy at high pressure may be determined. Lastly, the change in entropy with pressure, [dS/'d P J may be used to determine thermal expansion via the thermodynamic Maxwell's relation discussed above. To determine Cy the density of states and temperature T is required; the density of states is constructed from the Raman vibrational spectra and elastic data, while T is simply the room temperature. To estimate Cp both the thermal expansion (a) and Gruneisen parameter (y) are needed, and as Chopelas (1996) notes, values for these parameters may either be taken from independent estimates, or iteratively calculated, as was Chapter 5, page 478 done in her study. The initial estimate for the room temperature thermal expansion (a) was 2.2 x 10"5 K"1 (Ross and Hazen, 1989), while the final value from iterative substitution was 1.8(±0.1) x 10"5 K" 1. This value predicts a thermal Gruneisen parameter of 1.42 +0.07 (with Cp = 80.6 kJ/mole °K (Akaogi and Ito, 1993), Ks = 263 GPa (Weidner et al., 1993); see table 5.3), in good agreement with the approximation from the vibrational frequencies (y = 1.43). The room temperature and pressure value for the thermal expansion of Mg-perovskite of 1.8 x 10"5 K"1 is in agreement with the results of Wang et al., (1991; 1994), Funamori and Yagi (1993); Funamori et al., (1996), Utsumi et al., (1995), and the results from an early thermodynamic study, based on Raman spectroscopy (Navrotsky, 1989), and lastly, a recent Raman spectroscopy study of Gillet et al., (1996). The 5 estimates determined by Chopelas (1996) and the inferred curve for thermal expansion as a function of temperature are shown in figure 5.8 as is the calculated thermal expansion curve from Gillet et al., (1996). While there is very good agreement to 1000 °K, both studies, when extrapolated to very high temperatures (« 2000°K), appear to under predict the calculated thermal expansion curve of Funamori et al. (1996) which is based on in situ X-ray measurements at pressures of 21-29 GPa and temperatures of 300-2000°K (note that for the Funamori et al. (1996) experiments, the high temperature measurements were made while the sample was at a pressure inside the perovskite stability field). Chapter 5, page 479 Table 5.3 Comparison of thermoelastic data used in some recent studies. Note the change in room temperature value for the coefficient of thermal expansion. parameter Knittle et al., 1986 Mao et al., 1991 Wang et al., 1994e Chopelas, 1996 Gillet etal., 1996a a(298°K) 3.14 x IO"5 2.17 x IO"5 1.72 x 10"5 1.8 ±0.1 X 10"5 1.7±0.1 x 10"5 0 (°K) 825 1017 1094 Ks (GPa) 263d KT (GPa) 260 263 261 261 (dK,./dp)r 4.0 3.9 4.0 4.0 V 0 (cm3/mole) 24.39 24.46 24.46 24.44 24.426 Y 2.20 1.96 1.3±0.2 1.4210.07 1.30 87/ 7.0 3.73 4.8b 4.2 Cp (kJ/mole°K) 80.6C a, a(298°K) of Gillet et al., (1996) was read off their room temperature and pressure curve in their figure 4, which plots the calculated thermal expansion at different pressures and temperatures. b, recommended value for calculations extending over the full pressure range of the lower mantle. c, d, adopted from Akaogi and Ito (1993). e, average low temperature values for the thermal expansion and Gruneisen parameters at zero pressure and 77- 400 °K. Note that values which are adopted in the respective studies are listed in italics, while calculated values are in normal font. The major point of this discussion is that the coefficient of thermal expansion for Mg-perovskite is well determined, certainly for the room temperature and pressure value, and this value is significantly less than the early experimental values of Knittle et al. (1986) and Mao et al. (1991). I emphasize this because Zhao and Anderson (1994) assert that there is no compelling reason to reject or accept the high or low values for the coefficient of thermal expansion determined by Mao et al (1991) and Wang et al. (1994). Specifically, their arguments appear to rest in large part on their figure 1, re-plotted here as figure 5.9. This figure shows values for Mg-perovskite thermal expansion (solid circles) representing a temperature of 900°K and various pressures read from the calculated thermal expansion curves in figure 8 of Mao et al. (1991). Note that these circles are not experimental data, but Chapter 5, page 480 inferred values based on the fits Mao et al. (1991) made to their data. Also shown at zero pressure are a number of open triangles representing low and high temperature points taken from a variety of sources (see table 1 in Zhao and Anderson (1994)). Finally, solid diamonds represent some of the high temperature and pressure experimental data of Wang et al., (1994). Zhao and Anderson (1994) calculated three predicted curves for the thermal expansion at simultaneous high temperature (T = 900°K) and pressure with the constraint that the curves must satisfy the room temperature (a 2 9 8°K) and 36 GPa experimental datum of Funamori and Yagi (1993; 1.7(±0.2)xl0"5 K " 1 ) . They start with an adopted high temperature value for the Mg-perovskite thermal expansion coefficient at 900 K (a 9 0 0 ° K ) , which is inferred to represent an average value between room temperature (298°K) and the maximum temperature (« 1773 °K) to which they correct up the room temperature reference properties. The a 9 0 0 ° K value is then corrected to high pressure using an empirical relationship that depends on the adiabatic Anderson-Griineisen parameter (bg, see below) in conjunction with an estimate for the Gruneisen parameter (y) to approximate the isothermal Anderson-Griineisen parameter. The isothermal Anderson-Griineisen parameter is used in predicting the pressure dependence of the coefficient of thermal expansion via (O.L. Anderson, 1967; Chopelas and Boehler, 1989): f \ r ..\h? a where the 0 subscript is the zero pressure value, Vis molar volume, and 87. is the isothermal Anderson-Griineisen parameter. Anderson and Masuda (1994) note that this expression is Chapter 5, page 481 generally valid for the compression where the ratio (V/V0) is limited to (0.9 < V/V0 < l ) , and hence, should not be used over the lower mantle. Chopelas and Boehler (1992b) advocate a slightly modified version of the above relationship where the high temperature value of the Anderson-Grtineisen parameter is not treated as a constant but allowed to vary as a function of pressure: ^ 5 T ^ m\ • 1 where the empirical parameter m varies little between the compounds experimentally measured by Boehler (1981, 1982). As noted by Isaak (1993) the parameter m is related to the Anderson and Masuda (1994) parameter K via: K = Anderson and Masuda (1994) and Anderson et al. (1995; 1996) advocate a form for the Anderson-Gruneisen parameter which accounts for the affects of pressure via: where 8^'0ris the measured value at ambient pressure but high temperature, and K is a constant which controls the variation of hfo with pressure (like the constant m of Chopelas and Boehler (1992; see table 3 of Anderson and Masuda (1994) for a comparison between calculated K and m). This relationship for the isothermal Anderson-Gruneisen parameter results in the following expression for thermal expansion as a function of pressure (Anderson and Masuda, 1994): Chapter 5, page 482 a exp v a 0 y 'TO K where a 0 is the thermal expansion at ambient pressure, and 8 ^ is the isothermal Anderson-Griineisen parameter at high temperature (henee the "hiT") but ambient pressure. Anderson and Masuda (1994) argued that K = 1.5 on the basis of the fit between calculated expansivity and the high pressure expansivity data of Funamori and Yagi (1993) and Wang et al. (1994). They note that the values advocated for m (« 6.5) by Chopelas and Boehler (1992) result in calculated values for K « 1.33-1.64 but that the calculated high pressure expansivity is relatively insensitive to the particular value for K («1.5±0.7). In contrast, the calculated expansivity is sensitive to the value for hjl (see Anderson and Masuda, 1994 figure 5.9). Anderson et al. (1995) presented further arguments to emphasize that the calculated coefficient of thermal expansion, when expressed in the Suzuki equation, is sensitive to bjl and y0, but not K . They also re-iterated that their initial choices for 8^'0r and Yo? (5-0 and 1.5) in Anderson and Masuda (1994) were based on experimental data for MgO, but were based on thermodynamic arguments. Additional arguments in favor of slightly lower values of d^-= 4.2 and Y 0 = 1 -4 have recently been presented by Anderson et al. (1996). Recently, Chopelas (1996) has expressed the pressure dependence of thermal expansion as: „h,r\ V Chapter 5, page 483 where 8 ^ represents the high temperature value, used in correcting the thermal expansivity to high pressure. When this result is compared with that of Anderson and Masuda (1994), given above, I note that the expression advocated by Chopelas implies the parameter K = 1. In contrast, Zhao and Anderson (1994) invoked a high temperature and pressure approximation 6f^8s+y to express the pressure dependence of the high temperature thermal expansion of Mg-perovskite and magnesiowustite via: where the zero pressure thermal expansion cx0 = a 9 0 0 ° K . While the value for 8S was given in the table of thermoelastic properties, the values for both the Gruneisen parameter y, and the isothermal Anderson-Gruneisen parameter, S 7 7 are not listed, and consequently, it is not possible to determine exactly what value Zhao and Anderson (1994) used for the combined 8s+y term in correcting the coefficient of thermal expansion to high pressures. This uncertainty notwithstanding, Zhao and Anderson (1994) state that i f a high value for the 900°K thermal expansion of Mg-perovskite is chosen (e.g. a 9 0 0 ° K = 4.5 x 10"5 K" 1), it must be accompanied by a high value for 8S (e.g. 8S = 6.5), i f the room temperature but 36 GPa value of Funamori and Yagi (1993) is to be satisfied. This trade off between the values for a and 8s+y mirrors a similar comment of Mao et al. (1991) concerning the trade off between a and 8T. I point out that it is not clear why Zhao and Anderson (1994) fit combinations of a 9 0 0 o K and 8S to a single experimental data point at room temperature but high pressure. Nevertheless, because Zhao and Anderson (1994) believe there is no reason to reject the high or low experimental values for a, they felt justified in adopting a value for Chapter 5, page 484 a9oo°K which is not based on any experimental measurements, and simply lies approximately half-way between the Mao et al., (1991) and Wang et al. (1994) results (see adopted the middle curve in figure 5.9). They further state that significant trade offs existed between the adopted pairs of values for a and 8S and the Mg-perovskite content required to satisfy the seismic constraints, and finally conclude that neither the piclogite nor the pyrolite compositional models can be ruled out on the basis of fit between the predicted and observed Vs and Vp velocity profiles across the lower mantle. As I have noted above there are very good reasons, in large part, originally stated in Wang et al. (1994), for rejecting the high values for the Mg-perovskite coefficient of thermal expansion. The recent Raman spectroscopy results of Chopelas (1996) and Gillet et al. (1996), which largely agree with the preliminary study of Navrotsky (1989), further reinforce the case for rejecting the high values. An additional point, as noted by Mao et al. (1991), Wang et al. (1994), and Funamori et al. (1996), is that a particular fit of the polynomial expression of a(T) to the experimental P-V-T data is also coupled to the value of the thermoelastic properties {d KT/d rj and 5p. The resulting a 2 9 8 ° K also affects the calculated value of the Gruneisen parameter via the relationship y 0 = | a 2 9 8 Ks VQ/cp^. Alternatively, i f the Suzuki equation is used to fit the experimental data, the value of the Gruneisen parameter may be treated as an unknown and solved for, since the resulting curves are sensitive to this value. Returning to figure 5.6, note the progressive decrease in the magnitude of the calculated <x(7) curves for Knittle et al. (1986; y = 2.20), Hemley et al. (1992; y = 1.96), and Wang et al. (1994; y = 1.30). While the progression in these curves is not entirely due to the different values of the Gruneisen parameter (for example Anderson and Masuda (1994) argue Chapter 5, page 485 that the low value for the Debye temperature in the Knittle et al. (1986) set, also tends to elevate the resultant a(7) curve), these curves, nevertheless, do highlight the potential interdependency of a(7) and y. Thus, the analysis of P-V-T experimental data leads, ideally, to simultaneous constrains for a(7), y, [dKrjdT^ , and bj. Therefore, adopting a hypothetical value for a 9 0 0 ° K simply because it lies approximately half-way between experimental values effectively means that self-consistency between a(T) and the values for y, (a KTj d rj , and df, is lost, and it is unclear i f any of the associated parameters may be compared to other values which are derived directly from experimental data. A final point is that Zhao and Anderson (1994) use the {DLA} notation proposed by Anderson (1988) to express the temperature derivatives of the adiabatic bulk and shear moduli ( ( a ^ / a r ) (ap/ar) ) where {Kg}? and {p}P are defined via: {KS}P=5S=-\aKsj v a r j and ( 1 ^ G\ = p \a\xj 1dy^ KdTjr To compare the value Of (a p/a Tj used in Zhao and Anderson (1994) to that in this study, requires the room temperature value of ot 2 9 8°K, and not the high temperature average (a 9 0 0 ° K ) that Zhao and Anderson (1994) list in their table and figures, because the shear modulus, p is itself a function of temperature with the 900 °K value being calculated via the expression: Chapter 5, page 486 H-900 ~ M-298 + KdTJp (900-298). To compare the value of [dKs/dT^ is even more problematic because not only is a 2 9 8 0 K required (since K$, like p, is also temperature dependent) to estimate ^dKs/dfj , this property must then be converted to the isothermal equivalent via the expression (Sumino and Anderson, 1984): = (l + a 2 9 8 y 7 J -1 v dT j - ( a 2 9 8 Y KT} 1 + \a2gsj\dTj p where the parameter {da/d j j , which is not given by Zhao and Anderson (1994), must be obtained independently (Jackson and Ridgen (1996) provide a recent estimate for Mg-perovskite). Note also that existing P-V-T experiments on Mg-perovskite directly constrain the property KT/dT^ , but not [dKs/dT^ . As an aside, Duffy and Anderson (1989), while also utilizing the {DLA} framework, do list the temperature derivatives directly rather than as {DLA} parameters, and hence, these may be compared directly to the values estimated in this study. The principle reason for the above discussion is that I wish to stress that the thermoelastic data used in here differs (in some cases significantly) for both the properties which are experimentally measured (e.g. V0, Kj, {d KT/dTJ ,{d KT/d P^ , a(7), 87., y, p) and for those which must be inferred (e.g. ( d p / d r j , (5p/5PJ ). While it is natural to assume that any difference between the results in this and previous studies, largely reflects Chapter 5, page 487 different choices for the unmeasured temperature and pressure derivatives of the Mg-perovskite shear modulus, I emphasize that the measured properties, which I am adopting as "fixed" parameters in this study, also differ from that used in previous studies, and that for some parameters, such as the coefficient of thermal expansion, the differences are not trivial. I have estimated the full thermoelastic data set of Zhao and Anderson (1994) to facilitate comparison with the set used here (see table 5.4). The most significant assumption made in estimating their data set is the room temperature value for the Mg-perovskite thermal expansion -1 infer that since they adopt a high temperature value that is mid-way between the high temperature high and low experimental values, the room temperature value should also be mid-way between the equivalent experimental results. Thus, I infer a value of ct 2 9 8 ° K = 1.95 x IO -5 K"', which is half-way between that of Mao et al., (1991) and Wang et al.(1994) (see table 5.3). This in turn leads to an inferred value for the Gruneisen parameters of y = 1.55 (estimated via the expression y 0 = ( a 2 9 8 Ks V0/cp^ where the heat capacity is taken from Akaogi and Ito (1993)). These two parameters are then used to derive estimates for the remaining properties listed in table 5.4. I point out that the room temperature values inferred for the Zhao and Anderson (1994) temperature derivatives are only lower bound values, since within the framework of the {DLA} parameters, the absolute values of the temperature derivatives [i.e. {d Ks JdT^ , (Sp/c3r) ] increase with temperature (see Duffy and Anderson (1989) p. 1903), and hence, the similarity between these inferred values and those used in this study is misleading, since at the high temperatures expected for the lower mantle, the Zhao and Anderson (1994) temperature derivatives will have progressively deviated away Chapter 5, page 488 from the values used in this study (which are treated as constants). This will be illustrated in the next section where the method used in this study to estimate the values for the unmeasured shear moduli derivatives of Mg-perovskite ((dp/drj , (dp/dPJ ) are described. Table 5.4. Comparison of thermoelastic parameters for Mg-perovskite. parameter Mao et al., 1991 (fit B) Stixrude et al., 1992 Duffy & Anderson (1989) Zhao & Anderson (1994) this study Vo (cmVmole) 24.46 24.46+1.03XF e 24.46+1.03XF e 24.731 KS (GPa) - 266 260 -7^ 7 (GPa) 261 ±4.0 263 259.813 257.68a 261.50 {KS}P - - - 3.5 -(dKs/dT) GPa/K - - -0.0310 -0.0177b -(dKr/dT) GPa/K -0.0630 ± 0.005 -0.0598 -0.0600° -0.03 l lc -0.0295 (dKjdP)r - - 3.90 4.0 -[dKT/d />) 4.0 3.9 3.98" 4.06d 3.99 cx(298°K) K"1 2.17 x 10'5 3.14 x IO 5 1.95 x 7 0 ° 1.72 x 10"5 y - 1.96 2.55e 1.55e 1.50 87 6.50 ± 1.0 6.8 7.35*' 6.19* 5.00 65 - - 3.71 3.5 -K - 1.1 - - 1.45 p GPa - - 153 175 177.3 - - 2.00 1.60 1.62 - - 6.4 -(Su/ar) GPa/K - - -0.0280 -0.02188 -0.0224 Entries in italics in the Zhao and Anderson (1994) column are estimated from their listed {DLA} parameters as outlined below. a, the isothermal bulk modulus, Kj\s estimated via Ks = KT(l + a y T) where a is the coefficient of thermal expansion, y is the Gruneisen parameter, and Tis temperature with T= 298°K; b, calculated from the given {DLA} parameter {Ks}? = 3.5 and its definition: {Ks}r=Ss=-(l/aKsJdKs/dT)p together with the given room temperature thermal expansion a(298) and adiabatic bulk modulus Ks. c, this value is calculated at T= 298°K via the expression 26 in notations of table 1 in Sumino and Anderson (1984): Chapter 5, page 489 where the parameter a/9 Tj = 4.9 x 10s K"2, which was not given by Zhao and Anderson (1994), was taken from Jackson and Ridgen (1996; table 5); d, this value is calculated at T= 298°K via the expression 19 in notations of table 1 of Sumino and Anderson (1984): e, calculated from the definition: y = a Ks V0 j CP where Cp = 80.6 kJ/K mole is the heat capacity at constant pressure from Akaogi and Ito (1993) and the molar volume was calculated with the stated iron content of Xpe = 0.1. Note that the calculated Gruneisen parameter, when combined with the given value for ds, does not equal the calculated room temperature value of the isothermal Anderson-Griineisen parameter, 8 7 ; / this value is the room temperature estimate calculated from its definition: 8 r = -I l/ot Kr II d Kr jdTj using the calculated values for Kfand d Kr / d Tj and the inferred 5 . 8 Temperature and Pressure derivatives of the shear moduli The temperature and pressure derivatives of the elastic properties are central to any modeling study of shear and compression velocities in the mantle. Both the temperature and pressure derivatives of the magnesiowustite shear moduli may be considered known, at least relative to Mg- and Ca-perovskite, since measurements exist for periclase. High temperature experiments have directly measured the shear modulus for periclase (MgO) to 1800 °K (Isaak et al., 1989). I adopt the resulting temperature derivative 5p/ar) =-0.026 GPa/K and apply it magnesiowustite under the assumption that the relatively low iron content of the inferred magnesiowustite used here [(Mg 0 8 6Fe 0 M )O] will not significantly affect this property. In contrast, the value of the pressure derivative of the shear modulus for [dKT/dP)7 = (l + a y 7-)" (5 KS /dp)r -(y T/KT) (S Kr/d T) 1; Chapter 5, page 490 magnesiowustite (dp/dp) _= 2.36 used here is interpolated between by two experiments on magnesiowiistites with slightly different iron contents (see figure 5.3; Bonczar and Graham, 1982; Sumino and Anderson, 1984) and it is assumed that this property is well constrained. Thus, the derivatives of interest here are the temperature derivative of the shear modulus for M g - and Ca-perovskite (dp/dr) . To obtain initial estimates for the unmeasured temperature derivatives I use the empirical relationship between T , 8T, and (dKr/dP)T observed at high temperature (Isaak, 1992). He found that at a temperature above the Debye temperature, the following approximation was valid: r « oT*(dKT/dP)T where {dKr/d P) is the pressure derivative of the isothermal bulk modulus at ambient conditions, 8T is the Anderson-Griineisen parameter defined as: ( 1 ^ fdK^ \aKT) { dT) and T is the mathematically related form of Anderson-Griineisen parameter, but for the shear moduli: r = -r i ] (* \ U(r)u<r>J U r J The empirical approximation r « 8 T « (5^ 7 /5P) 7 , is relevant here because it indicates that estimates for the high temperature value of the temperature derivative of the shear moduli 5p/dP) may be obtained from the pressure derivative of the isothermal bulk modulus Chapter 5, page 491 {dKr/dP^ . Isaak (1992) found from experimental measurements that at high temperatures, both T and 5 T are approximately equal to the value of the pressure derivative {dKrldP)r. This observation allows an estimate of the unmeasured ( d p / s r ) by assuming T « (dKT/dP) in the thermodynamic relationship (Isaak 1992; his equation 16): P(T0) where To refers to room temperature conditions. This expression is first used to obtain a high temperature estimate for the shear modulus, p(T) from the room temperature value using the density ratio and (dKr/dP)T. \i(T) is then used, along with a high temperature value of the coefficient of thermal expansion, a(7) to estimate a value for [d p /o TJ via: r = - r i ] (a \ ap => 'dKTy [ 1 ] ( X \ op U(r)p(r>J UrJ I dP) T W(T) \l(T); [dTj or rearranging: ^5p^ ^TJ„ •a(T)\i(T) dP In an earlier study I used the above relationships to calculate ^d\i/df)p | for the p-olivine phase and compared this value to an experimental measurement that has recently been reported by L i et a l , (1996). For the Mg end member of p-olivine I predicted a value of (3p/c3rj =-0.0162 GPa/K, which is indistinguishable from the experimentally measured Chapter 5, page 492 value of ( d n / d r ) = - 0.016 GPa/K. Based on this success, I utilize the Isaak (1992) high temperature approximation to estimate (d p/<9 7") for the perovskite phases. For Mg-perovskite the values adopted here for the required parameters are; (8KT/dP)T = 3.99; the densities at room temperature and high temperature (T = 2200 K -this temperature is roughly a median value for the lower mantle) are p 2 9 g = 4.190 g/cm3 and p(T) = 3.9427 g/cm3. The density as a function of temperature is calculated with a room temperature molar volume of 24.731 cm3/mole which incorporates the aluminum and iron contents of Irifune (1994) in the molar volume expression of O'Neill and Jeanloz (1994) and the coefficient of thermal expansion of Funamori et al., (1996) as listed in table 5.3. Combining these parameters with a shear modulus of p 2 9 8 = 177.3 GPa (Yeganeh-Haeri, 1994), results in a predicted high temperature shear modulus of p22oo — 139.09 GPa. For a temperature of 2200 K, the coefficient of thermal expansion is 3.992 x 10"5 K which taken with p 2 2 0 0 and (8KT/dP)T results in a predicted value of (d\x/d r ) = - 0.0222 GPa/K. I add a factor of 0.0008 GPa/K to this estimate, following Isaak (1992), who noted that this high temperature approximation underestimates the true value by approximately this amount. Thus, a "corrected" prediction for {d p /5 fj is - 0.0229 GPa/K. This compares to the value d\i/dT}=- 0.0280 GPa/K listed by Duffy and Anderson (1989) and ( d p / d 7/) = - 0.0218 GPa/K inferred for Zhao and Anderson (1994). Turning to Ca-perovskite, the required parameters are; (dKT/dP)r = 4.8, the room temperature and high temperature (T = 2200 K) densities are p 2 9 8 = 4.235 g/cm3 and p(2200 Chapter 5, page 493 K) = 3.995 g/cm3 where the densities are calculated with a room temperature molar volume of 27.43 cmVmole and the coefficient of thermal expansion of Wang et a l , (1996). To estimate the high temperature value for the coefficient of thermal expansion, I utilized the expression of O.L. Anderson et al. (1992) to extrapolate this value to high temperatures (their eq. #31): 1 i + a r > e 5 r ( r - r e ) where 6 is the Debye temperature for Ca-perovskite (T e = 1100 K) , S x is the Anderson-Griineisen parameter which for Ca-perovskite 8X = 4.65 (Wang et al., 1996). Combining these parameters with an inferred shear modulus, determined earlier, of p 2 9 8 = 158.1 GPa, results in a predicted high temperature shear modulus of p2 oo = 119.56 GPa. For a temperature of 2200 K , the coefficient of thermal expansion is 3.690 x 10"5 K which taken with p 2 2 0 0 and (8Kr/dP)T results in a predicted value of (dp /d T}= - 0.0212 GPa/K. Again applying the 0.0008 GPa/K correction advocated by Isaak (1992) results in a "corrected" predicted value of ( d p / d r j = - 0.0219 GPa/K. This compares to an estimated value of ( 5 p / d r j = -0.0230 GPa/K by Duffy and Anderson (1989). I can cross check the value estimated above for Mg-perovskite by comparing it to the estimate obtained earlier from constrained adiabatic decompression of the seismic density and shear and compression velocity structure of the P R E M lower mantle. Based on the results from modeling density and bulk sound velocity profiles it was assumed in the decompression study that pyrolite is the lower mantle composition. Hence, the density, p0, and bulk modulus, Kso terms in the 4th order equation of state that was fit to the P R E M Chapter 5, page 494 seismic properties were fixed to the high temperature values for a simplified pyrolite composition comprising only Mg-perovskite and magnesiowustite. This gave a new estimate for the decompressed shear modulus of the lower mantle, p 0 which was used to constrain the Mg-perovskite shear moduli temperature derivative (dp/drj via the relationship: decompressed 7'=1607K 1^ 0 lower mantle ^ 0 Pyrolite mix where the simplified pyrolite composition is given by: 7=1607K / „ ,. \ 7=1607K ^Pyrolite ,„„ = 84 V O / % + 16 V O / % ^ ) \ I VRH mix with the predicted high temperature values for the shear moduli of Mg-perovskite and magnesiowustite calculated via the linear relationship: Mg-Pv ^ 1 6 ^ = Pv^ref + ( 5 ^ / 5 J ^ ' ' ( l 6 07° K - 298° KJ where 1607°K is the mantle potential temperature of the self-consistent adiabatic geotherm determined in modeling p and V® throughout the whole mantle. Because the parameter / , \ Mg-Pv ydix/dTj is the sole unknown in correcting the laboratory properties of the simplified pyrolite to equal the decompressed value of the lower mantle, I simply solve for it to satisfy / , \ Mg-Pv the equality. I obtained \d\ijdTj = -0.0224 GPa/K, a value that is in excellent agreement with that estimated above (-0.0229 GPa/K) using the high temperature approximation of Isaak (1992). / , \ Mg-Pv _ The close agreement between the two independent estimates for yd\x/dTj gives us confidence that this property is well constrained, and hence, of the two values, I arbitrarily Chapter 5, page 495 adopt (dp /dr j ^ = -0.0224 GPa/K, the value obtained via constrained adiabatic decompression, in this study. While I have no independent way of checking the value for Ca-perovskite, I assume, based cn the good agreement between the two estimates for Mg-perovskite discussed above, and on the close agreement between the calculated and experimentally measured value for p-olivine, that the value for Ca-perovskite given by the high temperature approximation is indeed a valid estimate, and thus, adopt it without modification. The values used here are compiled in table 5.5. Table 5.5. Shear moduli and associated temperature and pressure derivatives for the lower mantle phases used in this study. Shaded entries are estimated values as described in the text. Mineral P- {d\il dP)T (d\xl dT)P shear modulus GPa pressure derivative temperature derivative GPa/K Mg-Fe perovskite 177.30'1 1.61b -0.0224c Ca-perovskite 158.10d 1.61b -0.0212c magnesiowustite 118.53e 2.36f -0.0260g a, Yeganeh-Haeri, 1994; b, after Patel et al., 1996; c, estimated via the empirical approximation r « 8 r *(dKT/dp) , (Isaak, 1992) and the thermodynamic relationships: r = -illa \i\id\ildT\ , and \a(T)j \i{Trej j = \p(T)/ p(Tref j ; d, estimated from Mg-perovskite via mineral systematics of Bass (1984) and velocity-density systematics (Ita and Stixrude, 1992) n0K0 = Horef^orefJ e> Jackson and Niesler (1982), Richet et al., 1989; / Bonczar and Graham (1982), and Sumino and Anderson (1984); g, Isaak et al. (1989) and Fei et al. (1992). To illustrate the effect these estimates have on the high temperature value of the shear modulus, figure 5.10 shows the variation of p with temperature, where p(7) is calculated via the linear relationship: p ( r ,p r e / ) = p(r r e , ,p r e ,)+ ref ' -1 ref . (T-298), Chapter 5, page 496 Also shown are the experimental variation for a number of minerals relevant to the mantle (O.L. Anderson and Isaak, 1995) and the predicted behavior for Mg- and Ca-perovskite inferred by Duffy and Anderson (1989) and Zhao and Anderson (1994). Recall that within the {DLA} framework, the parameter {G} p is a constant (Anderson, 1988) and thus inspection of its relationship to the temperature derivative (see below) indicates that because both a and p are functions of temperature, then (dp/d r ) must increase with temperature to keep {G} p constant: r i ] fa } o p la(r)p(T)J To obtain an indication of this increase I used the tabulated value of {G} p in Zhao and Anderson (1994) together with a polynomial expression for the inferred thermal expansion coefficient: a{T)-a0 +ct]7' + a 2 IT1 where a 0 , ax, and ot2 are constants, which are typically determined by fitting experimental data, but in this case, are simply adjusted such that the predicted curve of a(7) falls between the curves estimated by Anderson and Masuda (1994) for y = 1.7 and 1.5 (see figure 5.11). For the Duffy and Anderson (1989) study, they adopted the Knittle et al. (1986) results for the Mg-perovskite cc(7) and thus, in this case the polynomial constants were adjusted to fit the Knittle et al. (19986) curve of Anderson and Masuda (1994). Next, I simply solved for the required value of ( d p / s r ) that satisfies the tabulated values for {G} p of Zhao and Anderson (1994) and Duffy and Anderson (1989) with the assumption that the temperature dependence of the shear modulus is expressed as: Chapter 5, page 497 p(7) = p 2 9 8 + VdTjp The predicted variation of d p / d T\ with temperature is shown in figure 5.12. It is clear that any similarity between the inferred room temperature value of yd p /3 Tj estimated for Zhao and Anderson (1994) and the value estimated in this study, disappears with increasing temperature. The values of Duffy and Anderson (1989) also show a similar variation with temperature such that the value applicable to the lower mantle is quite different from their tabulated room temperature estimate of id p/<3 T) . Anderson (1989) has a significant effect on the predicted high temperature value of the Mg-perovskite shear modulus. For the expected temperature range of the lower mantle (1850 -2500 °K), the predicted p ( r = 2500°K) « 90 GPa. By contrast, our predicted value for the same temperature is \i(T = 2500°K) « 130 GPa, a values which is also greater than that inferred for the Zhao and Anderson (1994) study. Lastly, note that the shape of inferred p(7) curves of Zhao and Anderson (1994) and Duffy and Anderson (1989) do not correspond to the linear trends seen in the experimentally determined curves of other minerals that are also plotted. 5.9 Mineralogicallv plausible estimates of (dp/d?j Anderson (1988), used the elasticity compilation of Sumino and Anderson (1984) to search for relationships (also referred to as "mineral systematics") between minerals of Returning to figure 5.11, it is clear that the variable Chapter 5, page 498 similar ionic radius, K$/\x, and y with the goal of establishing relationships to predict values for the unmeasured temperature and pressure derivatives (\d\i/d P) ,[d\i/d r ) ). Anderson (1988) and Duffy and Anderson (1989) argued that the data set demonstrated that arbitrary choices for the shear moduli derivatives could be ruled out. While the goal of these study were primarily concerned with the derivatives of p~ and y-olivine phases, Anderson (1988) also tabulated data for perovskite phases. Thus, to check i f the above estimates are mineralogically plausible, within the {DLA} framework advocated by Anderson (1988), I calculate a number of {DLA} parameters. First, I calculate{G}T, which Anderson (1988) defines as: G\ = T ^ 3p^ For Mg-perovskite, I have Kj= 261.50 GPa, p = 177.3, ( d p / d P J ^ 1.62) which results in calculated value of {G} x = 2.38. Anderson (1988) defines the parameter {G} P by: G = r = \ a p ; ''dp which is equivalent to T as used by Isaak (1992). In this study, I utilized the high temperature approximation of Isaak (1992), so { G } P is simply « r « (dKT/dPy = 3.99. Combing the two {DLA} parameters results in the ratio | G | = 0-59. For Ca-perovskite, the associated values are { G } T = 2.37, { G } P = T « [dKT/dP^ = 4.8, and l^i//(^} = ^ n e s e v a ^ u e listed in table 5.6 and show reasonable agreement with the Chapter 5, page 499 values tabulated by Anderson (1988) for silicates and perovskites. It is interesting to note that the ratio | G | f ° r m e perovskite values estimated in this study, bracket the average perovskite value tabulated by Anderson (1988), while that inferred for the Mg-perovskite in Zhao and Anderson (1994) appears to be too low. Table 5.6. Summary of calculated {DLA} parameters for the elastic parameters estimated in this and previous studies for Ca- and Mg-perovskite. {DLA} parameters mineral {G}T = ( r 7 . / p ) ( s p / a p ) 7 {G}P = ( l / a p ) ( d p / S 7 ^ {G} T / {G} P KS/[i Mg-perovskite this study 2.38 3.99 [{G} P«r*/c.;,] 0.59 1.47 Ca-perovskite this study 2.37 4.8 [{G}P*r«/4] 0.49 1.46 Mg-perovskite Zhao & Anderson (1994) 2.35 6.4 0.36 1.48 Mg-perovskite Duffy & Anderson (1989) 3.39 5.8 0.58 1.73 Mg-perovskite Anderson (1988) table 7 3.5 6.5 0.53 -Mg-perovskite Anderson (1988) table 7 2.8 5.7 0.49 -Ca-perovskite Duffy & Anderson (1989) 3.45 5.8 0.59 1.81 perovskites (Anderson, 1988) 2.7 5.0 0.54 -silicates (Anderson, 1988) 2.8 ± 0.2 5.4 ± 0.4 0.55 1.67 total data base (Anderson, 1988) 2.5 ± 1.3 5.7 ±1.9 0.44 2.01 An other way of viewing the temperature and pressure derivatives used for Mg-perovskite is shown in figure 5.13, modified from Duffy and Anderson (1989), which plots the temperature versus pressure derivatives for 55 minerals where both properties are Chapter 5, page 500 measured along with estimates determined here Mg-perovskite. Also shown as vertical lines are the inferred values for Zhao and Anderson (1994) and the Duffy and Anderson (1988). While the room temperature value inferred for Zhao and Anderson (1994) is very near that estimated here, this figure clearly shows that at the high temperatures relevant for the lower mantle, the associated values for (dp/c3r) are significantly greater. Finally, the recent estimate of Patel et al., (1996) for the unmeasured pressure derivative of Mg-perovskite is plotted as a vertical line with assigned error bounds of ± 0.2, which is adopted from the reported experimental error quoted for the recent high temperature and pressure value of the shear moduli pressure derivative for P-olivine in Zha et al. (1997). These error bounds are subjective estimates that represent likely error bounds that are associated with the latest experimental techniques. It is clear from this figure that the room temperature value of (d p / 3 Tj adopted by Duffy and Anderson (1989) is very high, while the value inferred here from Zhao and Anderson (1994) is comparable to our estimate. I re-iterate, however, that this similarity is misleading since their temperature derivatives are room temperature values which will increase as the temperature rises to lower mantle conditions. Lastly, the value for the Mg-perovskite pressure derivative (d p/d PJ adopted by Duffy and Anderson (1989) appears to be anomalous in terms of the estimate of Patel et al. (1996). In summary, I find that the method of Isaak (1992) allows a prediction of the temperature derivative \d\i/dfj for Mg-perovskite which is in excellent agreement with that independently determined via constrained adiabatic decompression. When the Isaak Chapter 5, page 501 (1992) method is applied to Ca-perovskite, this high temperature approximation predicts a value of (d p / d fj that is very similar to that estimated for the Mg end member, inspite of differing shear moduli, density, and thermal expansion, implying that these two silicate perovskites may exhibit indistinguishable shear moduli temperature dependence. When the adopted values are checked using some of the criteria which Anderson (1988) used to highlight implausible choices for the temperature and pressure derivative, it is found that the values used here are consistent with average values tabulated for perovskites, and hence, are mineralogically plausible, at least within the {DLA} framework. While the temperature derivatives of Duffy and Anderson (1989) and Zhao and Anderson (1994), when evaluated within the {DLA} framework appear to be consistent with the tabulated values of Anderson (1988), it is clear that when plotted against other compounds for which both temperature and pressure derivatives are measured (figure 5.13), the Duffy and Anderson (1989) set are anomalous and exceed the measured values for (d p / d T\ of other relevant mantle silicates. While the inferred value of the p /9 Tj that I estimate from the listed {DLA} parameters in Zhao and Anderson (1994) appears similar to the value estimated in this study, this similarity is an illusion, since the temperature derivative within the {DLA} framework increase with increasing temperature, and hence, migrate away from the value used here. With the values for this study which are listed in table 5.4,1 now turn to calculating Vs and Vp velocity profiles. p 5.10 Equation of State Chapter 5, page 502 The following section explains the general procedure used in calculating the high temperature and pressure elastic properties of the minerals that were used in this study. The steps are identical to that presented earlier in modeling density and bulk sound velocity profiles throughout the mantle, except the section concerning the shear modulus. 5.11 High Pressure Parameterization; density and bulk modulus I start by adopting the upper and lower mantle geotherms of Ito and Katsura (1989) and Akaogi and Ito (1993) respectively. This provides only an initial geotherm, since I later substitute an internally consistent adiabatic geotherm calculated directly from the elastic data and iteratively repeat this substitution until the geotherm and elastic parameters remain unchanged. This ensures that the geotherm used in the calculations is self-consistent with the adopted mineralogy, an approach outlined by Graham and Dobrzykowski (1976). I follow the recommendation of Bina and Helffrich (1992) regarding the temperature and pressure path to the T and P conditions of interest: to reach the high T-P conditions of the mantle, I first "step up" in temperature at room pressure (Tref^T, Pref), followed by a second correction in pressure at high temperature (T, Prej^>P) with 298 K and 1 bar being taken as the reference state. This reflects the fact that volumetric thermal expansion data (a(7)) are available for most minerals at room pressure, but this parameter is largely unmeasured at high pressure. The temperatures along the adiabatic geotherm are used to correct the standard temperature and pressure value of the isothermal bulk modulus, {Kr(Tref ,Pref)} to mantle temperatures using the following relationship: Chapter 5, page 503 KT(T,Pref) = KT(Tref,Pref) + ( r -298) where (dKr/8T)p is the isobaric temperature derivative of the isothermal bulk modulus, T = the temperature of interest along the geotherm, and 298°K represents the reference state at room temperature. In a similar fashion I correct the molar volume from room temperature and pressure v{Tref, Pref) to mantle temperatures (but room pressure) using the expression; V(T,Pref) = V(Tref,Pref) exp \a(T)dT 298 where a(T) is the thermal expansion coefficient and is used to express the volume change of a mineral due to a temperature change (Fei, 1995). Commonly the thermal expansion coefficient is reported as a polynomial expression: oc(r) = a 0 +a,7 + a 2 /T2 where a 0 , a , , and oc2 are constants determined by fitting experimental data. Substituting the polynomial expression in the above expression for molar volume and integrating gives: V(T,Pref) = V(Tref,Pref) exp; a , a 0 (7;-298) + ^ L ( r 2 - 2 9 8 2 ) - a 2 ( r _ 1 -298 ' 1 ) For Ca-perovskite, I utilized the expression of O.L. Anderson et al. (1992) to extrapolate the high temperature value experimentally determined by Wang et al. (1996; 3.06 x 10~5 K _l)to high temperatures (O.L. Anderson et al., eq. # 31): 1 i + a R > E 5 r ( r - 7 ; 6 Chapter 5, page 504 where 0 is the Debye temperature (0 = 1100 K), 87 is the isothermal Anderson-Gruneisen parameter (87= 4.65) and I assume that C X 7 > 0 = 3.06 x 10"5 K" 1 (all data from Wang et al., 1996). To evaluate the pressure dependence of the volume at high temperature, V(T, P) I insert the high temperature value of the isothermal bulk modulus, KT(T, Pref), the volume at high temperature and 1 bar v(T,PKf}, the pressure derivative of the isothermal bulk modulus (5 7£7. /5 P ) T , and pressure, P (from PREM) into the 3rd order Birch-Murnaghan equation and iteratively solve for V{T,P) in 1 km intervals over the pressure range of interest for the particular mineral: ^2 KT(T,Pref) V(T,P) J I V(T,P) dp J j J V(T,P) x 2 / ^ / 3 Following Bina and Helffrich (1992) I determine the pressure dependence of the isothermal bulk modulus at high temperature via the third order formulation of Davies and Dziewonski (1975): KT(T,P) = KT(T,Pref) 5/\ 1 + 2 1 (V(T>P«)) % -1 / 2 < 1 + r 3 (dKr) - 5 1 (V(T,P«)) 2 { V(T,P) J I SP ) T / 2 { V(T,P) J The pressure dependence of thermal expansion coefficient at high temperature is evaluated using the expression (Anderson, 1967; Chopelas and Boehler, 1989; Anderson, et al., 1990); a(T,P) <T,PreJ) f Tr/rr, rVl \ &T V{T,P) V(T,PR 4 J Chapter 5, page 505 where 87. is the isothermal Anderson-Griineisen parameter. For Mg-perovskite 87. decreases according to the relationship 8, = o\7 • V(T,P) V{T,Pref)j where k= 1.5 (Anderson and Masuda, 1994; O.L. Anderson et al., 1995). For Ca-perovskite and magnesiowustite, I adopt the empirical relationship suggested by Chopelas and Boehler (1992) based on mineral systematics because the data for these minerals have yet to be analyzed within the framework used by Anderson and Masuda (1994). Hence, 8 r decreases according to the relationship: 8, f V(T,P) A V(T,Pref)) • m-l where m = 6 for magnesiowustite and I assume m = 6.5 for Ca- perovskite (Chopelas and Boehler, 1992). The Gruneisen parameter, defined as y = pCy) , is corrected to high pressure by the following relationship: J(T,P) y(ref) V(T,P) The exponent q is often assumed to be a constant equal to 1, but I have followed the conclusions of Anderson, O.L., et al. (1993) on MgO and linearly decreased the exponent q from a value of 1.09 across the mantle to a 0.8 at the base of the lower mantle. Independent Chapter 5, page 506 arguments in support of decrease in q with increasing pressure have also been raised by Duffy and Ahrens (1993). Ita and Stixrude (1992; 1993) assume that q = 1 ± 1. The high temperature and pressure adiabatic bulk modulus, KS(T,P) is calculated from the isothermal value, KT(T, P) via the relationship: Ks(T,P) = KT(T,P)[l + Ta(T,P)y(T,P)] where T is the high temperature of interest, a(T, P) is the thermal expansion coefficient, and y ( r ,P) i s the Gruneisen parameter, with both parameters at the high T-P conditions of interest. 5.12 High Pressure Parameterization; Shear Modulus I correct the room temperature and pressure value of the shear modulus, \i{Trcf ,Pref) to mantle temperatures using the linear relationship; V-(T,Pref) = \i{Tref,Pref) + va ry (7-298) where {d p/5 f)p is the temperature derivative of the shear modulus. Again, following Bina and Helffrich (1992) I determine the pressure dependence of the isothermal shear modulus at high temperature via the third order formulation of Davies and Dziewonski (1975): p(r,/>) = p(r,;v) 1 + 2 V(T,P) V\ T, >Pref) V(T,P) f 5p^ KdPj Chapter 5, page 507 where (d\i/dP)T is the pressure derivative of the shear modulus. Although I use a third order expansion of the Birch-Murnaghan equation of state to extrapolate to the pressures of the Earth's interior, I stress this is largely one of convenience since the experimental data does not warrant expanding the terms to forth order. Finally, density, p(T, P), and the isotropic Vs and Vp velocities are calculated by substituting the shear modulus, p(r, P), the adiabatic bulk modulus, KS(T, P), the molar volume, V(T, P), all at high T-P conditions, into their definitions V ' V(T,P) Vs(T,P) = p (, w>p) \KS(T,P) + U(T,P) V,, (T,P) = J * . ' 1 P(T,P) where M is the molar mass of the mineral. 5.13 Self-consistent Adiabatic Geotherm For the pyrolite model I adopt without modification the adiabatic geotherm calculated earlier in modeling density and bulk sound velocity profiles (see figure 5.14), but for completeness, I document below how this geotherm was constructed. I calculate an adiabatic geotherm from the mineral physics parameters that were calculated to estimate density and the bulk sound velocity: this geotherm is then used in subsequent calculations for refined estimates of p(T, P) and V^iT, P). Although I are Chapter 5, page 508 assuming that the appropriate geotherm for the Earth's mantle is indeed adiabatic, I test this assumption when the predicted density and bulk sound velocity profiles are compared to the observed seismic profiles. A close match between the predicted and observed density and bulk sound velocity profiles across the full depth extent of the mantle would imply, that in addition to placing constraints on bulk mineralogy, the geotherm, to first order, is indeed adiabatic. If the mantle deviated progressively with depth to a sub-adiabatic geotherm (e.g. Jeanloz and Morris, 1986; 1987) then I would expect to see a progressive and systematic divergence between the predicted and observed p(T, P) and V^,(T, P) profiles (Weidner, 1986, p. 262). The adiabatic temperature gradient is calculated via the following expression (Graham and Dobrzykowski, 1976): rdT\ _Ty(T,P) KdP)~Ks{T,P) where y (T, P) and Ks (T, P) are the V R H average of the Gruneisen parameter and the adiabatic bulk moduli respectively. To anchor the adiabatic temperature profile, I assign a temperature at 100 km depth in the upper mantle, the "top" of the upper mantle considering in this work, while in the lower mantle, the anchor point is located on the underside of the 660 km seismic discontinuity. The temperature at 100 km depth is chosen such that when the upper mantle adiabat is extrapolated to the surface, the resulting potential temperature agrees with independent estimates of the mantle potential temperature determined from decompression melt studies of MORBs (1330-1350 °C; White and McKenzie, 1995; Iwamori et al., 1995). I initially elected to tie the anchor temperature of the lower mantle geotherm to that temperature predicted from the upper mantle geotherm. For the piclogite Chapter 5, page 509 composition, the anchor point was increased to 3208°K, to reflect the affects of a thermal boundary layer between a piclogite lower mantle and a pyrolite upper mantle. The temperature jumps associated with the latent heat of phase changes at the 410, 520, and 660 km seismic discontinuities are calculated via the method of Navrotsky and Akaogi (1984) but with the modification that instead of calculating the change in molar volume associated with the phase change from reference molar volumes at room temperature and pressure (e.g. AV(Tref ,Pref), values at the mantle temperature and pressure of interest are utilized: change v_* p where T is the temperature immediately above the onset of the phase change, and yd is the value of the Clapeyron slope of the phase change and the subscript d indicates the depth of the phase change. I adopt y 4 1 0 = +3.0 MPa/K for 410 km and y 5 2 0 = +5.1 MPa/K for 520 km olvine phase changes from Katsura and Ito (1989), and y 6 6 0 = -2.0 MPa/K for the 660 km phase change (Bina and Hellfrich, 1994). C p is the heat capacity with appropriate values adopted from Akaogi and Ito (1993) and Akaogi et al. (1989). The adiabatic geotherm is calculated from 100 km depth down until intersecting the top of a phase change, the thickness of which is taken from the widths given in the diagram of mineral proportions of Ita and Stixrude (1992; 1993) and reproduced and used here (see figure 5.2 and 5.3). Thus, the thickness of the phase change is not calculated, but assigned in constructing the adiabatic geotherm. Seismological studies which imply relatively thin phase changes, are in conflict with the equilibrium width calculated via thermodynamics for the 520 km, and to a lesser degree, the 410 km phase changes. I stress, that this discrepancy is Chapter 5, page 510 not addressed in constructing our geotherm since I am adopting as fixed, the equilibrium widths inferred by Ita and Stixrude (1992; 1993). A more complete study that incorporates the changing phase boundary width as a function of temperature (e.g. Helffrich and Bina, 1994) is beyond the scope of this study. The temperature jump associated with the phase change is linearly added to the geotherm. Once the depth region of the phase change is exited, the temperature at the base of the phase change is used as the anchor point for the next leg of the geotherm. In this way, the upper mantle geotherm is calculated down to, and through, the 660 km phase change. In the lower mantle I follow Ita and Stixrude (1992; 1993) and assume there are no phase changes within this region, an assumption supported by thermodynamic calculations on the stability of the assemblage of Mg-perovskite and magnesiowustite (Stixrude and Bukowinski, 1992; 1993), and molecular dynamics simulations on the structural stability and breakdown of Mg-perovskite (Stixrude and Cohen, 1993; Warren and Ackland, 1996). To ensure convergence, I substitute the new adiabatic geotherm calculated above and iterated through all the above steps until both the geotherm and elastic parameters remain unchanged for a particular set of temperature anchor points. 5.14 Aggregate properties Following Ita and Stixrude (1992; 1993), I used the Voight-Reuss-Hill averaging scheme (Watt et al., 1976) to determine volume averaged properties for the mineral assemblages. Implicit in this scheme is that the mineral assemblage is homogeneous, isotropic aggregate. This is a reasonable assumption since tomographic studies that include the affects of anisotropy in the seismic model find that strong anisotropy is largely Chapter 5, page 511 concentrated above « 250 km depth and decreases rapidly within the depth interval of 250 to 350 km depth and is unresolvable at 400 km depth (Montagner and Tanimoto, 1991). While more restrictive schemes are available for averaging material properties such as Hashin-Shrikman bounds, Bina and Helffrich (1992) demonstrate that while the Hashin-Shrikman method gives tighter bounds than the V R H method, the averages for both are identical. 5.15 Results Figure 5.14 shows the inferred adiabatic geotherm of Zhao and Anderson (1994) together with the upper and lower mantle adiabatic geotherms used in this study for the pyrolite composition. Zhao and Anderson (1994) did not diplay the geotherm used in their study, so I simply show a representative geotherm pinned to their reported surface "foot" of the lower mantle geotherm (1500°C). Note that the adopted temperature structure, used by Zhao and Anderson (1994) for both a pyrolite and piclogite compositions, is offset to higher temperatures than that calculated by both Ita and Stixrude (1992; 1993) and this studies. As I have noted earlier, it is invalid to model a uniform compositional model in the lower mantle along a geotherm that is not concordant to the upper mantle geotherm. Likewise, it is invalid to use the same geotherm to model the velocity and density profiles for a lower mantle in which the bulk composition differs from that of the upper mantle. Consequently, to model the piclogite composition in the lower mantle, I adopt an anchor point of the lower mantle geotherm of 3108°K, consistent with the average offset between geotherms determined from 3D numerical simulations of whole mantle and enforced, 2-layered convection in the Earth (Glatzmaier and Schubert, 1993) (see figure 5.15). Chapter 5, page 512 Figure 5.16 shows both of the predicted pyrolite Vs and Vp profiles together with the corresponding velocity profiles from the akl35 and akl35-F seismic reference models (Kennett et al., 1995; Montagner and Kennett, 1996). It is clear from inspection of this figure that the predicted profiles give an excellent fit to the seismic profiles. This agreement becomes even clearer when the shear and compression velocity profiles are plotted separately (figure 5.17 and 5.18). To obtain an indication of the misfit between the predicted and observed, I plot in figure 5.19 and 5.20 the percent difference between the calculated velocity curves and akl35 or akl35-F reference profiles. It is clear that the percent difference is slight and never exceeds ± 0.5 %. While the misfit is slightly greater i f akl35-F is used as the reference seismic model, the difference is insignificant. By contrast, figure 5.21 shows the predicted piclogite. Vs and Vp profiles together with the corresponding velocity profiles from the akl35, akl35-F, and P R E M (Dziewonski and Anderson, 1981) and SP6 (Morelli and Dziewonski, 1993) seismic reference models. The predicted profiles clearly misfit the expected seismic profiles by a significant degree. Note that, unlike the upper mantle and transition zone, the recent seismic models for the lower mantle are nearly identical and largely differ in details directly below the 660 km seismic discontinuity and directly above the D" region at the base of the mantle. Thus, the inferred uncertainty for the lower mantle velocity profiles is slight (while there are no quoted errors given with the reference seismic models, it is typically stated that the lower mantle velocities are uncertain to « ± 0.9 % (Ita, 1992) over the lower mantle. 5.16 Discussion Chapter 5, page 513 It is clear from an inspection of figure 5.16 and 5.21 that the pyrolite, composition provides an excellent fit to the seismic Vs and Vp profiles across the lower mantle, whereas the piclogite model does not. The misfit between the piclogite model and the seismic models exceeds any plausible uncertainty for the lower mantle seismic models, and consequently, may be rejected with confidence. Our conclusion that piclogite is not a viable candidate for the composition of the lower mantle differs from the findings of Zhao and Anderson (1994), which used different thermoelastic data and a different geotherm to model both the pyrolite and piclogite models. They considered a simplified two phase mixture of Mg-perovskite and magnesiowustite and were able to match the P R E M Kg, p and density profiles across the lower mantle for both models, supporting their claim that neither compositional models can be rejected. The opposing conclusions reflect a number of differences between the two studies. This study includes the effects of Ca-perovskite on the lower mantle mixture, and incorporates A l into the Mg-perovskite phase (based on the synthesis experiments of Irifune (1994) and Wood and Rubie (1996). In addition, the Fe content in magnesiowustite and Mg-perovskite differ with the iron content in this study based on the experiments of Irifune (1994)). While these factors contribute to the different conclusions drawn by Zhao and Anderson (1994) and the present work, there are two major factors which contribute to our conclusion that the piclogite model may be rejected. First, for the experimentally measured thermoelastic properties for Mg-perovskite, the values used here are firmly based on experimental measurements, whereas some of those in Zhao and Anderson (1994) are not. While they claim there are no reasons to reject or accept particular experimental results, I Chapter 5, page 514 believe, like others (Hill and Jackson, 1989; Wang et al., 1991; 1994; O.L. Anderson et al., 1995; 1996) that there is sufficient grounds to favor the recent experimental results over the earlier pioneering studies. Second, I calculate the predicted velocities (and density) for piclogite along a lower mantle adiabat that is 1200 °K hotter than the upper mantle and transition zone geotherms, whereas Zhao and Anderson (1994) calculate both models along the same geotherm. As noted earlier, the particular geotherm adopted by Zhao and Anderson (1994) is invalid for both the pyrolite and piclogite models. For a uniform whole mantle, such as the pyrolite model, the lower mantle geotherm must be concordant with the upper mantle and transition zone geotherms, which theirs is not. Likewise, for a distinct chemical composition for the lower mantle, such as the piclogite model, the lower mantle geotherm must be is offset to higher temperatures than the upper mantle, to reflect the affects of a thermal boundary layer which must exist at the chemical boundary separating the upper and lower mantles. Chemical layering within the mantle demands that a thermal boundary layer coexists at the boundary separating the different layers (Jeanloz and Richter, 1979; Spohn and Schubert, 1982; Jeanloz and Morris, 1986). While there is complete agreement that such a thermal boundary layer must coincide with a chemical boundary, the magnitude of the temperature jump across it is less constrained with estimates ranging from 500-1200 °K (e.g. Jeanloz and Richter, 1979, Spohn and Schubert, 1979; 1980; Glatzmaier and Schubert, 1993). In this study, I adopt a 1200°K temperature jump across the 660 km seismic discontinuity as determined by three-dimensional numerical simulations of enforced layered convection (Glatzmaier and Schubert, 1993). This value represents the average offset between the whole mantle and layered mantle geotherms calculated in that study (shown with Chapter 5, page 515 the pyrolite and piclogite adiabatic geotherms in figure 5.15), and in this study I add this amount to the lower mantle anchor temperature for the piclogite model. I stress that modeling the predicted properties for the piclogite model along a geotherm that is either concordant with an upper mantle geotherm, or equal to the one used in modeling a pyrolite mantle, is simply incorrect. Thus, in addition to the differences in the adopted thermoelastic data, this study approached modeling the piclogite lower mantle quite differently than that of Zhao and Anderson (1994). For example they claim that the experimental data is too imprecise to estimate the lower mantle chemistry uniquely from the seismic data. I would agree with this statement, inspite of the fact that this study uses the latest thermoelastic data, simply because, I doubt that a unique chemistry could ever be determined from seismic models. Thus, since the pyrolite model is consistent with the seismic constraints, I consider it an acceptable, but not unique, compositional model. On the other hand, i f a change of composition occurs between the upper and lower mantle, then the predicted velocities and density for the proposed lower mantle composition must be calculated along a hot geotherm with respect to the overlying geotherm. I find that when this factor is considered, a piclogite model may be confidently rejected. 5.17 Conclusion The purpose of this study was to resolve the discrepancy between the conclusions drawn from our previous study of modeling density and bulk sound velocity profiles and those deduced from modeling Vs and Vp velocity profiles. Recent studies comparing predicted Vs and Vp velocity profiles for various bulk chemical compositions to Chapter 5, page 516 seismological models have concluded that the lower mantle may be chemically distinct from the upper mantle and transition zone (Zhao and Anderson, 1994). This is in conflict with the results of modeling p and profiles: for these properties a uniform composition provides an excellent fit to the seismic observations along an adiabatic geotherm concordant to the upper mantle geotherm. In contrast, for a piclogite composition the predicted p and K 0 profiles, do not fit the seismic observations. To resolve the discrepancy between the conclusions based on Vs and VP versus p and F 0 1 extend the modeling to calculate Vs and Vp profiles. Using third-order Birch-Murnaghan finite strain theory, Vs and Vp velocity profiles are calculated for a pyrolite bulk composition throughout the lower mantle along an adiabatic geotherm previously calculated from modeling p and V0. For consistency, all of the thermoelastic parameters used in modeling p and V& are treated as fixed parameters, leaving only the shear moduli temperature and pressure derivatives as unknowns. I estimate the temperature derivatives for the Mg-and Ca-perovskite shear moduli [ (dp/dp) ] via the high temperature approximation of Isaak (1992) and for Mg-perovskite, cross-check this value against that determined via constrained adiabatic decompression of the lower mantle seismic properties. The two predictions are virtually identical, implying that the temperature derivative estimates are robust. Consequently, these are held fixed to their predicted values and not treated as adjustable parameters in fitting the seismic profiles. For the unmeasured pressure derivative of the perovskite shear moduli (dp /SPJ I assume that the Ca- and Mg-perovskites have similar values and perturbed the calculated Mg-perovskite value of Patel et al. (1996; [ c p / s p ] = 1.51) to optimize the fit between the Chapter 5, page 517 predicted and observed Vs and Vp velocity profiles. If the stated experimental error reported for the latest values for (<9 p /d i 5 ) (e.g. Zha et al., 1997; ± 0.2) are equally applicable to the molecular dynamics value of Patel et al. (1996), then the final value used here falls within the uncertainty of molecular dynamics value. I rationalize this "tuning" of the predicted profiles using a single parameter, because I know apriori, from modeling p and V®, that the pyrolite model can satisfy the lower mantle seismic observations along this adiabatic geotherm, and hence, must also satisfy the seismic Vs and Vp observations. Of course there is no guarantee that this will indeed occur, since the actual pressure dependence of the perovskite shear modulus, may require higher terms than simply those in a 3rd order Birch-Murnaghan equation of state. Although not a rigorous test, the resulting set of shear moduli derivatives are evaluated to determine i f they are mineralogically plausible when compared to other perovskite compounds. I find that the predicted Vs and VP velocity profiles for a pyrolite mantle can fit the lower mantle akl35 seismic profiles to <± 0.5% uncertainty. Thus, together with the results of a previous study for the upper mantle and transition zone, I find a uniform composition can fit the whole mantle seismic Vs and Vp observations along a single adiabatic geotherm. In contrast, when I use an appropriate hot lower mantle geotherm for a convectively isolated lower mantle, the predicted profiles for the piclogite model fail to match the seismic constraints. The misfit is not a subtle feature and consequently, the piclogite model may be rejected with confidence. I did not explore any tradeoffs between different thermoelastic data sets, as did Zhao and Anderson (1994), simply because I "fix" the measured properties to the most recent Chapter 5, page 518 values, and thus, focus on constraining the unmeasured shear moduli derivatives, whereas they believe the measured experimental results are only poorly constrained and elect to adjust these parameters. While our inference for their room temperature value for the temperature derivative of the shear modulus, (c3p/d7J is similar to ours, at the high temperatures of the lower mantle, the Zhao and Anderson (1994) choice will be significantly greater and exceed that measured for any relevant mantle mineral. In contrast, the value adopted here is not abnormal and hence, does not require iron enrichment (Weidner and Zhao, 1992) and or volatile-rich partial melts (Duffy and Ahrens, 1992) to satisfy the seismological observations. Therefore, away from chemical and thermal boundary layers that characterize the surface and basal thermal and chemical boundary layers of the mantle, a pyrolite composition with its associated phase changes, satisfies all the seismic constraint ( F 0 and p, and Vs and VP ). There is no need to invoke any thermal or compositional breaks within or between the upper or lower parts of the Earth's mantle. 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Chapter 5, page 529 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 V o l u m e % P i c l o g i t e Figure 5.2 Volume percentage of the mantle minerals present in the piclogite model as a function of depth. Figure redrawn from Ita and Stixrude (1992). Chapter 5, page 530 C O C O 2.50 2.45 2.40 2.35 2.30 2.25 2.20 2.15 F-2.10 F-2.05 |_i i i i i y i i | i i i i i i i i i | i i i i i i i i i | i i i i i i i i i_ Bonczar & Graham (1982) : 2.00 ' i i i i i i I I I E C L 0.00 0.10 0.20 0.30 0.40 F e c o n t e n t i n M a g n e s i o w u s t i t e Figure 5.3 (d^i/dT\ versus iron content in magnesiowustite. Chapter 5, page 531 400 800 1200 1600 2000 2400 T e m p e r a t u r e ( K ) Figure 5.4 Theoretical Expansivity of Mg-perovskite as a function of temperature and Gruneisen parameter. Figure redrawn from Anderson and Masuda (1994). Chapter 5, page 532 0 100 200 300 400 500 600 700 800 900 1000 T ( K ) Figure 5.5 Theoretical Expansivity of Mg-perovskite as a function of temperature compared to experimental data. Figure Wang et al., (1994). Chapter 5, page 533 300 600 900 1200 1500 1800 2100 2400 T e m p e r a t u r e ( K ) Figure 5.6 Theoretical Coefficient of thermal expansion of Mg-perovskite as a function of temperature and Gruneisen parameter. Figure redrawn from Anderson and Masuda (1994). Chapter 5, page 534 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 T e m p e r a t u r e ( K ) Figure 5.7 Experimentally constrained Coefficient of thermal expansion of Mg-perovskite as a function of temperature. Chapter 5, page 535 7.0E-5 b 1 I 1 I 1 I 1 I 1 I 1 I 1 \ / I ^ 6 . o OE-5 E-OE-5 I K86 Z high Tfit 4.0E-5 +-* O 13 o O 3.0E-5 OE-5 1.0E-5 M91 fit A •D&A89 Z&A94^ wmmm:— ywer mantle ^ ^ ^ ^ ^ t CO CO 15 300 600 900 1200 1500 1800 2100 2400 T e m p e r a t u r e ( K ) Figure 5.8 Experimentally constrained Coefficient of thermal expansion of Mg-perovskite as a function of temperature. Also shown are the recent results of Gillet et al., (1996) as a function of pressure. Chapter 5, page 536 o io F-ed o U P H 20 F 30 40 i i i i i i i i i I I i i i i i i I i i i i i i i i i I i i i i i i i i i < note that this symbol is not a real experimental data point, but I I I I I I I I I I I •xt his ymbol is not a h the adopted a 9 0 0 K value Msed by Zhao and Anderson (1994) • • wm s circles represent calcufc ted values of a 900 Mstimate^ ire %Fig. 8 of Mao et al. (44- >' for their fit A andfit B. 7't are not experimental data4 joints. 4.6 xlO" adopted values in Zhao and Anderson (1994) a 9 0 o] f 3.0 x l 0 " 5 i / K a900K= 1.8 x 1 0 " l / K 85 =0.5 50 1.0E-5 ± 1 1 1 1 1 1 1 a2p5j=l.7(±oj)xlO-5K-J Funamori & Yagi (1993). This single result was used as a constraint on the adopted pairs of a andhs in Zhao and Anderson (1994). i i i » i i i i i I i i i i i i i i i I i I - i t 2.0E-5 3.0E-5 4.0E-5 5.0E-5 t h e r m a l e x p a n s i o n ( 1 / K ) Figure 5.9 Coefficient of thermal expansion of Mg-perovskite as a function of pressure. Figure redrawn from Zhao and Anderson (1994). Chapter 5, page 537 1 I 1 I ' I ' I 1 I ' I 1 I 1 I 1 I 1 I ' I 1 I 1 ,Mg-Pv (Yeganeh-Haeri, 1994) 300 600 900 1200 1500 1800 2100 2400 T e m p e r a t u r e ( K ) Figure 5.10 Shear modulus as a function of temperature. Chapter 5, page 538 7.0E-5 U | I | I | i | i | i | i | i | i | i | I | i N G6.0E-5 F-e o S5.0E-5 X 03 4.0E-5 E-o c o 3.0E-5 1.0E-S2 .0E-5 B Knittle etal, (1986) high Tfit polynomial fit to Suzuki curve of Knittle et al, 1986 used with Duffy & Anderson (1989) 200 400 600 800 10001200140016001800200022002400 T e m p e r a t u r e ( K ) Figure 5.11 Inferred coefficient of thermal expansion of Mg-perovskite for Duffy and Anderson (1989) and Zhao and Anderson (1994). Chapter 5, page 539 -0.040 -0.035 h -^0.030 h H C O C O •0.025 h --0.020 1 I 1 I 1 I 1 I 1 I 1 I 1 I Mg-perovskite Duffy & Anderson (1989) I 1 I 1 I 1 •4 « lower mantle _| temperature range 300 600 900 1200 1500 1800 2100 2400 T e m p e r a t u r e ( K ) Figure 5.12 Inferred behaviour of (du ldl\ for Mg-perovskite as a function of temperature for Duffy and Anderson (1989), Zhao and Anderson (1994) and this study. Chapter 5, page 540 -0.040 -0.035 -0.030 g-0.025 ^-0.020 C O ^ 0 . 0 1 5 -0.010 -0.005 0.000 i i i i | i i i i | i i i Mg-perovskite (dix/dP) molecular dynamics sim " Patel etal, (1996) Mg-perovskiU i this study fi-olivinei& t H » « I l l l l l l i i i T value ^Jiigh T value D&A89 298 K value Z&A94 y-olivine ' ' ' CO J rv" i i 0.00 0.50 1.00 1.50 2.00 ( % / 3 P ) 2.50 3.00 Figure 5.13 Plot of (dp Idl \ versus (dp /dP)rfor measured compounds with the inferred values for Mg-perovskite from Duffy and Anderson (1989), Zhao and Anderson (1994) and this study. Also shown is the recent estimate of (d\ild?\ from molecular dynamic computer simulations (Patel et al., (1996). Chapter 5, page 541 Mid-Ocean Ridge mantle potential temperature 1330-1350 C(= 1603-1623 K 0 i- i i i i i i i Hot-Spot mantle potential temperature . 1450-1550 C (=1723-1823 K) • i l l 1200 1400 1600 1800 2000 2200 2400 T e m p e r a t u r e ( K ) Figure 5.14 The adopted pyrolite adiabatic geotherm for the upper mantle, transition zone, and the upper part of the lower mantle. This geotherm is calculated self-consistently from the mineral physics parameters used in calculating whole mantle profiles of density and bulk sound velocity. Chapter 5, page 542 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 Temperature (K) Figure 5.15 Pyrolite geotherm compared to the whole mantle and enforced layered mantle geotherms calculated from 3D numerical simulations of mantle convection (Glatzmaier and Schubert, 1993). The adopted piclogite lower mantle geotherm used in this study is also shown. Chapter 5, page 543 5.00 6.00 7.00, 8,00^ 9.00 10.00 11.00 12.00 13.00 14.00 Velocity (km/sec) S wave, P wave Figure 5.16 Comparison of the predicted bulk VS and VP velocity profiles of pyrolite as a function of depth in the lower mantle to the global reference seismic models akl35 (Kennett et al., 1995), akl35-F (Montagner and Kennett, 1996). 599 5.80 6.00 6.20 6.40 6.60 6.80 7.00 7.20 7.40 Shear Velocity (km/sec) Figure 5.17 Comparison of the predicted bulk VS velocity profiles of pyrolite as a function of depth in the lower mantle to the global reference seismic models akl35 (Kennett et al., 1995), akl35-F (Montagner and Kennett, 1996). 800 1000 1200 1400 ^1600 - S i 800 OH ^2000 2200 2400 2600 I I I I I I I 1 I l l i i i I I I I ' T l 1 i I ' I akl35-F P wave calculated Chapter 5, page 545 270 km D" PREM, ak 135 & SP6 D" = ISO km \ — 2800 M i -u i 1 1 1 1 1 1 /CMR i i i 1 i i i i 1 i i i i 1 i y \ i i 1 i i i i 1 i i i i 1 i I i I l a tr cn 6. > o 11.00 11.50 12.00 12.50 13-00 13.50 14.00 14.50 Compression Velocity (km/sec) Figure 5.18 Comparison of the predicted bulk VP velocity profiles of pyrolite as a function of depth in the lower mantle to the global reference seismic models akl35 (Kennett et al., 1995), akl35-F (Montagner and Kennett, 1996). Chapter 5, page 546 800 h 1000 1200 1400 h ^ 6 0 0 H £ 1 8 0 0 Q 2000 h-2200 h 2400 2600 h 2800 \ --4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 Percent difference between calculated Vs profile and akl35 Vs Figure 5.19. Percentage difference of the predicted pyrolite VS velocity profile from theakl35 and ak 135-F profiles. Chapter 5, page 547 -4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 Percent difference between calculated Vp profile and akl35 Vp Figure 5.20 Percentage difference of the predicted pyrolite VP velocity profile from the akl35 and akl35-F profiles. Chapter 5, page 548 <2000 J— 2100 h 2200 2300 2400 2500 2600 2700 2800 2900 5.00 6.00 7.00 8.00 9.00 10.00 11.00 12.00 13.00 14.00 Velocity (km/sec) S wave, P wave Figure 5.21 Comparison of the predicted bulk VS and VP velocity profiles of piclogite and Pyroltie as a function of depth in the lower mantle to the global reference seismic models akl35 (Kennett et al., 1995), akl35-F (Montagner and Kennett, 1996). Chapter 6, page 549 Chapter 6 Vs and VP velocity profiles in the Earth's lower mantle revisited; incorporating experimental values for the temperature and pressure dependence of the Mg-perovskite shear modulus. Chapter 6, page 550 6.1 Abstract Recent studies comparing predicted Vs and V,, velocity profiles for various bulk chemical compositions to seismological models have been forced to infer values for the unmeasured temperature and pressure derivatives of the shear modulus for MgSi0 3 perovskite. In the previous two chapters I used constrained adiabatic decompression of the reference seismic models to first estimate a value for the temperature derivative, and then by trial and error, adopt a mineralogically reasonable value for the pressure derivative to obtain a match between the predicted and observed velocity profiles. This is less than satisfactory, but in the absence of experimental data, a reasonable approach. However, with the recent publication of high temperature experimental and theoretical values for the bulk and shear moduli, the question of whether or not an isochemical pyrolite mineralogy can match the seismic shear and compression velocity profiles needs to be revisited. Here I incorporate the experimental measurements for (d\i/8T)p and {d\i/dP)r for M g S i 0 3 perovskite by Sinelnikov et al. (1998) together with the molecular dynamic, high pressure predictions of Kg and p by Karki et al. (1997) to obtain updated equation of state parameters for MgSi0 3 perovskite. I find that to satisfy both the ultrasonic measurements of Sinelnikov et al (1998), previous static diamond anvil measurements, and the high pressure predicted Ks and p profiles of Karki et al. (1997), the Birch-Murnaghan equation of state for M g S i 0 3 perovskite must be extended to 4 t h order for both the bulk and shear moduli. Similarly, recent high pressure experimental (Chopelas, 1996; Duffy et al., 1995) and molecular dynamics predictions (Karki et al., 1997b) for MgO indicate that it too should be fit by a 4 t h order equation of state. Using 4 t h order Birch-Murnaghan finite strain theory, I calculate Vs and VP velocity profiles for a pyrolite bulk composition across the lower mantle along an adiabatic geotherm previously calculated from modeling p and V0. I find that the predicted Vs and Vp velocity profiles for a pyrolite mantle provide an excellent fit to the lower mantle akl35 seismic profiles to <± 0.2% uncertainty. Thus, together with the results of a previous study for the upper mantle and transition zone, I find a uniform composition can fit the whole mantle seismic Vs and VP observations along a single adiabatic geotherm. While these results are identical with that found earlier using estimated values for the temperature and pressure derivatives of the Mg-perovskite shear modulus, these conclusions are now based on experimentally measured values, and therefore, more robust than the predictions given in the previous chapter. Therefore, away from chemical and thermal boundary layers that characterize the surface and basal thermal and chemical boundary layers of the mantle, a pyrolite composition with its associated phase changes, satisfies all the seismic constraints. This conclusion supports the conclusion deduced from modeling of p and V0 profiles and argues strongly that the present day style of convection within the Earth extends across the whole mantle. Chapter 6, page 551 6.2 Introduction Because M g S i 0 3 perovskite comprises « 77 vol% of the lower mantle (assuming a Pyrolite mineralogy) the particular thermo-elastic properties of this mineral are, without question, the most important mineral physics properties with regard to undertaking any modeling study of the Earth's lower mantle. As outlined in detail in Chapters 3 and 4, one of the major stumbling blocks in modeling the shear and compression velocity profiles in the lower mantle is the lack of experimental values for the temperature and pressure derivatives of the Mg-perovskite shear modulus (d p/3 T)p and (d \i/dP)p . Chapter 4 outlined a way in which a constraint could be placed upon the temperature derivative (d\i/dT)p via constrained adiabatic decompression, while chapter 5 used this value, together with the results from chapter 2, to rationalize a search for an appropriate value for (d\i/dP)p, assuming a 3 r d order Birch Murnaghan equation of state, that resulted in fitting the predicted shear and compression velocities to the reference seismic model profiles. Such a procedure was justified on the basis of the excellent fit between the predicted and observed density and bulk sound velocity profiles, for which the necessary thermo-elastic parameters are experimentally measured. While the fit of the calculated Vs and Vp profiles to the seismic ones is excellent, this in itself is not surprising since the unknown pressure derivative of the shear modulus was freely adjusted to maximize this fit. Therefore, the fit cannot be taken as strong evidence in support of the pyrolite model, but simply as additional evidence "consistent" with such a composition model. Chapter 6, page 552 Subsequent to this work on calculated lower mantle Vs and Vp profiles, first presented at the 1996 Gordon Conference, direct mineral physics experiments have recently been performed on Mg-perovskite to measure the temperature and pressure derivatives of its shear modulus [(dii/dT)p and (d[i/8P)p]. These measured properties provide key constraints on the ability of various compositional models to satisfy the seismic profiles. For instance, in the previous chapter I concluded that a piclogite mineralogy could not satisfy the seismic observations. However, because I utilized a value for the pressure derivative of the shear modulus for Mg-perovskite which had been adjusted to maximize the fit between the isochemical pyrolite model and the seismic observations, it may be argued that it is inappropriate to simply adopt the same value for {d\i/dP)p when modeling a piclogite composition. Thus, adopting values for "free parameters" which were adjusted for the pyrolite model may inherently result in poor fits when subsequently used for non-pyrolite compositions. Such problems, however, disappear i f experimentally measure values for the temperature and pressure dependence the shear modulus of Mg-perovskite are used. In this short chapter I incorporate the first experimental values for (d p/9 T)p and (d \x./dP)p for Mg-perovskite into modeling lower mantle Vg and Vp profiles. However, these values cannot simply be substituted into the equations - I find that to satisfy the high pressure diamond anvil experimental observations and the recent molecular dynamics predictions of the pressure dependence of KS and m across the full pressure range of the lower mantle, higher order terms for the perovskite equation of state (e.g. (d2 [i/dP2)p ) are required. Chapter 6, page 553 6.3 Experimental values for Mg-perovskite (d p/d T)r and (d \x/dP)r Sinelnikov et al. (1998) present the first experimental measurements for both the temperature and pressure dependence of the Mg-perovskite shear moduli. They first synthesized relatively large polycrystalline samples of pure MgSi0 3 in a multi-anvil press at pressures greater than 24 GPa and temperatures in excess of 1700 K. Careful quenching paths resulted in recovery of 1.5 mm diameter samples suitable for ultrasonic experiments. Three samples were subjected to simultaneous in-situ acoustic and X-ray diffraction at simultaneous high temperature and pressure. Because the ultrasonic experiments only extend to a maximum 8 GPa pressure, and hence, are well below the thermodynamic stability range of natural Mg-perovskite (>24 GPa), the maximum temperature was limited to 820 K to avoid retrogressive breakdown of the samples. Each sample was recovered after the experiments and subjected to additional zero pressure and room temperature X-ray, Raman Spectroscopy, density, and length measurements to check that no irreversible changes had occurred. The measured ultrasonic acoustic travel times were converted into shear velocities and moduli using the Wang et al. (1994) equation of state parameters and were fitted as linear functions of both temperature and pressure. The resultant values of p, (d\i/8T)p and (d^i/dP)p are given in table 6.1. Inspection of table 6.1 shows there is excellent reproducibility in the values of p, (Sp/Sr)^ and (d^./dP)p inspite of using different polycrystalline samples in each experiment. Sinelnikov et al (1998) average the results from the three experiments to obtain robust estimates for (d p/3 T)p = -0.029 ± 0.003 GPa/K and (dyi/dP),, = 1.8 ±0.4. Chapter 6, page 554 Because of the relatively limited pressure range (0-8 GPa) which was explored during the experiments, as compared to the natural pressure range (24- 135 GPa) of Table 6.1. Summary of shear moduli properties for Mg-perovskite from Sinelnikov et al. (1998). Mg-perovskite specimen density P- (dp/ dP)T (d\il dl)P (kg/m3) Shear Modulus (GPa) pressure derivative temperature derivative (GPa/K) 2997 4.03 ± 0.002 175.0 1.8 ±0.1 -0.030 ±0.001 3020 4.06 ± 0.002 176.0 ±5.0 1.9 ±0.3 -0.029 ± 0.002 3081 4.10±0.002 174.0 ±7.0 1.8 ±0 .4 -0.028 ± 0.003 average 1.8 ±0 .4 -0.029 ± 0.003 Yeganeh-Haeri, 1994 4.107 + 0.002 177.0 ±4.0 - -Patel et al., (1996) 1.51 -values used in chapter 5 177.3 1.62 -0.0224 Mg-perovskite there exists the possibility that the full pressure dependence of Mg-perovskite has not been documented (Sinelnikov personal communication). Indeed, his preliminary analysis of unpublished data indicates that (d Ks/dP)F may be « 4.5, a value which lies at the upper bounds of existing experimental values (e.g. recommended value for (d Ks/dP)r = 4.0; Jackson and Ridgen, 1996). The possibility that additional higher order terms are required to describe the pressure dependence of the shear moduli for Mg-perovskite is independently suggested by recent molecular dynamics predictions of the pressure dependence of both Kg and p. Chapter 6, page 555 6.4 Theoretical predictions of K^P) and for Mg-perovskite: (d \i/dP)r and (a2 p/sp2), In addition to the experimental values summarized above, recent theoretical advances now allow the elastic constants for MgSi0 3 perovskite to be predicted from first principles (Karki et al., (1997b). Karki et al. (1997b) present the nine elastic moduli and density for orthorhombic Mg-perovskite as a function of pressure up to 140 GPa and zero temperature. The zero pressure calculated isotropic bulk and shear moduli are tabulated together with these properties as a function of pressure. The calculated zero pressure values of Karki et al. (1997b) are Ks = 258 GPa and p = 175 GPa, in excellent agreement with the experimental values of Yeganeh-Haeri (1994; Ks = 264 ± 4 GPa and p = 177 ± 4 GPa) and Sinelnikov et al. (1998). In addition, the calculated high pressure isotropic bulk and shear moduli values are within experimental error of existing static, diamond anvil room temperature measurements. The significant feature of the molecular dynamics predictions is that the calculated profiles of Ks(P) and p(P) extend over the full pressure interval of the lower mantle, and thus provide much greater sensitivity of the pressure dependence than the ultrasonic experiments of Sinelnikov et al. (1998). Thus, they provide an excellent datum to constrain possible higher order terms for the pressure dependence of Mg-perovskite. I digitized the Ks and p profiles as a function of pressure from figure 1 of Karki et al. (1997b) which is reproduced in figure 6.1. These profiles were compared to calculated room temperature profiles of Ks(V) and p(P) using both 3 r d and 4 t h order Birch-Murnaghan finite strain theory. Both the 3 r d and 4 t h Chapter 6, page 556 order equation of state predictions adopted the experimental value of (d \x/dP)p = 1.8 ± 0.4 and (d KT/dP)p = 4.5 from Sinelnikov et al. (1998), while the 4 t h order predictions adopted an initial estimate of (d p 2/dP 2) p = -0.026 GPa"1 from the experimental study on MgO to 227 GPa (Duffy et al., 1995) and then adjusted this to maximize the fit to the molecular dynamics prediction. The fit and the resulting parameters are shown in figure 6.2. Lastly, these values for the pressure dependence were utilized in a high temperature 4 t h order Birch-Murnaghan EOS prediction using the lower mantle pyrolite adiabatic geotherm. This is shown in figure 6.3 and the resulting Mg-perovskite properties were used to predict lower mantle velocity profiles. Slight adjustments were made to (d Kr/dP)T (decreasing it from 4.52 to 4.49) and the higher order bulk moduli term (d K2/dP2)p (decreasing it from -0.036 GPa"1 to -0.045 GPa"1). In addition, when modeling the lower mantle velocities with a 4 t h order Birch-Murnaghan EOS, the value of the temperature derivative,(d Kr/dT)p was decreased from -0.0295 GPa/K to -0.035 GPa/K, a value which is consistent with that determined experimentally from high pressure (to 57 GPa) P-V-T laser-heated diamond anvil measurements (Fiquet et al., 1998; mean value(d KT/dT)p = -0.035 GPa/K for room temperature to 2000K isotherm values). Lastly, the Gruneisen (y) and isothermal Anderson-Gruneisen (87) parameters were reduced slightly to reflect the experimental values of Chopelas (1996; y = 1.42 ± 0.07; 87 = 4.8), while the parameter K was increased slightly from 1.45 (Anderson and Masuda, 1994; Anderson et al., 1995) to 1.50 to conform with the recommended value of Anderson (1998). Chapter 6, page 557 Table 6.2. Comparison of thermoelastic parameters for Mg-perovskite using a 4 t h order Birch-Murnaghan EOS compared to the values used in the previous chapters (which utilized a 3 r d order Birch-Murnaghan EOS). parameter 3 r d order Birch- Sinelnikov et al. 4 t h order Birch-Murnaghan EOS (1998) Murnaghan EOS Vo (cmVmole) 24.731 24.731 KS (GPa) - -Kj (GPa) 261.50 259.0 (dKr/dT) GPa/K -0.0295 -0.0350 (dKr/dp)r 3.99 «4.50 4.49 (dK2/dP2)r - -0.045 GPa"1 a(298°K) K"1 1.72 x l O ' 5 - 1.72 x 10"5 r 1.50 - 1.42 87' 5.00 - 4.80 K 1.45 - 1.50 p GPa 177.3 177 ± 7 179.0 1.62 1.8±0.4 1.81 - - -0.022 GPa"1 {dll/dT^ GPa/K -0.0224 -0.029 ± 0.003 -0.027 6.5 Magnesiowi ist i te ( M g 0 8 6 F e 0 M ) Q Following the many experimental and theoretical studies on periclase which document higher order pressure terms than simply (d n/dP)F (Jackson and Niesler, 1982; Duffy and Ahrens, 1995; Karki et al., 1997a; Duffy et al., 1995). I adopt the pressure dependence of MgO as deduced by Duffy and Ahrens (1995; KT0 = 160.3 GPa; {dK,,/dP)T = 4.09 ± 0.09; (dK2/dP2)p = -0.019 ± 0.004 GPa"1; p = 130.9 GPa; (dn/8P)P = 2.5 ± 0.1; (d^/dP2)p = -0.026± 0.045 GPa"1) and assume this pressure Chapter 6, page 558 dependence applies equally well to magnesiowustite composition used here [(Mg 0 8 6 Fe 0 1 4 )O]. The room temperature, high pressure predictions of the adiabatic bulk and shear moduli are plotted in figure 6.4 together with the 4 t h order predictions of Chopelas (1996) and Karki et al. (1997a). Also plotted is the high temperature and pressure predictions as calculated along the pyrolite lower mantle geotherm using the high temperature, 4 t h order Birch-Murnaghan EOS. 6.6 Results The effect on the lower mantle V$ and Vp profiles of incorporating these modifications to the pressure and temperature dependence of Mg-perovskite and magnesiowustite is shown in figure 6.7 which plots both of the predicted pyrolite Vs and VP profiles together with the corresponding velocity profiles from the akl 35 and akl 35-F seismic reference models (Kennett et al., 1995; Montagner and Kennett, 1996). To obtain an indication of the improvement in the fit between the pyrolite mantle and the seismic profiles figure 6.8 and 6.9 plot the percent difference between the calculated velocity curves and the akl 35 reference profile for the 3 r d order equation of state from chapter 5 and the 4 t h order EOS outlined here. There is improvement in fitting both the shear and compression profiles when using a 4 t h order equation of state together with the experimental values for the temperature and pressure dependence of the Mg-perovskite and periclase shear moduli, although it must be admitted that the improvement is relatively small. Nevertheless, the excellent fit using experimentally measured values for Mg-perovskite is significant in its own right. Thus, predicted Vs and Vp profiles for a pyrolite Chapter 6, page 559 mantle are consistent with the results from modeling density and F 0 profiles and demonstrates that a Pyrolite mantle satisfies the seismic observations across the whole mantle. 6.1 Conclusions The purpose of this study was to incorporate the results from recent experimental and theoretical studies on Mg-perovskite which provide much more direct constraints on the temperature and pressure dependence of the shear modulus of Mg-perovskite than was possible in the previous chapters. To satisfy both the ultrasonic and molecular dynamics results, I extended the pressure dependence to higher order terms and modeled the variation of both the adiabatic bulk and shear moduli with a 4 t h order Birch-Murnaghan equation of state. In addition, the pressure dependence of magnesiowustite was also extended to include 4 t h order terms, consistent with a number of independent experimental observations. With these changes I find that the predicted lower mantle Vs and Vp profiles give a better fit to the seismic observations than the previous 3 r d order equation of state profiles which had to rely on estimates for both {d p/9 T)p and (d \x./dP)p . Significantly, the results found here are entirely consistent with those deduced earlier in chapter 2, 3, and 5; a uniform pyrolite composition provides an excellent fit to the seismic observations along a self-consistent adiabatic geotherm. While this may appear redundant, in that this chapter reaches the same conclusions as the previous chapters, I note that unlike chapter 5, the predicted lower mantle Vs and VP profiles are much more robust. Chapter 6, page 560 Therefore, away from chemical and thermal boundary layers that characterize the surface, and basal thermal and chemical boundary layers of the Earth's mantle, a pyrolite composition with its associated phase changes, satisfies all the seismic constraints via the pairs of parameters V0 and p, and Vs and Vp . Together, the results from this chapter and of chapters two and three strongly argues that the present day mantle is isochemical and hence the style of convection within the Earth is whole mantle convection. Chapter 6, page 561 6.8 References Anderson, O.L., 1998. Thermoelastic properties of MgSi0 3 perovskite using the Debye approach. American Mineralogist, vol., 83, 23-35. Anderson, O.L., and Masuda, K., 1994. A thermodynamic method for computing thermal expansivity, a, versus T along isobars for silicate perovskite. Physics of the Earth and Planetary Interiors, vol., 85, 227-236. Anderson, O.L., Masuda, K., and Guo, D., 1995. Pure silicate perovskite and the P R E M lower mantle model: a thermodynamic analysis. Physics of the Earth and Planetary Interiors, vol., 89, 35-49. Anderson, O.L., Masuda, K., and Isaak, D.G., 1996. Limits on the value of 8f and y for M g S i 0 3 perovskite. Physics of the Earth and Planetary Interiors, vol., 98, 31-46. Chopelas, A. , 1996. The Fluorescence sideband method for obtaining acoustic velocities at high compressions: application to MgO and M g A l 2 0 4 . Physics and Chemistry of Minerals, vol., 23, 25-37. Chopelas, A. , 1996. Thermal Expansivity of lower mantle phases MgO and MgSi0 3 perovskite at high pressure derived from vibrational spectroscopy. Physics of the Earth and Planetary Interiors, vol., 98, 3-15. Duffy, T.S., and Ahrens, T.J., 1995. Compressional sound velocity, equation of state, and constitutive response of shock-compressed magnesium oxide. Journal of Geophysical Research, vol., 100, 529-542. Duffy, T.S., Hemley, R.J., and Mao, H-K., 1995. Equation of state and shear strength at Multimegabar Pressures: Magnesium Oxide to 227 GPa. Physical Review Letters, vol., 74, 1371-1374. Jackson, I., and Niesler, H. , 1982. The elasticity of periclase to 3 GPa and some geophysical implications. IN: High Pressure Research in Geophysics. Akimoto, S., Manghnani, M . H . , (eds.) Center of Academic Publishing of Japan, Tokyo, pp. 98-113. Karki, B.B. , Stixrude, L. , Clark, S.J., Warren, M.C. , Ackland, G.J., and Crain, J., 1997a. Structure and elasticity of MgO at high pressure. American Mineralogist, vol., 82,51-60. Karki, B.B. , Stixrude, L. , Clark, S.J., Warren, M.C. , Ackland, G.J., and Crain, J., 1997b. Elastic properties of orthorhombic MgSi0 3 perovskite at lower mantle pressures. American Mineralogist, vol., 635-638. Chapter 6, page 562 Sinelnikov, Y.D. , Chen, G., Neuville, D.R., Vaughan, M.T., Liebermann, R.C., 1998. Ultrasonic shear wave velocities of MgSi03-perovskite at high pressure and temperature and the composition of the Lower Mantle. Science (in press). 100 200 300 400 500 600 700 800 E l a s t i c M o d u l i ( G P a ) Figure 6.1 Comparison between the molecular dynamics prediction of the pressure variation of the isotropic adiabatic bulk and shear moduili of Mg-perovskite and a 3rd order EOS prediction with the pressure derivatives of Sinelnikov et al. (1998). Chapter 6, page 564 E l a s t i c M o d u l i ( G P a ) Figure 6.2 Comparison between molecular dynamics predictions of Karki et al. (1997b) and a 4th order EOS prediction. Chapter 6, page 565 (177 ±4) (264 ±5) ml ll 11 J | i i i i i i i i i | i l i i i i i i i [ i i i i i i i i i | i i i i i i i i i | i i i i i i i i i | i i i i i i i i | 100 200 300 400 500 600 700 800 E l a s t i c M o d u l i ( G P a ) Figure 6.3 Comparison between the high temperature and pressure prediction of Mg-perovskite using a 4th order EOS and the lower mantle pyrolite adiabat and the zero temperature molecular dynamics prediction of Karki et al. (1997b). Chapter 6, page 566 100 200 300 400 500 600 700 E l a s t i c M o d u l u s ( G P a ) Figure 6.4 Comparison of predicted pressure variation of the adiabatic bulk and shear moduli at room termperature and along the pyrolite lower mantle geotherm. Also shown are the molecular dynamic predictions of Karki et al. (1997a) and the experimental predictions of Chopelas (1996). Chapter 6, page 567 5.00 6.00 7.00 .8.00, 9.00 10.00 11.00 12.00 13.00 14.00 Velocity (km/sec) S wave, P wave Figure 6.5 Comparison of the predicted bulk VS and VP velocity profiles of pyrolite as a function of depth in the lower mantle to the global reference seismic models akl35 (Kennett et al., 1995), akl35-F (Montagner and Kennett, 1996). 800 1000 1200 1400 ^1600 £ 1 8 0 0 O H Q 2000 2200 2400 2600 2800 Chapter 6, page 568 1 I 1 akl35 4th order EOS akl35 3th order EOS ± i i 1 x i tr CO -4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 Percent difference between calculated Vs profile and akl 35 Vs Figure 6.6. Percentage difference of the predicted pyrolite VS velocity profde from the akl 35 profile for the 3rd order EOS with estimated parameters and the 4th order EOS with measured parameters. Chapter 6, page 569 -4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 Percent difference between calculated Vp profile and akl35 Vp Figure 6.7 Percentage difference of the predicted pyrolite VP velocity profile from the ak l35 profiles using the 3rd order EOS with estimated parameters versus the 4 t h order EOS with measured values. Chapter 7, page 570 Chapter 7 Mineral Physics estimates of the ratio of Relative Vs and VP velocity heterogeneity (d l n F 5 / d \nVp)p in the mantle. Chapter 7, page 571 7.1 Abstract Seismic tomographic models of the mantle demonstrate that Vs andVP velocity variations are spatially correlated with Vs anomalies larger than the associated Vp anomalies. The dimensionless logarithmic ratio(91nF s/91nF / J) p relates lateral variations in Vs to lateral variations to VP and may be estimated via: d\nVs y~d^VpJp Vp{dVs/dT)p Vs {dVP/dT)p Lateral variations in Vs andVP are expected to be correlated and proportional i f they result from lateral temperature variations associated with mantle convection. A regional seismic study of the Caribbean has indicated (d lnVs /d \nVP ) p = 1.70 (Bokelmann & Silver, 1991) for the upper part of the lower mantle whereas early comparisons of global Vs and Vp tomographic models find globally averaged values of 2.0-2.5. From free oscillation splitting functions, a lower mantle average value for (d \nVs/d \nVp ) p is constrained between 1.66 and 2.60 with a preferred value of 2.27 (Li et al., 1991b). In contrast, recent joint Vs and Vp models tomographic models, based on ISC P and S travel time data, find a lower value that varies gradually from «1.6 to 1.8 from 660 to 1500 km depth followed by an abrupt increase to a peak value of 3.0 at 2200 km depth before dropping back to values « 0-1.0 at the C M B (Robertson & Woodhouse, 1996a). However, whole mantle joint Vs and Vp models, based on either large data sets of absolute and differential long-period seismic data sets, or short-period multi-ISC seismic phases, find that the ratio of rms S to P velocity is nearly constant across the whole mantle (Bolton, 1996; Vasco and Johnson, 1998). These seismic values are larger than laboratory measurements performed at ambient pressures (range of 0.7-1.4), implying that lateral temperature variations may not be the only factor affecting the seismic velocities. An alternative interpretation of (dlnVs/dlnVP)p is that the high value reflects either lateral chemical variations or widespread regions of partial melt, since for a melt, the depth averaged value for the ratio is expected to be « 2.4. In essence, the problem in interpreting the underlying cause of the lateral variations in seismic velocity imaged by tomography is whether it is possible to reconcile mineral physics estimates of (d lnVs /d lnVp ) p at high P and T with the seismic results. I use the pyrolite mineral physics model to calculate Vs and Vp temperature derivatives throughout the mantle, by re-calculating the model 100°K above and below our reference mantle adiabatic geotherm and taking the average of the two estimates (e.g.): dVP dT AT = (1/2) ^^vKf - VHl"^ v p v p ^Hol (l/ref + VreJ - VL p v p Cold \ -<ref •iCold p v y p \ V * *• / V * * * ; These temperature derivatives are combined with the predicted Vs and Vp profiles to calculate the ratio (d lnF s/d \nVp ) p throughout the mantle and this radial profile is then compared to the most recent seismic estimates. In the lower mantle the mineral physics estimate is nearly uniform, with (d\nVs/dlnVP)p ranging from 1.70 to 1.78 from 660 km to C M B . Our mineral physics Chapter 7, page 572 estimate is in excellent agreement with the Caribbean estimate and the latest tomographic estimates, derived by the ratio of rms velocity amplitudes, for the lower mantle (e.g. Bolton, 1996; Vasco and Johnson, 1998). I. speculate that the anomalously high values of (d lnVs /d \nVP ) p > 3.0 found by some studies (e.g. Robertson and Woodhouse (1995; 1996); Ritzwoller and Lavely, (1995); Dziewonski and Masters (1997)) are an artifact that reflects the loss of resolution in the Vs tomographic models, relative to the P-wave model, at depths greater than «1350 km. Of note is that the ratio (31nF s/31nF /,) p for a partial melt increases smoothly from 2.4 at the top of the lower mantle to 2.65 at the core-mantle boundary and does not exhibit a "hump" at 2000 km depth. Therefore, the unusual shape derived from lower-mantle-only, joint S and P-wave tomographic models is not easily explained by the presence of partial melt. I conclude that the melt-free Pyrolite mineral physics estimate of (dlnVs/d\nVr)p agrees very well with the recent and most robust seismic observations across the whole mantle and indicates that to first order, lateral variations in Vs and Vp simply reflect lateral variations in temperature. Chapter 7, page 573 7.2 Introduction Seismic tomographic models demonstrate that lateral Vs andVp velocity variations are spatially correlated within the mantle but with the Vs anomalies larger than the associated Vp anomalies. The dimensionless logarithmic ratio (d lnVs/d \nVP ) p represents the ratio of relative Vs andVP velocity heterogeneity as inferred by the seismic models, which from the ratio of the rms velocity amplitudes in independent S- and P-wave models, was found to be « 2.0-2.5 (Dziewonski and Woodhouse, 1987). Thus, Vs anomalies are roughly twice as great as associated Vp anomalies at the same geographic position. Indeed, lateral variations in Vs and VP are expected to be both spatially correlated and proportional to one another i f the velocities anomalies result from a common process, such as lateral temperature variations associated with thermally-driven mantle convection. However, the seismic values of (d lnVs/d \nVp ) p are larger than room pressure laboratory measurements, which generally range from (d\nVs/d\nVp)p =0.7-1.4 (Anderson and Isaak, 1995; see table 7.1 and figure 7.1) and it has been suggested that pressure does not have a significant affect on (d lnVs /d \nVP ) p (Graham and Hilbert, 1988), implying that these values would not increase significantly across the full pressure range of the mantle. This discrepancy between the seismic inferences and the low pressure experimental results implies that lateral temperature variations may not be the dominant process responsible for the variations in seismic velocities recovered by seismic tomographic studies. If this is indeed the situation, then the interpretation of seismic tomographic models would become much more complicated than presently envisioned. Alternative factors that Chapter 7, page 574 influence (d \nVs /8 \nVp ) p include pervasive lateral chemical variations (Anderson, 1975; Yuen et al., 1993), widespread regions of partial melt (Anderson et al., 1987; Duffy and Ahrens, 1992), or strong and pervasive anisotropy (Robertson and Woodhouse, 1996b). For example, for a partial melt, which affects the shear modulus (and hence V$) much more than the bulk modulus (and hence Vp), the depth averaged value for the ratio (d \nVs /8 lnVr ) p is expected to be « 2.4, a value which is broadly consistent with some of seismic inferences (see below for additional details). Thus, the process responsible for generating the observed seismic anomalies, be it thermal, compositional, or a combination of both, can be elucidated by studying the relative ratio of shear to compression velocities. Table 7.1. High temperature experimental values for compounds relevant to geophysics (Anderson and Isaak (1995). Material (dlnVs/8lnVr)p High temperature, room pressure experimental value Seismic value Dziewonski & Woodhouse (1987) Lower mantle - 2.0-2.5 NaCI 1.08 KC1 1.19 CaO 1.22 MgO 1.23 MnO 1.58 A1 2 0 3 Corundum 1.58 M n 2 S i 0 4 1.20 Co 2 Si0 4 0.96 Fe 2 Si0 4 Fayalite 0.60 M g 2 S i 0 4 Forsterite 1.20 Olivine (Fo90, FalO) 1.19 Pyrope garnet 1.06 Grossular garnet 1.32 M g 2 A l 2 0 4 Spinel 0.90 Chapter 7, page 575 The purpose of this research is to assess the discrepancy between the seismic and mineral physics estimates of (d lnVs /d lnVp ) p by calculating, using the pyrolite compositional model, an updated, self-consistent radial profile of (dlnVs/8\nVp)p for the whole mantle. Preliminary results were presented by Armstrong and Calderwood (1996); with the incorporation of new thermoelastic parameters, the conclusions from this study are qualitatively unaffected. First, I review the seismic estimates of (dlnVs /d\nVP)p and conclude that this ratio is actually lower than the often quoted value of 2.0-2.-5. This is important because it is these anomalously high seismic inferences which have led to appeals to non-thermal mechanisms. Next I briefly review previous mineral physics estimates of (d \nVs jd lnVp )p . Lastly, the pyrolite mineral physics model described in previous chapters is used calculate the temperature derivatives of Vs and Vp ((d Vs/d T)p(r) , (d Vp/d T)p(r)) as a function of depth throughout the mantle. These two parameters are then combined with Vs and Vp profiles to calculate a radial profile of (d lnVs /d \nVp ) p (r) via the relationship (e.g. Isaak, 1992): Vp (dVjdT) ^ J P Vs (8Vp/dT)p • I find that the pyrolite mineral physics estimate for (91nF s/91nF / )) p is in excellent agreement with the latest seismic estimates implying that lateral temperature variations are sufficient to account for the virtually all of the observed lateral seismic variations recovered by seismic tomography. However, there remains two areas within the lower-most mantle, the South Pacific and South African D" regions, where the latest high-resolution joint S- and P-wave tomographic models recover anomalously high values for (d\x\Vs/d\nVP)p « 3.5 Chapter 7, page 576 (Bolton, 1996). If real, I speculate that these high values, i f indeed real, may represent the effects of either minor amounts of interconnected partial melt or concentrated dregs of oceanic crust (or both). It is unlikely that partial melt could explain the anomalies on its own given that the highest value for this effect is calculated to be roughly 2.56. The interpretation of partial melt + ocean crust is plausible from a geodynamic viewpoint, given that both the South Pacific and South African D" regions underlie large-scale slow velocity anomalies that extend from the base of the lower mantle up to the base of the transition zone, and hence, have been interpreted as "mega-plumes" representing large-scale upwelling mantle associated with convective instabilities originating in the thermal and chemical boundary layer in the D " layer. Discriminating between a partial melt or oceanic crust interpretation may be made on the basis of seismic attenuation, which from published reference models, demonstrates that the lower mantle is characterized by very low shear attenuation (therefore high seismic Qs), an observation incompatible with the presence of widespread partial melt. Alternatively, there is the possibility that the anomalously high values for (d\nVs/dlnVP)p are artifacts, since an independent, joint S- and P-wave, whole mantle tomographic model (Vasco and Johnson, 1998) that incorporated many core-seismic phases (e.g. SKS, PKPab, be, df), which were not used by Bolton (1996), and which solved for topography on the core-mantle boundary, do not find such high values. While the relative magnitude of the S- and P-wave models does exhibit an increase approaching the core-mantle boundary, the increase found by Vasco and Johnson (1998) in (d\nVs /8lnVp)p is relatively modest, increasing from 1.8 to only « 2.1. This increase is in marked contrast to Chapter 7, page 577 that determined by Bolton (1996) which goes from 1.8 to » 3.5 over roughly the same depth interval. Assuming for sake of argument that the Vasco and Johnson (1998) model is correct, then a value of (d lnVs /d InV,, ) p =2.1 is only slightly higher than what I calculate below for a pyrolite uniform composition mantle, suggesting that if this discrepancy is due to plausible chemical heterogeneities in the lowermost part of the lower mantle, such as subducted slabs, then these chemical heterogeneities do not result in a large increase in Alternatively, the small discrepancy may reflect anelastic effects recovered in the Vasco and Johnson (1998) model, which are not incorporated into the purely elastic mineral physics model constructed below. 7.3 Previous Seismic estimates of (d lnVs/d \nVP)p Here I review various seismic estimates of the relative Vs and Vp velocity heterogeneity within the Earth's mantle. I begin with "shallow" estimates for the upper mantle and progress deeper into the mantle via regional followed by global studies. Those familiar with the various seismological estimates will find the preferred seismic estimates summarized in section 7.9, while the previous mineral physics estimates are summarized in section 7.15. The methodology used to calculate new, self-consistent profiles of (d \nVs Id lnVp )p , 65 and T for a pyrolite uniform whole mantle composition are is outlined in 7.16. The latter two dimensionless parameters are useful in evaluating inferred 85 and T profiles which are required to explain some of the high seismic {d\nVs/dlnVP)p values. Section 7.17 presents and discusses the new results in relation to the preferred seismic profiles advocated here. Chapter 7, page 578 7.4) Upper mantle (d lnVs /d \nVP )p from the ratio of PP-P and SS-S differential travel time residuals. Woodward and Masters (1991a) used digital data from the Global Digital Seismograph Network, collected over the period 1976 to 1986, to obtain a large, global set of long period PP-P and SS-S differential travel times. These phases have wavelengths on the order of a few hundred kilometers, and hence, average out small scale structure (which strongly affects short period data (« 1 second) such as ISC P-wave arrival times) allowing large scale mantle structure to be studied with confidence. Differential travel times have the added advantage that they are relatively insensitive to errors in earthquake source location and reduced sensitivity to the local velocity structure around the earthquake source and receiver regions. Indeed, because these rays follow very similar paths near the earthquake source and receiver, these regions contribute little to the total differential travel time, with most of signal reflecting upper mantle velocity structure near the SS (or PP) surface bounce point (see figure 7.2). When the PP-P and SS-S travel time residuals (5722 PP-P and 6504 SS-S measurements) are averaged within a tectonic province and these regional averages compared, the ratio of residuals (btss_s /btpp_p ) is ~ 2.0 to 2.5 (see figure 7.3). This estimate may, in turn, be converted to the logarithmic ratio (d lnVs /d \nVp ) p , a dimensionless ratio expressing the relative magnitude of the shear to compression velocity, via Fermat's Principle (Souriau and Woodhouse, 1985; Bolton, 1996): (dlnVs/dlnVP\*Z^{otss_s/otPP_P) , ' 7' Chapter 7, page 579 where Vs and VP are the mean shear and compression velocities in the upper mantle ((VS/VP ) = 0.5472 calculated from the akl35 seismic reference model (Kennett et al., 1995). The above ratio of travel time residuals results in (d \nVs /d \nVp ) p « 1.10 to 1.38 for the upper mantle. However, a more precise estimate may be determined by restricting attention to only PP-P and SS-S travel time residuals where the PP or SS bounce point occurs in oceanic areas. Because of the near-uniform thickness («7±1 km) and composition of normal M O R B ocean crust, SS (or PP) phases with bounce points in oceanic regions have virtually none of the complications due to lateral variations in crustal thickness, composition (including partial melt), and temperature that plague phases with bounce points in continental regions. Therefore, data sets consisting of "oceanic", as opposed to "continental" paths, are ideal for isolating upper mantle velocity structure (e.g. Shearer, 1996). Furthermore, a linear trend is expected as a function of square root of seafloor age i f the cooling and thickening of oceanic lithosphere follows the predictions of the cooling half-space model (see figure 7.4). To test i f this is indeed the case, Woodward and Masters (1991a) plotted their oceanic data as a function of seafloor age (see figures 7.5; note that each point in these figures represents an average of more than 100 individual measurements). Inspection of these two figures reveals a clear and strong linear correlation (correlation coefficient of 0.72 for PP-P and 0.84 for SS-S versus square root of seafloor age) for both &tss_s and 5tpp_p versus t^1 with the least-squares best fit lines having slopes of -0.51 + 0.01 sec/(Myr)1/2 and -0.18 ±0.01 sec/(Myr)1/2 . The ratio of these two values gives a global, oceanic average for ($tss_s jhtPP_P) of 2.83 ± 0.2 which translates into Chapter 7, page 580 (d \nVs/d lnVP ) p = 1.55 ± 0.10. This "oceanic" upper mantle value is only slightly greater than high temperature but room pressure experimental measurements for mantle minerals (see figure 7.6) implying that, at least for the upper mantle, there is no large discrepancy between experimental and seismological inferences. However, this "oceanic" upper mantle estimate is less than previous upper mantle estimates which are based on continental station corrections (e.g. Souriau and Woodhouse, 1985). The later study recommends a preferred value of (d lnVs/d lnVp ) p = 2.02 +0.07, a value which lies outside the error estimate of Woodward and Masters (1991a). Nevertheless, The Souriau and Woodhouse (1985) estimate is based on comparing measured P-wave static station corrections to predicted .S-wave station corrections using an upper mantle S-wave tomographic model, a procedure which is less than ideal. Continental station corrections and their corresponding upper mantle inferences for (d lnVs /d lnVP ) p are discussed in more detail next. 7.5) Upper mantle (dlnVs/d\nVp )p from Global S and P station corrections. In constructing the tomographic models, which are discussed in various sections of this chapter, it is necessary to isolate the "3D mantle signal" from the total travel time observation and this is done, in its simplest form, by breaking the observed travel time down into three distinct components (Cleary and Hales, 1966; Dziewonski, 1984; Robertson and Woodhouse, 1995): earthquake 3D mantle ^residual ^obs ^_ ^calc ^source _j_ ^signal ^reciever Chapter 7, page 581 where §tres"iua' is the travel time residual which represents the difference between the earthquake observed travel time, t"bs and a predicted time, toalc ; btso"rce is the earthquake source component, §trec'ever represents the receiver component, both of which represent a signal that 3D mantle originates in the upper mantle and crust, while bts,s"al is the mantle propagation component reflecting the signal of interest to mantle tomography. Recent tomographic studies, which consider many more individual seismic phases, have added additional travel time components that have expanded this expression (e.g. Vasco and Johnson, 1988): earthquake mantle ^residual ^source ^propagation _j_ ^reciever g^ 410/«/w _j_ ^660 topo ^CMB topo ^^ICB topo ^aniso where boundary topography is explicitly included on the major mantle (the 410, and 660 km discontinuities), and core (core-mantle boundary, C M B ; inner-outer core boundary, ICB) discontinuities, together with a term for inner core anisotropy. Nevertheless, in this and the simpler 3 component expression given above, the receiver term (also termed a station correction) is the same and corrects for systematic effects that reflect local site (shallow sedimentary units, topography, local crustal geology) and instrument (short-period versus long period seismometers) affects together with systematic mis-picks of arrival times. Conventionally these are calculated by either averaging the set of travel time residuals at the particular station (e.g. Souriau and Woodhouse, 1985; Morelli and Dziewonski, 1991; Robertson and Woodhouse, 1995; Vasco et al., 1994; 1995; Vasco and Johnson, 1998) or fitting an azimuthal dependent term to the residuals (e.g. Dziewonski and Anderson, 1983). The relative sizes of the S and P station corrections have been used to infer the mantle properties below the station (Souriau and Woodhouse, 1985), specifically by Chapter 7, page 582 invoking Fermat's Principle it is argued that the ratio of the S to P station corrections (hCkmIbt^""" ) is related to {d\nVs/d\nVP\ via: TT e , station (dhiVs/dlnVP)p « 4 ^ ^ — . Souriau and Woodhouse (1985) summarize many of the earliest studies and note that many have determined relatively high ot?"0"/dtp1"10" values (« 3.0 - 4.5) that cannot easily be explained by only temperature perturbations effecting a dry mantle. This difficulty lead many researchers to invoke the presence of partial melt, which although satisfying the high ratio of station corrections, brought with it additional problems. For instance, such a mechanism may be a valid explanation for oceanic areas, but because high btsa'im'lbtPa'i0" values have also been inferred beneath the Canadian Shield (e.g. Wickens and Buchbinder, 1980), an area which is believed to be characterized by a relatively "cold" conductive geotherm which lies well below the mantle solidus. Consequently, invoking partial melt as a global mechanism responsible for high 8^'°"°" /btPa""" values below continents is difficult to accept. Romanowicz and Cara (1980) note that an alternative explanation for the anomalously high values is that they reflect the effect of erroneously combining station corrections from widely different tectonic regions. They suggest that i f the stations were separated correctly by tectonic province (e.g. active orogenic zones, Archean cratons, etc.) would give much lower btf"0" /btp0"0" ratios. Previous studies are listed in Table 7.2 together with the calculated value of the logarithmic ratio (d\nVs ld\nVP\ . The latter values are also plotted in figure 7.7. Inspection of this figure clearly reveals the very wide range of estimates for the upper mantle which ranges from as low as 0.99, a value in the Chapter 7, page 583 middle of the high temperature, but room pressure experimental values, to as high as 2.59, a value only slightly greater than that estimated by Dziewonski and Woodhouse (1987) for the lower mantle. Inspite of this wide range, note that the latest global estimate from station corrections (Robertson and Woodhouse, 1998) is in excellent agreement to the independent estimate for oceanic upper mantle (Woodward and Masters, 1991a). Robertson and Woodhouse (1998) originally accounted for both azimuthal variations (Cleary and Hales, 1966; Dziewonski and Anderson, 1983) and take in angle (Zhou and Wang, 1994) at the ISC stations after correcting for elevation and crustal structure (Mooney et al., 1997). However, numerical experiments revealed that the dip dependent terms trade off with the static and azimuthal terms, and hence, this factor was dropped from the final calculation of station corrections. Robertson and Woodhouse (1998) admit there is also a trade off between the signal absorbed into the station correction term and the residual mantle propagation term reflecting 3D mantle structure. From synthetic data generated by ray tracing through a whole mantle tomographic model they concluded from numerical experiments that their parameterization had sensitivity evenly distributed throughout the upper mantle and transition zone down to the top of the lower mantle (hence, our choice in plotting the station correction estimates of (d lnVs J8 lnVp ) p in figure 7.7. across the upper mantle and transition zone). Chapter 7, page 584 Table 7.2. Summary of upper mantle estimates (d]nVs /8\nVp)p derived from station corrections with an adopted upper mantle and transition zone mean ratio (VS/VP ) = 0.5472 calculated from the akl35 seismic reference model (Kennett et al., 1995). Reference Region Data g ^ station j g ^ station ( d l n ^ / d l n F ^ p Doyle & Hales, 1967 USA Direct readings 3.72 ±0.43 2.03 ± 0.24 Hales & Roberts, 1970 USA Direct readings 4.24 2.32 Jeffreys & Singh, 1973 Honshu Direct readings 2.3-2.8 1.26-1.53 North America 3.7 2.02 Europe 3.0-4.6 1.64 -2.52 Romanowicz & Cara, 1980 USA ISC 4.75 + 1.0 2.59 ±0.55 Western US 2.54 ±0.8 1.39 ±0.44 Central US 2.33 ± 1.1 1.27 ±0.60 Wickens & Buchbinder, 1980 Canada Direct readings 3.76 ±0.46 2.05 ± 0.25 Poupinet, 1977 Global ISC 1.81 0.99 Wickens & Buchbinder, 1980 Global ISC 2.40 ±0.11 1.31± 0.06 Souriau & Woodhouse, 1985 Global ISCP (Dziewonski and Anderson, 1983 ISCS (Dziewonski, personal communication 2.53 + 0.21 68% confidence limit 1.38 ± 0.11 Global (Preferred) ISCP ^-synthetic 3.69 ±0.13 2.02 ±0.07 Robertson & Woodhouse, 1995;1996 Global ISC 3.50 1.91 Robertson & Woodhouse, 1998 Global ISC 2.85 ±0.19 1.56 ±0.10 They note that conceivably, it would be possible to over-parameterize the station corrections in such a way as to leave little residual signal to be explained by volumetric mantle structure, and consequently, there exists a subjective choice on how much of the total travel time residual they attempt to explain via a station correction. They elect to follow a procedure similar to Dziewonski and Anderson (1983) which results in minimal station corrections. Note that because their joint tomographic models (Robertson and Woodhouse, 1995) are Chapter 7, page 585 only lower mantle models, the loss of upper mantle velocity heterogeneity into the station correction term was deemed acceptable. In contrast, Bolton (1996) elected not to use any station correction terms in constructing joint, long period, whole mantle S and P-wave tomographic models. Because he included many different seismic phases with excellent upper mantle sensitivity (free-oscillations, Rayleigh and Love surface waves, PP-P and SS-S differential travel times) in his models, there existed the problem of incorrectly assigning upper mantle heterogeneity into station correction terms. To ensure that this did not occur he made only crustal corrections using the global CRUST 5.1 model (Mooney et al., 1997)). As mentioned above, Romanowicz and Cara (1980) pointed out that lumping all station corrections together when estimating a global value for htga"°" /btp""0" was less than ideal because baseline shifts due to systematic differences between tectonic regions might be the cause of the anomalously high values that have been reported. With this in mind, Robertson and Woodhouse (1998) split their station corrections into subsets comprising active orogenic zones, shields, and Paleozoic continents and solved for both the dts"""""/dtp"""" ratio and possible baseline shifts. The resulting correlation between the S-and P-wave station corrections is high (0.83) with a global mean 5^""'""/dtp"1'"" = 2.85 ± 0.19. While the individual tectonic regions show some variability, the distributions overlap at 1 sigma level, and hence, Robertson and Woodhouse (1998) argue that the global mean is representative of the upper mantle value (active tectonic regions dtga"°" /bt']!"""" =2.62 + 0.32; shields St«a,hn/8tpia'lon = 3.14 ±0.60; Paleozoic continents ht™h" = 2.58 ±0.16). Chapter 7, page 586 With regards to the global mean advocated by Robertson and Woodhouse (1998), it is interesting to note that although Souriau and Woodhouse (1985) recommended a relatively high value of (d \nVs /d \nVP )p = 2.02 ± 0.07, based on comparing predicted S-wave station corrections to a set of measured P-wave station corrections (Dziewonski and Anderson, 1983), when they substituted an unpublished set of S-wave station corrections of Dziewonski's for their predicted S-wave corrections, the resulting ratio was substantially less ((dlnVjdlnVpX = 1.38 ± 0.11) and is within error of the recent ISC S- to P-wave based estimate of Robertson and Woodhouse (1998). As noted by Souriau and Woodhouse (1985), their predicted S-wave station corrections depend upon the validity of the upper mantle tomographic model M84C (Woodhouse and Dziewonski, 1984), and on the attenuation correction (PREM Q) made to this long-period S-wave tomographic model to shift it to correspond to the shorter-period (1 second) ISC P-wave measurements. Thus, the 1 discrepancy between the preferred value of Souriau and Woodhouse (1985) and those derived by Robertson and Woodhouse (1998) and Woodward and Masters (1991a) may indicate that M84C and/or the attenuation correction (PREM) is in error. In terms of upper mantle 3D velocity structure, the adopted crustal correction is of paramount importance. Although the data used in seismic tomography typically does not have the ability to accurately model the affects of continental crust, the observed travel times are very sensitive to the crustal signature (distribution, topography, thickness, velocity and density structure). Mooney et al. (1997) compiled a global distribution of refraction seismic data to derive a new global model of oceanic and continental crust together with associated Vp, Vg and density estimates for the various crustal, sedimentary and ice layers. Because Chapter 7, page 587 most mantle tomography studies utilize "crustal corrections" to remove the crustal signal in the data sets, and that this correction can have a significant effect on the residual velocity amplitudes for the upper mantle, an accurate crustal correction is critical in resolving mantle velocity structure. For example, Ritzwoller and Lavely (1995) find that half of the amplitude difference between the Harvard upper mantle tomographic model M84C and Scripps tomographic model SH.10c.17, is solely due to the different crustal corrections used by the two groups. When Mooney et al. (1997) used their crustal model to make "crustal corrections" at 85 global digital broadband stations, they found that CRUST 5.1 significantly decreased the scatter between the mean S- and P- station travel time residuals (where the mean reflects a minimum of 100 measurements of both S and P arrival times). The global correlation results in a ratio of 5^""""' /8tP""i0" « 3.0, which corresponds to a global "crust-free" upper mantle value of (d \nVs /8 lnVF ) p = 1.64. This value is slightly higher than, but still within error, of the preferred global value (1.56 ± 0.10) of Robertson and Woodhouse (1998) and the oceanic value (1.55 ± 0.10) of (Woodward and Masters, 1991), but slightly less than the formers continental shield estimate (1.71 ±0.32). The difference between the Mooney et al. (1997) and the Woodward and Masters (1991a) estimates likely reflects "chemical" effects, since the Mooney et al. (1997) value implicitly includes a component reflecting passage through the thick (up to 350 km), chemically differentiated, continental lithospheric root (Jordan, 1975; Jordan etal., 1989). Of all of the upper mantle estimates illustrated in figure 7.7, the excellent agreement between the global, oceanic estimate (91nF s./91nF / J) p = 1.55 ± 0.10, based on comparing Chapter 7, page 588 digital long-period SS-S and PP-P differential travel times (Woodward and Masters, 1991a) and the continental estimate (d \nVsfd InV,, ) p = 1.56 ± 0.10 determined from comparing ISC short period S and P static station corrections (Robertson and Woodhouse, 1998) is encouraging (see figure 7.8). Both estimates result from comparing measured, joint Vs and Vp data sets that are of the same frequency and were processed identically by the respective authors. Inspite of the admitted tradeoff between the parameterization of the station correction and the residual upper mantle signal, the similarity between the two results implies that the particular choice of Robertson and Woodhouse (1998) has not resulted in mapping upper mantle signal into the station correction terms (note however, from table 1, that the station corrections used when they constructed their joint, lower mantle tomographic models (Robertson and Woodhouse, 1995; 1996) indicates that some upper mantle structure was incorrectly mapped into the station correction term). In terms of advocating a preferred upper mantle value, I adopt (d\nVs/d\nVP)p =. 1.55 ± 0.10 based on the oceanic observations of Woodward and Masters (1991a) (see figure 7.8). 7.6) (d \nVs/d \rvVp)p at the top of the Lower Mantle from the Caribbean anomaly Jordan and Lynn (1974) analyzed PcP-P and ScS-S differential travel times and absolute S-wave travel times recorded across North America from two deep South American earthquakes. The differential travel times outlined an unusually fast velocity anomaly located from « 600 to 1400 km depth in the lower mantle beneath the Caribbean region. To isolate the depth interval they produced scatter plots of the travel time residuals (with respect to the Chapter 7, page 589 Jeffreys and Bullen (1967) reference model) 6 ^ versus otScS-S> a n d o7 S c S versus otScss-While the 8tScS versus otSQss plot showed no correlation, a strong negative correlation was found between ots and otScss demonstrating that the velocity anomaly responsible for the anomalous travel time residuals exists along the path of the S phase and not along the raypath of the core reflected ScS phase. When they plotted the PcP-P travel time residual against the corresponding ScS-S travel time residuals, a clear linear trend was evident with the slope of the linear trend g iv ing (5 r & s _ s /otPcP_p) = 3.0. The average ratio S- to P-wave velocity, (Vs/Vp) is 0.565 (Jeffreys and Bullen, 1967; hereafter denoted JB) or 0.555 (akl35, Kennett et al., 1995) for the 660-1400 km depth interval. When these values are combined with the ratio of travel time residuals, they result via Fermat's Principle: {d\nVs/d\nVp\^^f^, * P ®tpcP-P in (d lnVs/d lnVp ) p = 1.695 (JB) or 1.668 (akl35). Subsequent independent seismological studies have verified the Caribbean anomaly and concluded that it represents subducting Farallon oceanic lithosphere (e.g. Vidale and Garcia-Gonzalez (1988), van der Hilst and Spakman (1989), van der Hilst and Engdahl (1991), Grand (1987; 1994); Grand et al. (1997)) Recently Bokelmann and Silver (1993), using South American earthquakes recorded on a temporary array in North America, re-evaluated the Caribbean anomaly using digital data collected from an array of broad-band (5 second) and short period (1 second) stations. After correcting for earthquake source and receiver contributions, via station corrections, they isolate S and P-wave variations for raypaths bottoming around 1200 k m depth (see figure 7.9(left)). This figure plots the maximum residual travel time anomaly as a function of Chapter 7, page 590 turning depth in the mantle, the depth at which the raypath "bottoms out" and begins its leg back up to the Earth's surface. They state that a tradeoff exists between the length of the anomalous zone associated with the Caribbean anomaly and magnitude of the velocity anomaly, but that the shallowest raypaths offer the best constraint, since they have the shortest raypath in the lower mantle. For these values, the corresponding logarithmic ratio, (d\nVs/d\nVP)p = 1.70 ±0.20, and increases slightly to 2.09 for the events at 2100 km depth (see figure 7.9(right)), although Bokelmann and Silver (1993) state that the associated error for these deeper signals is larger (however, the error estimate was not published, but Bokelmann (personal communication) believes it was roughly 1.5 times as large as the shallow estimate). These estimates are lower than previous inferences for the lower mantle (e.g. Dziewonski and Woodhouse, 1987; (d lnVs /d lnVP ) p = 2.0-2.5) that were based on comparing independent, 5*- and P-wave tomographic models which were constructed using different period seismic data. Thus, similar to what emerges from the previous review of the upper mantle, when self-consistent seismic data (self-consistent in that both shear and compression wave observations are recorded on the same seismometers and processed in the same way) is used to calculate (d \nVs /d \nVp ) p , the resulting value (e.g. Jordan and Lynn, 1974; Bokelmann and Silver, 1993) is less than that inferred using independent data sets. Thus, in moving deeper into the mantle, the results from the Caribbean anomaly indicate that increases going from the transition zone into the top of the lower mantle, but only modestly (1.55 ±0.10 to 1.70 ± 0.02). However, one caveat regarding this inference is that the Caribbean anomaly is a measure of the relative shear to compression wave velocity through a cold subducting slab of Chapter 7, page 591 oceanic lithosphere, and consequently, the derived (d \nVs /d lnVp )p values may not be applicable to the ambient convecting mantle if one believes that the gradational chemical layering in the upper 50 km or so of oceanic lithosphere, that reflects the residuum left after mid-ocean ridge decompression melting, has a profound affect on the subsequent mineralogy of the slab (e.g. Anderson, 1987b). Recent modeling studies which have coupled phase diagrams to the predicted temperature and pressure path of subducting lithosphere (Ita, 1992) find that the predicted mineralogy of the depleted residuum is significantly different than that advocated by Anderson (1987b), and consequently, does not have a dominant affect on the calculated density or velocity structure of slabs in the transition zone. Note that while Helffrich et al. (1989), Helffrich and Stein (1993) and Gubbins et al. (1994) have all invoked mineralogical effects in explaining at least a portion of their seismic observations from slabs, they are all invoking the effects of abrupt mineralogical changes between the thin oceanic crust on the subducting slab and the adjacent mantle. Therefore, while I acknowledge that the regional Caribbean anomaly may not be a good example of the "ambient" global lower mantle, it should be recognized that the principle argument in support of such a claim, that the mineralogical arguments that the slab mineralogy is grossly uncharacteristic of the ambient mantle, has been shown to be overstated (e.g. Ita, 1992). 7.7 Lower mantle (d lnVs/d InV,,)p from the ratio of ScS-S and PcP-P differential time residuals (§tPcP_P /§tScS_s) and the ratio of absolute S and P travel time residuals. As discussed above, the Caribbean anomaly indicates that the top of the lower mantle has a value of (d lnVs /d \nVP )p = 1.70 ± 0.2. However, in addition to concerns over whether Chapter 7, page 592 or not a signal due to rays traversing a subducting slab is relevant to the properties of the ambient mantle, there is also the concern that this estimate may be systematically biased due to some unforeseen regional effects. In the following sections I review "global" estimates that are based on information that sample far greater volumes of the Earth's lower mantle. One global estimate of lower mantle S-to-P velocity heterogeneity may be constrained by the ratio of PcP-P and ScS-S differential travel times (otPcP_p/otScS_s ) which record the relative difference in arrival time for body waves that reflect off the core-mantle boundary and direct body waves (see figure 7.10). The logarithmic ratio (d\nVs/dlnVP)p may be estimated via Fermat's principle: 8lnVs d\nVP Vs ZtScS_s V 8 r r P u 1 PcP -p where Vs and Vp represent the mean lower mantle shear and compression velocities, while otPcP_P and otScS_s are PcP-P and ScS-S differential travel times, respectively (the observed arrival time minus a predicted arrival time calculated by ray-tracing through a seismic reference model). Pulver and Masters (1990) undertook a preliminary study by comparing co-located, cap-averaged values of §tScS_s and otPcP_P and determined a lower mantle average value for (d lnVs /d lnVp ) p of 1.70. Based on Woodward and Masters (1991b), who studied an expanded data set of ScS-S differential and absolute S travel times and concluded that the ScS-S signal was reflecting velocity anomalies on the ScS leg, the Pulver and Masters (1990) value represents an average value over the bottom 800 km of the lower mantle. Chapter 7, page 593 Subsequently, Bolton and Masters (1996) have compared co-located, cap-averaged long-period absolute P and S travel time residuals (see Bolton (1996) for a full account) across the depth extent of the lower mantle. One advantage of using absolute travel times is that measurements may be made over a wider epicentral distance (25°-150°) than differential estimates (see figure 2-4 in Bolton, 1996). They used digital recordings with a dominant period of « 20 seconds (recall that ISC arrival times are for phases with a much shorter period of 1 to 4 seconds) and developed interactive algorithms to calculate and fit a synthetic waveform to the observed waveform (but they concentrate only on matching the first swing of the waveform representing only the direct P- and S- arrivals). This procedure, fully described in Bolton (1996), has been applied to digital data from 1976 through 1992 and has resulted in 34,962 S and 38,114 P absolute travel times at teleseismic distances (>25° epicentral distance). After removal of outliers and the de-trending the total data set of residuals (to remove the systematic affects of adopting a constant attenuation operator in the construction of the original synthetic waveforms), the de-trended data were plotted on the Earth's surface in 5° spherical caps for 4 depth slices through the lower mantle (see figure 7.11). Systematic trends were very clear and to further analyze the data in each depth interval they plotted the co-located, cap-averaged S- and P- residuals against one another, and by least squares, fit a line through the scatter plots, which are re-plotted here (see figure 7.12). The slope of the line gives the global average value for (§ts/5tP ) for that depth interval in the lower mantle which may be translated into (d lnVs /d lnVp ) p via Fermat's Principle. The resulting (d lnVs /d \nVP ) p values are plotted as a function of depth in figure 7.13 where they are compared against other seismic estimates. Chapter 7, page 594 It is clear from inspection of figure 7.13 that (dlnVs/d\nV,,)p undergoes a progressive increase with depth across the lower mantle from a value of 1.70 at the top of the lower mantle to 3.40 directly above the core-mantle boundary. However, this increase may not be a robust feature. Bolton (1996) re-binned their lower most depth interval (2300-2890 km) into two separate depth intervals and noted that only the lowermost interval (2600-2890 km) exhibited a large value for (dlnVs /d\nVp)p ..He further noted for the 2300-2890 km depth interval that it is only a few anomalously positive S-wave residuals which are controlling the slope of the line, and these anomalous S-wave residuals are concentrated in two regions in the Pacific, with the most anomalous residuals being located just south of Hawaii (see figure 7.14). These particular S-wave residuals are anomalous in that while they exhibit large positive residuals in S, there is little or no complimentary positive P-wave residuals. Consequently, these residuals have the affect of rotating the line to a steeper slope. A steeper slope, in turn, corresponds to greater values for (d \nVs /d InV,, ) p . Bolton (1996) found that when the caps containing the anomalous S-wave residuals in the 2300-2890 km depth bin were removed from the data prior to least squares fitting of the line, the resultant slope was significantly shallower such that the value for (d \nVs /d lnVp ) p = 1.70, a value identical to that calculated at the top of the lower mantle (see figure 7.13). This raises the intriguing possibility that the progressive increase in {d\nVs/dlnVP)p with increasing depth over the whole of the lower mantle illustrated in figure 7.13 also reflects the presence of geographically restricted "anomalous" S-wave residuals. It is widely accepted, on the basis of numerous, independent lower mantle tomographic models, that two large-scale "superplumes" exist in the lower mantle, one Chapter 7, page 595 located southeast of Hawaii, the other located below South Africa (see for example Dziewonski and Woodhouse, 1989; Su et al., 1994; Woodward et al., 1993; Vasco et al., 1993; 1994; 1995; Robertson and Woodhouse, 1995; L i and Romanowicz, 1996; Vasco and Johnson, 1998;). These two superplumes extend from the core-mantle boundary up to roughly the base of the transition zone and both are characterized by slow shear wave anomalies. Unfortunately, Bolton (1996) did not try the same numerical experiments (in terms of isolating and excluding the Pacific superplume cap averages) within the two intermediate depth intervals (1100-1700 km and 1700-2300 km), and therefore, it is uncertain i f the relatively high values of 2.10 and 2.30 for (d lnVs/d lnVP ) p that he determined for these two depth intervals reflects truly global properties of the lower mantle, or instead, reflect a "smeared" signal skewed by anomalous, and geographically-restricted, travel time residuals from these two areas. To illustrate how little the slope of the line must be rotated to shift (d lnVs /d lnVr ) p away from 1.70, I have plotted hypothetical lines, all going through [(btr;xld"al , Stf'"" ) = (0, 0)] and which have a slope giving (d\nVs/d\nVP)p = 1.70 (see figure 7.15). A visual comparison between these red lines and the least-squares blue lines of Bolton (1996) demonstrate that the difference between the two lines in either the 1100-1700 km or 1700-2300 km depth interval is only very slight. Close inspection of these two intermediate depth bins also reveals that both bins do indeed possess some cap averages which exhibit anomalous shear wave behavior where the 8trsex'd""' > 7-8 seconds but the corresponding §tpS'dual « 0-2 seconds, values which are characteristic of the anomalous ones that Bolton (1996) recognized were skewing the results in the deepest depth bin. Unfortunately, it is not possible to determine the geographic location for these particular Chapter 7, page 596 cap-averages from Bolton (1996; although he plotted his calculated residuals, he chose not to tabulate the data). Fortuitously, Bolton (1996) also constructed joint S- and P-wave whole mantle tomographic models which provide an independent estimate of (dlnVs/d\nVr)p by comparing the rms velocity amplitudes of the two models. This technique, and studies which utilize it, are discussed in next. 7.8 Ratio of RMS velocity amplitudes of S and P-wave tomographic models As mentioned in the introduction, one of the earliest estimates of the relative magnitude of Vs to Vp anomalies for the lower mantle was made by Dziewonski and Woodhouse (1987) who calculated the ratio of the depth dependent root-mean-square (rms) amplitudes of their Vs seismic model SHU84L85 (Woodhouse and Dziewonski, 1987), a model based on modeled waveforms of horizontally polarized shear body waves (denoted SH), to the rms amplitude of the lower mantle Vp model V3 (Morelli and Dziewonski, 1987b), a model based on ISC P-wave traveltime residuals. The ratio of the seismic anomalies is determined via: rms [SHU84L85] r , - 2 . 0 rms[V3J d\nVP where the rms amplitude of the seismic model as a function of radius, r is defined as (Ritzwoller and Lavely, 1995): rmsir) = — L - /J]m(r,BA) m0(r) V J Chapter 7, page 597 where the volumetric tomographic model m{r, 9, O) is defined in terms of radius r, colatitude 6, and longitude O, and the amplitude of the tomographic model is normalized relative to the P R E M radial velocity profile m0(r). Dziewonski and Woodhouse (1987) noted that their estimate of (d \nVs/d \nVp ) p was greater than that calculated from high temperature but room pressure experimental studies on a small number of compounds relevant to geophysics (Anderson et al., 1968; see figure 7.1) but did not attempt to explain the discrepancy between experimental and seismic values. However, before too much is read into this discrepancy it should be stressed that later workers have emphasized that estimates of (dlnVs/8lnVP)p derived from the ratio of rms velocity amplitudes of two independent tomographic models is not a robust estimate: in general, both of the independent tomographic models have imperfect and different resolution within the lower mantle, such that either model may under, or over-represents the true amplitude of the velocity heterogeneities. For example, Shearer (1993) notes that the velocity amplitudes of the Harvard group's shear wave tomographic model SH8WM13 (Woodward et al., 1993) is about twice the amplitude of the S-wave tomographic model SH.10c.17 (Masters et al., 1992) constructed by the Scripps group. While the differences between subsequent S-wave tomographic models constructed by the two groups has decreased substantially (see Flanagan and Shearer (1998)) this variance, just between two S-wave models, illustrates the potential problems when determining a ratio that depends upon the velocity amplitudes from independent P- and S-wave tomographic models. Furthermore, the data used in constructing independent P- and S-wave models are, in general, of different frequency (the P-wave model V3 is based on traveltime anomalies of waves with a Chapter 7, page 598 characteristic period of 1 second whereas the S-wave model SHU84L85 involves S-waves with a characteristic period of 60 seconds), there exists the possibility that the velocity heterogeneity recovered in the two models is frequency dependent, which may lead to a systematic bias in the estimate of(31nF v/91nF / )) p . In addition, the S- and P-wave data sets are often parameterized differently (e.g. smoothing) during processing such that the resultant S- and P-wave tomographic models may not be directly comparable, at least not to the level required to calculate an accurate estimate of (d lnF 5 /3 lnF,, ) p . Examples of radial profiles of rms relative velocity perturbation for some P-wave and S-wave models are shown in figures 7.16 and 7.17, respectively. Due to the parameterization of the various tomographic models plotted in these figures, some of the profiles only extend across the lower mantle (e.g. P-wave models V3 and JLM4P6), while others encompass the entire mantle (e.g. P- and S-wave models WE1997, P16B30 and S16B30). In general, all of these curves exhibit some common features; the amplitude of each of the models is greatest at the surface and declines with increasing depth to reach a minimum at about 1200-1500 km depth and then gradually increases to peak again in the D" layer at core-mantle boundary. Of note is that the addition of seismic phases that are sensitive to the deepest part of the lower mantle (e.g. ScS-S and SKS-S differential travel times) appear to increase the rms amplitude in the lower mantle, especially approaching the D" layer (compare the S-wave models SH12WM13 (Su et al., 1994) to SKS12WM13 (Liu, et al., 1994)). This implies that for those models that are largely based on a single velocity type or datum (e.g. ISC arrival times used to construct JLM4P6 and JLM4S6; Robertson and Woodhouse, 1995), the resultant rms velocity profile may not be robust near the perimeter of the raypath coverage. Chapter 7, page 599 The curves in figures 7.16 and 7.17 are shown to emphasize the variation in rms velocity that exists between the various tomographic models that have been published to date, and to illustrate the large change in rms amplitude when additional data sets of seismic phases are combined with previous models. For example, compare models SH12WM13 and SKS12WM13 across the lower mantle. Both models are from the Harvard University tomography group with SKS12 being an updated version of the SH12WM13 model but with the addition of SKS-S differential travel times (BtSKS-S) t 0 m e total database used in constructing the model. Likewise, compare the models SAW12D and SAW12 TD. Again, both models come from the same group (in this case the Berkley Seismology Lab) and differ in that SAW12 TD also has added data sets of SS-S and ScS-S differential travel times (otScS-S a n d &tsS-S) t 0 m e original data sets used in constructing SAW 12D. In both cases where data sets that are sensitive to the lower most mantle (otScS-S a n d ^SKS-S) have D e e n added, the newer models (SKS12WM13 and SAW12TD) undergo an increase in rms velocity amplitude in the lower mantle compared with their starting models). Casual inspection of these curves reveals that arbitrary combinations of the various independent S-and P-wave rms velocity profiles would result in significantly different values for(d\nVs/d]nVp)? which are unlikely to reflect the true relative ratio of velocities within the Earth's mantle. These concerns over the use of rms velocity ratios derived from independent tomographic models to estimate (d \nVs/d\nV,,)p have been highlighted in a recent review of tomographic models (Ritzwoller and Lavely, 1995). They use several recent global tomographic S-wave models (SH12WM13 (Su et al., 1994), SH.10c.17 (Masters et al., Chapter 7, page 600 1992), and M D L S H (Tanimoto, 1990)) to calculate (d\nVs/dlnVP)p from the models rms velocity amplitudes. In each case, the adopted P-wave model was L02.56 (Dziewonski, 1984; which is an earlier version of the P-wave model V3 discussed earlier). Ritzwoller and Lavely (1995) concluded from their comparisons that the rms-ratio technique was of dubious merit, at least for the global models they utilized, because of the physically unrealistic value of the ratio ((d\nVs/d\nVp)p >4.0) (see figure 7.18) and because the high variance exhibited between the (d \nVs /d lnVP )p profiles for the different shear wave models. They found that these seismic models predict abnormally high values of (SlnP^/dlnF,,),, when only the even-degree 2 terms of the spherical harmonic expansion of the lateral velocity perturbations is used (range of 5.00-7.10); values as large as this are physically implausible (see figure 7.19). Therefore, these results emphasize caution in accepting the early estimate of 2.0-2.5 of Dziewonski and Woodhouse (1987), since this value is based on comparing two independent, and first-generation, tomographic models. Nevertheless, one way of circumventing many of the problems noted above concerning the rms technique for calculating (<3 lnVs /d \nVP ) p is to compare joint P-and S-wave tomographic models. As noted by Ritzwoller and Lavely (1995), the ratio (d\nVs/dlnVp)p should only be interpreted when the spatial correlation between the S- and P-wave models is high and this is best achieved when both S- and P-wave tomographic models are derived using common data sources and a common parameterization. For example, Robertson and Woodhouse (1995, 1996a) have derived joint, lower mantle S- and P-wave models from the same short-period ISC data set (the P-wave arrivals have a dominant period of «1 second while the S-wave Chapter 7, page 601 arrivals have a dominant period of « 4 seconds) and found that their S- and P-wave models are highly correlated spatially in the upper part of the lower mantle (« 0.7) with a general decrease in correlation down to the D" layer 0.4) (see figure 7.20). Because the S-wave arrival times in the ISC data set are likely to be contaminated by miss-identified SKS and ScS arrivals at depths greater than 2000 km and because the number of direct S-waves bottoming below 2000 km rapidly drops off with increasing depth (see figure 7.21), Robertson and Woodhouse (1995, 1996a) state that their radial profile of (d\nVs/d\nV,,)p is only valid across a depth interval from 660 km to « 2000 km in the lower mantle. However, Vasco et al., (1994), who use the same ISC data set to construct whole mantle joint models, note that the resolution of their S-wave model begins to degrade in the depth interval 1270-1470 km, which is also plotted in figures 7.21 and 7.22. Vasco et al. (1994) parameterize their models in terms of shells of varying thickness (on average 200 km thick) from the surface to the core-mantle boundary which contrasts with that utilized by Robertson and Woodhouse (1995), who use Legendre polynomials in terms of depth (expanded to degree 4)). In contrast, Masters et al. (1996) adopt natural cubic splines to parameterize their latest whole mantle S-wave model (S16B30) in terms of radius. They note that both Legendre or Chebyshev polynomials, the functions commonly used to parameterize tomographic models as a function of radius (e.g. Su et al., 1992; 1994; Woodward et al., 1993, Robertson and Woodhouse, 1995) have the undesirable attribute that they are capable of mapping structure located at one radius to adjacent depth intervals. In figure 7.22 I plot the Robertson and Woodhouse (1995) radial profile of (d lnK. /d lnVP ) p calculated from the ratio of rms velocity amplitudes from their joint Chapter 7, page 602 models. This profile is approximately constant at « 1.70 across the depth interval 660 to 1300 km whereupon it undergoes a rapid rise to a peak at a value of « 3.2 at 1900 km after which it drops back to a value of « 1.0 at the core-mantle boundary. Of interest is that the depth at which the (d lnVs /8 lnVp ) p profile abruptly begins to rise coincides with the depth interval across which Vasco et al. (1994) note their S-wave model begins to lose resolution relative to their joint P-wave model. Thus, inspite of the claims by Robertson and Woodhouse (1995, 1996a) that their (d lnVs /d \nVP ) p profile is robust to « 2000 km depth, there exists the strong probability that below « 1350 km their S-model (and thus, (d lnVs Id \nVp ) p ) are suspect. In a subsequent study, Robertson and Woodhouse (1996a) stated that calculating a radial (d lnVs fd lnVP ) p profile via rms velocity amplitudes, even when using their joint tomographic models, is less than ideal because the amplitudes in the two models depend to some degree upon the damping used in the inversion algorithm, which reflects the data coverage of the mantle. Because the data coverage is different for the P- and S-wave models (there is approximately three times as many P- than S-wave summary rays that forms the original data set used in constructing their joint tomographic models), the damping is different, and hence, the (d lnVs /d \nVP ) p ratio may be systematically biased. To determine if this was indeed the case, they filtered their ISC data such that only arrival times where both P- and S-times are recorded on the same seismograms were used in the inversion for joint models. This particular data set, although smaller than the full data base, samples the mantle virtually identically and consequently, the resultant radial profile of {d \nVs Jd \nVp ) p should be free from the affects of different degrees of damping (this profile Chapter 7, page 603 is also plotted in figure 7.22). The "filtered" profile is very similar to the profile using the complete data set and demonstrates that, contrary to their concerns, damping effects are not significant in their joint inversion for S and P tomographic models. Nevertheless, Robertson and Woodhouse (1996a) argue that a better method for estimating a (d lnVs /d lnVp ) p profile is to explicitly assume 100% proportionality between the S- and P-wave models and simultaneously invert both S and P travel time residuals simultaneously for a single Vp tomographic model and radial profile (dlnVs/dlnVp)p(r) which controls the relative amplitude of a corresponding "scaled- V$" tomographic model, where the later is simply the P-wave model multiplied by the (dlnVs/d\nVp)p(r) profile. The (d]nVs/dhiVp)p profile is then iteratively adjusted to improve the fit of the Vp and "scaled Fg" tomographic models to the combined data set. In this approach, both the scaled Vg and Vp tomographic models are damped identically in the inversion, albeit at the expense of assuming that there exists 100% proportionality between S- and P-wave velocity anomalies. Because the spatial correlation profile between the, S-and P-wave anomalies demonstrates unambiguously that 100% proportionality for the Robertson and Woodhouse (1995) joint S- and P-wave tomographic models is never achieved (see figure 7.20), it is not clear that this particular approach in estimating a (d lnVs /8 lnVp ) p profile is to be preferred over the simple rms ratio approach. Indeed, none of the whole mantle, joint S- and P-wave tomographic models (see WE1997 and S16B30/P16B30 in figure 7.24), which are based on march larger data sets than utilized by Robertson and Woodhouse (1995), possess 100% spatial correlation. Qualitatively, since the correlation coefficient between the joint S- and P-wave models decreases with increasing depth across the lower mantle, the assumption of Chapter 7, page 604 100% proportionality will force the derived (d \nVs/d]nVp)p profile to progressively deviate away from the "true" profile with increasing depth to accommodate the ever greater proportion of S- and P-wave velocity anomalies which are not spatially correlated. With these concerns in mind, in figure 7.23 I show their results for two (d lnVs Id lnVF ) p depth profiles where the logarithmic ratio has been parameterized radially in terms of Legendre polynomials using either 2 (j = 0, 1) or 4 (j = 0, 1, 2, 3) terms in the expansion (Robertson and Woodhouse, 1996a). The criteria they used to discriminate between particular profiles, which are expanded to ever-greater number of terms, is the variance reduction of the S data (the greater the variance reduction, the better the "scaled-S"-wave tomographic model in fitting the data). While they note that including more terms results in greater variance reduction, Robertson and Woodhouse (1996a) settle on the profile with only two terms as their preferred choice because going to either 3 of 4 terms did not result in significant improvements in the variance reduction (as compared to the improvement in variance reduction going from one to two terms). Indeed, the 4 term (d lnVs Id XnVp ) p profile, while plotted in their pre-print, was left out of the final published paper. However, a comparison of the (d lnVs /d lnVP ) p profile derived from the ratio of rms velocity amplitudes (for either the full or the "filtered" data sets) and the two profiles derived from explicitly assuming 100% proportionality in a common inversion reveals that agreement exists only between the 4-term radial profile and the rms derived profiles. Because Robertson and Woodhouse (1996a) demonstrate that damping during the inversion for two joint S- and P-wave tomographic models is not a significant effect, then their rms Chapter 7, page 605 ratio-based profiles are, in fact, a relatively robust estimate (at least to « 1350 km depth). Therefore, the observation that the 2-term profile differs significantly from the 4-term profile, and furthermore, does not agree with either of the rms ratio derived profiles (except at the very top of the lower mantle), strongly suggests that the 4-term radial expansion of (d lnVs Jd \viVp ) p is to be preferred over that advocated by Robertson and Woodhouse (1996a). The uncertainty expressed above for the derived (d lnVs jd InJ7,, ) p profile of Robertson and Woodhouse (1995, 1996a) also stems, in part, from their choice to construct joint tomographic models that cover only the lower mantle. Vasco et al., (1994; 1995) also use short period ISC data to construct joint S- and P-wave tomographic models but they parameterize their models across the whole mantle. These latter two studies are part of a sequence of papers elucidating first the P-wave 3D velocity structure of the mantle (Pulliam and Johnson, 1992; Pulliam and Stark, 1994; Pulliam et al., 1993; Vasco et al., 1993) followed by studies providing joint 3D S- and P-wave velocity structure (Vasco et al., 1994; 1995; Vasco and Johnson, 1998). The Vasco et al., (1994) study was similar to Robertson and Woodhouse (1995, 1996a) in that only first arrivals of P and S-waves from the ISC data base were utilized, albeit to study the whole mantle. Vasco et al. (1995) expanded the number and types of seismic phases by incorporating data sets of P P and SS arrival times together with data sets of SS-S4]oS, and SS-SfifioS differential travel times of Shearer (1993) into their previous joint S- and P-wave study. The addition of P P and SS arrival times significantly increases the global upper mantle coverage (relative to that when only S and P arrival times are utilized) while the addition of the 410 and 660 precursor differential travel Chapter 7, page 606 times reduces the known trade off between variations in internal mantle boundary topography and adjacent volumetric velocity variations. Thus, Vasco et al. (1995) invert for both velocity and boundary variations in an attempt to reduce artifacts due to aliasing un-modeled boundary topography into the joint S and P tomographic models. Recently, Vasco and Johnson (1998) have extended their S- and P-wave tomographic models even further by incorporating ISC arrival times for 10 compression and shear phases (P, PP, PcP, PKPa0, PKPbc, PKPdf, S, SS, ScS, SKSac) together with the SS-S4 JOS, and SS-SfifinS differential travel times (Shearer, 1993) to derive joint whole Earth (i.e. mantle and core) 5*- and P-wave tomographic models (see profiles labeled WEI 997 in figures 7.16 and 7.17 for the rms velocity profiles). With the addition of these seismic phases, Vasco and Johnson (1998) have significantly better ray coverage across the lowermost mantle than Robertson and Woodhouse (1995) and hence, their models do not suffer from the drop off in resolution with increasing depth in the lower mantle. There are additional concerns about the joint lower mantle tomographic models presented by Robertson and Woodhouse (1995) that go beyond simply a difference in the number of seismic phases. First, as remarked upon earlier, the S- and P-wave models of Robertson and Woodhouse (1995, 1996a) only extend across the lower mantle, and consequently, upper mantle velocity structure, which is accounted for by station corrections and earthquake source terms, may leaks into the upper 200-300 km of their lower mantle models i f either of the two terms are poorly parameterized. Robertson and Woodhouse (1995) acknowledge that some leakage has in fact occurred because their rms velocity profiles at the top of the lower mantle begin to increase away from the lower mantle trend. They note this feature is characteristic of leakage of the upper mantle signal into the top of Chapter 7, page 607 the lower mantle models (compare the smooth whole mantle profiles of WE1997 or S16B30 at 660 km depth in figure 7.16 and 7.17 to the lower mantle rms velocity profiles of JLM4P6). Second, there are problems with the joint tomographic models that reflect the procedures adopted by Robertson and Woodhouse (1995) in processing the ISC data. Van der Hilst and Spakman (1989), van der Hilst et al. (1991), van der Hilst and Engdahl (1992), and van der Hilst et al. (1993) have emphasized both the importance of the adopted seismic reference Earth model, and the requirement to accurately re-locate the reported ISC hypocenters prior to inversion in the construction of tomographic models based on ISC data. As noted in these studies, the inversion of ISC P-wave travel times is a nonlinear inversion problem that is usually "linearized" by applying Fermat's Principle (which states that the arrival time is insensitive to perturbations of the ray path about the true ray path in the Earth), about trial earthquake locations and a reference seismic model. Hence, the use of a poorly constructed reference seismic model, such as the Jeffreys-Bullen or P R E M model, introduces systematic bias into the tomographic inversion. At the ISC, the earthquake source locations are determined relative to the Jeffreys-Bullen model, which is a smooth radial velocity model lacking any mantle discontinuities (e.g. 410, 520, 660, or 730 km), van der Hilst and Engdahl (1991) showed that the variance reduction of P-wave data (with associated earthquake relocation) calculated with the iasp91 reference velocity model (Kennett and Engdahl, 1991) was about 17% less than the variance of ISC P-wave data calculated using the Jeffreys-Bullen velocity model. They note that this variance reduction is of the same order of magnitude that is found in the variance reduction in tomographic inversions of ISC P-wave residuals. In contrast, Robertson and Woodhouse (1995) elected to use the P R E M Chapter 7, page 608 model, which although an improvement over the Jeffreys-Bullen model, is known to give inadequate predicted travel times when compared to either iasp91 or aki35(Kennett et al., 1995). In constructing P R E M , Dziewonski and Anderson (1981) used 1,500,000 P-wave arrival times from the ISC to construct a P-wave travel time curve which, together with free-oscillation and other types of data, was used to derive the velocity and density profiles. However, the ISC earthquakes were not relocated prior to using the arrival times and consequently, the data set of arrival times will carry over some imprint of the Jeffreys-Bullen model into P R E M (Dziewonski and Anderson, 1983; p. 3295). Thus, the use of P R E M as a reference model when better models, such as iasp91, are available is not a prudent choice. In addition, van der Hilst et al. (1991) and van der Hilts and Engdahl (1992) have demonstrated the importance of incorporating the surface-reflected pP phase in the earthquake relocation procedure during tomographic inversion. The original earthquake hypocenters as calculated by the ISC, are based solely on P-wave travel times (van der Hilst and Engdahl, 1992) and consequently are known to contain a depth error by up to 30 km. The addition of the pP phase in the relocation procedure gives better constraints on the focal depth since the regional bounce points associated with this phase, located in the immediate area above the earthquake hypocenter, act, in effect, like local receivers. Thus, by using both P and pP seismic phases to relocate earthquakes prior to the inversion, the uncertainty in hypocenter location is minimized, and consequently, the trade-off between source relocation and the amplitude of the inferred velocity anomalies in the tomographic model is significantly reduced. Van der Hilst et al., (1993) note that by following a two step procedure of first relocating all the earthquakes using P and pP seismic phases within the iasp91 reference model, and then inverting the resulting travel time residuals for 3D mantle Chapter 7, page 609 structure, the resulting contrasts in velocity in the tomographic model was increased relative to that reported previously. Recently, Engdahl et al. (1997) have used akl35 together with arrival times for regional and teleseismic P-phases, regional S-phases, depth phases (pP, pwP, and the converted phase sP ( the latter are phases which are initially upgoing phases that reflect/convert off the underside of the Earth's surface) and the PKPrff branch to relocate all teleseismically well-constrained ISC earthquakes that occurred in the period 1964-1995. This relocation of events means that depth errors in the original ISC catalogue and the mapping of earthquake source region heterogeneity into mislocation are minimized. The result of this procedure is a new global data set of uncontaminated P (and pP, and pwP) and S arrival time residuals for use in tomographic models (e.g. Widiyantoro and van der Hilst, 1997; Kennett et al., 1997). While this particular data set is obviously unavailable to Robertson and Woodhouse (1995), the arguments used in justifying such steps when constructing tomographic models had been published (e.g. van der Hilst and Engdahl, 1991; 1992). Robertson and Woodhouse (1995) also relocated the ISC data for new source locations, but, as noted above, used the reference velocity model P R E M rather than iasp91, and significantly, did not use any regional seismic phase, such as pP in the earthquake relocation step. Indeed, they admit that because they did not utilize any information below teleseismic distances (<28°), they actually obtain a less accurate earthquake location than listed in the original ISC data base (where traveltimes from epicentral distances less than 28° are used during source location). Therefore there exists the strong possibility that the hypocenter location is less than optimal in the Robertson and Woodhouse (1995) study with the result that some component of the signal due to the 3D velocity structure of the mantle Chapter 7, page 610 has been lost in earthquake mislocation and unavailable to constrain the velocity structure inferred in the joint P and S lower mantle tomographic models. In contrast, it is interesting to note that Pulliam et al. (1993) and Vasco et al. (1993) used the Jeffreys-Bullen P-wave reference model, but in extending their models to joint S-and P-wave models Vasco et al. (1994; 1995) elected to relocate the ISC data relative to the iasp91 reference velocity model, while Vasco and Johnson (1998) relocate the ISC data relative to the akl35 model. In their first joint S- and P-wave tomographic model Vasco et al. (1994) noted that while the spatial pattern of S- and P-wave anomalies in their models is robust, the absolute magnitude of the velocity amplitudes was poorly constrained because of the smoothing constraints in the inversion. They adopt a philosophy that both large velocity anomalies which occur in poorly constrained areas of the mantle (i.e. have only a few crossing rays), and rough velocity models should be penalized. The latter idea reflects the fact that tomographic models are large-scale averages of the Earth's internal velocity heterogeneity and consequently, small scale structure is not expected to be recovered. Thus, "rough" models with abrupt spatial variations in heterogeneity are likely to be an artifact and hence, a "smoothing" constraint is introduced to deal with this effect. Consequently, while the rms amplitudes for the S- and P-wave models is roughly equal in the Vasco et al. (1994) study implying [ (d \nVs /d lnVp ) p = 1.0], they stress that this is largely due to the constraints adopted during the inversion procedure, and not necessarily, a real feature of the Earth. In their most recent study, the relative damping of S- and P-wave anomalies was identical and resulted in shear wave heterogeneity which systematically exceeded the P-wave heterogeneity. The correlation coefficient between the S- and P-wave models is shown Chapter 7, page 611 in figure 7.24 while the radial profiles of rms velocity amplitudes are plotted in figure 7.25. The correlation coefficient is moderate at shallow mantle depths (0.5) and decreases with increasing depth in the lower mantle following the general trend exhibited by other joint tomographic models. Because both the Robertson and Woodhouse (1995) and Vasco and Johnson (1998) used ISC data, albeit the latter used many more types of phases, it is not clear why there should be such a large difference in the degree of correlation found between the S- and P-wave models. Also shown in figure 7.24 is the correlation between S16B30 and P16B30, joint whole mantle, long-period joint S- and P-wave models (Bolton, 1996). S16B30 (Masters et al., 1996; see figure 7.25) and P16B30 (Bolton, 1996; see figure 7.26) are constructed using a large data base (30,000 each) of digital, long-period (20-30 seconds) absolute S and P-wave travel time residuals, 5000 PP-P, 10,000 SS-S (extended sets from Woodward and Masters, 1991a), and 5000 each of ScS-S and PcP-P (extended sets from Woodward and Masters, 1991b) long period differential travel time residuals, 2034 spheroidal normal mode structure coefficients (Smith and Masters, 1989; Ritzwoller et al., 1986, 1988) and 10,000 Rayleigh and Love wave phase and amplitude velocity measurements of various periods between 70 and 250 seconds (Laske and Masters, 1996). The later two data sets have their greatest sensitivity in the upper 1000 km of the mantle, and hence substantially aid in constraining the amplitude and geographic position of the velocity structure in the upper mantle and transition zone (in constructing the joint tomographic models, Bolton (1996) adopted (d ln^ /51nJ^) p = 1.70 and (dlnp/dlnVj,)p = 0.68 to use the structure coefficients and Rayleigh wave data in the inversion algorithm for the P-wave tomographic model). The Chapter 7, page 612 addition of the surface wave and free-oscillation data to the long-period absolute and differential travel times, results in S- and P-wave models that are highly correlated at the surface followed by a decrease with increasing depth. Nevertheless, the correlation is highly significant and exceeds the 95% significance level throughout the mantle (see figure 7.24). In figure 7.27 the rms velocity amplitudes for the Vasco and Johnson (1998) and Bolton (1996) whole earth, joint S- and P-wave models are plotted, and it is immediately clear from this figure that the ISC based models have systematically lower rms amplitudes, although the relative difference between the S- and P-wave models is still recovered. One feature found in S16B30 that is not seen in WEI997 is the large increase in rms velocity amplitude directly above the core-mantle boundary. This increase may be an artifact that reflects poor resolution in the basal most part of the lower mantle in S16B30/P16B30 compared to WEI997, since the latter model utilized a large number of core phases and also allowed topography on the core-mantle boundary. Both features would give the WE 1997 models better resolution directly above the C M B than in Bolton's (1996) joint models. The ratio of rms velocity amplitudes, (d\nVs /dlnVP)p for both WE 1997 and S16B30/P16B30 are shown in figure 7.28 together with that estimated from the joint, lower mantle models of Robertson and Woodhouse (1996a). Also shown in this figure are the average (d]nVs/dlnVP)p for the upper mantle (Woodward and Masters, 1991a; Robertson and Woodhouse, 1998), the Caribbean anomaly (Jordan and Lynn, 1974; Bokelmann and Silver, 1993), and the early estimate of Dziewonski and Woodhouse (1987). The (d\nVs/dlnVP)p profiles derived from WE1997 and S16B30/P16B30 are very similar across the whole mantle, and demonstrate that inspite of the difference in absolute magnitude Chapter 7, page 613 of the rms velocity (see figure 7.27), the relative difference in rms velocity is similar in the two tomographic models. The inclusion of the surface wave and free-oscillation data in the Bolton (1996) models is likely responsible for the better agreement between the S16B307P16B30 (d InF, /d l n ^ ) p profile and the average upper mantle estimate based on Woodward and Masters (1991a) as compared to that of WE 1997. Because the WE 1997 models rely heavily on ISC teleseismic S- and P-wave arrivals, which travel through the upper mantle on near vertical raypaths, the upper mantle velocity structure in Vasco and Johnson's joint models is poorly constrained relative to S16B3G7P16B30 over this depth interval (the vertical rays only allow the mean slowness (1/velocity) to be inferred beneath the station). In contrast, in the lowermost mantle, the addition of many "core" seismic phases in WEI997 (PKPab, PKPbc, PKPdf SKSac) which are not included in S16B30 and P16B30, likely gives WE1997 better resolution in the D" layer than Bolton's joint models. Thus, the very large increase in the S16B30/P16B30 (d\nVs/dlnVP\ profile in the lowermost 600 km of the mantle may not be a robust feature (the joint whole mantle S16B30 and P16B30 models are currently being augmented by a large data base of long period S-wave mantle discontinuity precursor differential travel times (otss_s ^ , otss_S;wS , otss_SmS ; Flanagan and Shearer, 1998), a parallel P-wave precursor data set (otpp _Pm p , §tpp_p p , 6tPP_PmP ; Flanagan and Shearer, in progress), PKP(ab-df) differential travel times (e.g. Shearer and Toy, 1991), and an expanded set of normal mode structure coefficients (e.g. He and Tromp, 1996; Resovsky and Ritzwoller, 1988). The above data sets will decrease the trade off Chapter 7, page 614 between volumetric and boundary structure in the transition zone and at the core-mantle boundary (Masters, personal communication)). A n additional point worth stressing from figure 7.28 is that both the WE 1997 and S16B30/P16B30 rms-ratio derived(dlnVs /dlnVp)p profiles clearly disagree with that inferred from Robertson and Woodhouse (1996a), with neither of the whole mantle models exhibiting the large hump, beginning at 1300 km depth and peaking at (d\nVs/dlnV,,)p = 3.2 at 2000 km depth. I speculate that these features of the Robertson and Woodhouse (1996a) profile are not real features of the Earth, and instead reflect the progressive loss in S-wave resolution due to a lack of data. Consequently, the only part of their profile which I consider reliable lies between 900 and 1300 km depth, where it is within error of the Bolton (1996) and Vasco and Johnson (1998) profiles. In figure 7.29 I compare the WE1997 and S16B30/P16B30 rms-ratio derived (d \nVs jd \x\Vv ) p profiles to the (d lnVs /d \nVr ) p values estimated in 4 lower mantle depth bins of Bolton (1996) discussed earlier. While there is only agreement between the three estimates in the 660-1100 km depth interval, I repeat the earlier caution that the increase in (d lnVs /d InV,, ) p for the lower 3 depth bins may reflect the effects of a few geographically-restricted anomalous S-wave residuals, and hence, the increase in (d \nVs /d \nVP ) p may not be representative of the bulk mantle. Note that when the anomalous S-wave cap averages are removed in the lowermost bin, the resulting (d \nVs Id h\Vp ) p value drops to 1.70, a value extremely near that estimated via the rms ratio technique for the two tomographic models. Chapter 7, page 615 In figure 7.30 I plot a radial profile of (dlnVs/d\nVp)p calculated assuming that the joint whole mantle S- and P-wave velocity anomalies in S16B30 and P16B30 are 100% spatially correlated in the mantle (Bolton, 1996). The procedure adopted by Bolton (1996) is similar to that of Robertson and Woodhouse (1996a) where both the S and P-wave data are inverted together to seek a P-wave tomographic model and a radial (d lnVs/d\nVP ) p profile which gives the best fitting "scaled S-wave" tomographic model (where the "scaled S-wave" model is determined via the relationship, (dVsf Vs ) = (d InVjd lnVp)v (BVP/VP )). In the Bolton (1996) inversion, surface Love and Rayleigh waves possess some sensitivity to density heterogeneity and consequently, the unknown density to shear velocity scaling factor was held fixed at (d In p/d In Vs ) p = 0.40. The resulting profile, together with its error bars, is plotted as the thick blue curve in figure 7.30. It is interesting to note that while this curve is in good agreement with the Robertson and Woodhouse (1996a) curve expanded radially with 2 terms, neither of these profiles agree with those (d \nVs /d lnVp ) p profiles derived from the ratio of rms velocity amplitudes. Further note that while the Robertson and Woodhouse (1996a) profile which utilizes only 2 terms in the radial expansion is very similar to the trend of the "100%-(d\np/d\nVs)p " profile of Bolton (1996), the profile which includes 4 terms is not, and instead approximates the rms-ratio derived (d\nVs /dlnVp)p profiles. I restate the observation that while performing a joint inversion of the combined S- and P-wave data sets has the benefit that both data sets are "damped" identically, Robertson and Woodhouse (1996a) demonstrate with their filtered data set, that this effect has a negligible effect on the rms-ratio based (d lnVs /d \nVP ) p profile, and thus, is not a factor that significantly biases Chapter 7, page 616 profiles based on the rms-ratio method (at least where sufficient data coverage exists). On the other hand, it is not clear that the assumption of 100% spatial correlation is warranted given that none of the joint tomographic models exhibit such a high correlation especially across the lower mantle (recall that while the correlation between the spherical harmonic expansions of S16B30 and P16B30 exceeds the 95% significance level across the whole mantle, the correlation coefficient still decreases from 1.0 at the top of the upper mantle to roughly 0.5 at the core-mantle boundary (see figure 7.24)). Although both Robertson and Woodhouse (1996a) and Bolton (1996) favour the radial (d \nVs /8 InV,, ) p profiles which assume 100% S- to P-wave spatial correlation, I disagree and would favour the profiles derived from the ratio of rms velocity amplitudes of the S- and P-wave tomographic models. Additional evidence in support of the rms-ratio derived (d \nVs /8 \nVp ) p profiles comes from a statistical analysis of the ISC S- and P-wave travel time residuals which allows a lower mantle average value for (d lnVs /8 InV,, ) p to be determined. This is discussed next. 7.9 Stochastic inversion of ISC P and S traveltimes Gudmundsson, Davies, and Clayton (1990) developed a stochastic inversion method to analyze ISC P- wave travel time residuals, grouped in bundles of rays (within their framework, bundles of rays are travel time residuals that fall within the same epicentral distance (binned in 2° windows from 0° to 100°) and source depth (six depth bins) windows and share the same source and receiver grid cells), to estimate the spectrum of lateral heterogeneity as a function of depth through the mantle. This technique allows them to estimate both the spatially incoherent and coherent variance of the travel time anomalies. The Chapter 7, page 617 spatially incoherent variance is attributed to random errors in the ISC catalogue which may potentially reflect any one of a number of potential causes (miss-identified seismic phases, earthquake mislocations, earthquake complexity, and potentially biased local picking of seismic phases). In contrast, the spatially coherent variance is attributed to the real heterogeneity in the Earth's mantle and it is analyzed in a number of ways. First, they simply plotted the variance as a function of depth and epicentral distance to obtain an idea of any systematic behavior. They find that as the scale size of the summary rays increase, the variance increases, likely reflecting the fact that as the effective cross section of the summary ray tube increases ever more rays are traveling through uncorrelated velocity anomalies. With increasing earthquake depth, the variance decreases, reflecting the fact that with increasing earthquake depth (and keeping all other parameters constant), the length of the raypath within the Earth decreases, and hence, the total length of heterogeneity that the ray "sees" decreases. Lastly, the variance decreases with increasing epicentral distance (20-90° range), an observation which implies that the strength of the velocity heterogeneity is concentrated at shallow depths (if the heterogeneity was uniform, then the variance would increase as the total path length increased and hence as epicentral distance increased). They also develop a forward linear theory to relate the variance of the travel time residuals in rays of different size to the spectra of seismic heterogeneity as a function of depth in the mantle. They then invert this relationship to obtain a robust description of the lateral variance as a function of depth in the mantle. They obtain an estimate of the traveltime scattering power which is the product of the average scale length of heterogeneity and the root mean square (rms) of the velocity slowness perturbations (slowness = 1/velocity). Because they can also estimate the scale length of heterogeneity independently, they can Chapter 7, page 618 isolate the rms slowness perturbations as a function of depth (see figure 7.31). They find that most of the P-wave heterogeneity is concentrated in the upper mantle and transition zone and subsequently decreases with increasing depth into the lower mantle with a sharp increase in the D" layer at the core mantle boundary. These results are consistent with the behavior found earlier by simply plotting the summary rays. A result, which is not determined in conventional tomographic models, is that Gudmundsson et al. (1990) are able to determine that of the total scattering power, much of the upper mantle power is in small scale features (spherical harmonic degrees > 50; horizontal wavelength < 300 km) while in the lower mantle, small scale power is indistinguishable from zero. While this may reflect a real feature of the Earth indicating that the lower mantle is in fact dominated by long-wavelength features (e.g. Su and Dziewonski (1991, 1992), Gudmundsson et al. (1990) caution that the absence of small scale power in the lower mantle may instead, simply be due to diffraction effects such that perturbations to the seismic wavefront that occur in the lower mantle would "heal" as the wavefront propagated to the surface. Whether or not the mantle has significant small scale power is important in terms of interpreting the tomographic models because i f indeed the lower mantle is devoid of small-scale structure, then the relatively coarse parameterizations of lateral velocity heterogeneity only out to degree 6-10 are capturing all of the signal. On the other hand, i f significant small scale structure exists, then truncating the parameterization of lateral velocity heterogeneity at relatively low degrees will result in significant aliasing effects (short wavelength structure incorrectly attributed to long-wavelength structure by the inversion). Recent comparisons of regional, detailed upper mantle tomographic models (Griot et al., 1998; Zielhuis and van der Hilst, 1996) with global models (Ekstrom et al., 1997; Zhang Chapter 7, page 619 and Tanimoto, 1993) have demonstrated that the power spectrum for both types of models is consistent with each other and decays with harmonic degree / raised to a negative power, l'a where the constant, a is between 1 and 2 for degrees below « 8 and increases to range between 2 and 3 for degrees up to 36 (Chevrot et al., 1998; degree 36 « horizontal wavelength of 550 km). Comparisons in the lower mantle are more difficult because the highest lateral resolution of the global models is to spherical harmonic degree 16 (wavelength « 1500 km) and thus it is not possible to determine i f the spectral power continues to decreases at higher spherical harmonic degrees like the upper mantle. Recently Hedlin et al., (1997) studied the amplitude structure of short-period precursors to the PKPaD or PKPoc phases and argued that the observations were consistent with random small scale (« 8 km) velocity heterogeneities (rms perturbations of 1%) distributed throughout the whole mantle. Of note is that they concluded the scattering producing the precursors was not concentrated in the D" layer, but distributed evenly throughout the lower mantle. Their conclusions imply that the sharp drop off in the wavelength of mantle heterogeneity inferred from the decrease in power spectrum with angular order observed for upper mantle tomographic models may not be extrapolated to very short scale lengths in the lower mantle. Davies, Gudmundsson and Clayton (1992) applied the same statistical techniques which they originally developed for P-wave variance to ISC S-wave data and found this data set mirrored the overall features of the P-wave data, although they were forced to restrict their S-wave study to epicentral distances from 31° to 75° since at approximately 80°, the reported S-wave arrivals in the ISC data set are contaminated by mis-identified SKS arrivals. In general, they found that the shear wave heterogeneity was heavily concentrated in the Chapter 7, page 620 upper mantle compared to the lower mantle (greater than an order of magnitude larger) with a similar correlation half-width to that determined from the P-wave data (350-600 km for S and 450-550 km for P in the upper mantle, while in the lower mantle the S correlation half-width is poorly constrained at 400-5000 km, but nevertheless, still straddles the 1200 km value of P; see figure 7.32). They compare the estimated rms S-wave slowness with their previous P-wave results to calculate a globally averaged value for (9In Vs/dln VP)p assuming that the S-and P-wave velocity perturbations in the mantle are spatially correlated (note that unlike tomographic seismic models, the statistical techniques used by Davies et al. (1992) and Gudmundsson et al., (1990) return radial profiles of variance and consequently, possess no lateral spatial information). They find (dlnVs/d\nVP)p = 1.80, which is applicable to a depth interval of 660-2400 km (see figure 7.33). This value is less than the range of 2.0-2.5 advocated by Dziewonski and Woodhouse (1987) by comparing the rms velocity amplitudes from independent S- and P-wave tomographic models. Davies et al. (1992) note that their estimate of 1.80 is based on comparing data of the same period range and hence is immune to possible complications due to comparing models based on different seismic frequencies (recall that Dziewonski and Woodhouse (1987) compared the lower mantle part of their waveform-based, SH-wave model (characteristic period of 60 seconds) to V3, a travel-time residual based P-wave model (characteristic period of 1 second) and found (d lnVs /d lnVr )p « 2.0-2.5). In comparison to the {d\nVsld\nV,,\ profiles derived from the ratio of rms velocity amplitudes (Bolton, 1996; Vasco and Johnson, 1998), the statistical inference of Davies et al. (1992) is very similar in exhibiting little depth dependence, but differs in that it is shifted to slightly higher absolute values. Chapter 7, page 621 Although in this chapter the focus is on (51nF s./31nF / J) p , one last point raised by Davies et al., (1992) is worth noting. Both the S- and P-wave models of radial variance in the residual travel times demonstrate that there is much more power in the upper mantle than the lower mantle. Therefore, i f the upper mantle velocity structure is not accounted for correctly in tomographic models, leakage of any un-modeled upper mantle signal into the lower mantle could significantly contaminate the lower mantle tomographic model. Gudmundsson and Clayton (1991) undertook synthetic 2D models to assess this affect and found that lower mantle models are severely affected by upper mantle structure. This bears upon the lower mantle S- and P-wave tomographic models constructed by Robertson and Woodhouse (1995) where upper mantle velocity structure was not explicitly modeled in the inversion, being only accounted for by static station corrections and earthquake source terms. Since the ratio of the global mean S- to P-wave travel time residuals, 5ts/8tp derived for the station correction in Robertson and Woodhouse (1997; 2.58 ±0.19) is significantly different from that used by Robertson and Woodhouse (1995; 3.50, a 27% decrease), there is good reason to believe that their joint, lower mantle S- and P-wave models are in fact biased. 7.10 Lower Mantle average from free oscillation seismology The relationship between S- and P-wave mantle heterogeneity may also be constrained by studies of free oscillation seismology (termed "free" in the sense that the Earth's oscillations are self-exciting, in contrast to externally "forced" oscillations, such as those produced by the impact of a giant asteroid). A n amplitude spectrum of a digital time series recorded after a large, deep earthquake reveals many resonance peaks. Each individual Chapter 7, page 622 resonance peak represents a free oscillation of the Earth, also termed a normal mode. Two types of normal modes are produced; toroidal and spheroidal, the latter being of interest here. Spheroidal normal modes, in the context of surface waves, are equivalent to large-scale Rayleigh waves, albeit with substantially greater depth resolution and form the basis of normal mode studies. These normal modes also have the property that they are equivalent to standing waves produced by the constructive interference of wave trains that travel around the Earth in opposite directions. Thus, free oscillations provide large-scale "averages" of the Earth's structure that are predominantly sensitive to its "even" structure (the term "even" refers to heterogeneity that is symmetric upon reflection through the Earth's center; heterogeneity that does not satisfy this constraint is termed "odd" structure). Most free oscillation studies have concentrated on determining even structure only, since this, mathematically, is more straightforward, involving only the features of an isolated resonance peak, than attempting to determine both even and odd structure, which requires consideration of coupling between overlapping resonance peaks (see Rosovsky and Ritzwoller (1995) for the first coupled mode study). If the Earth were perfectly spherical, was not rotating, and the velocity and density structure was correctly described by spherically symmetrical reference models, such as akl 35, then the observed shapes and frequencies of the peaks could be predicted with accuracy. However, none of the above features are true, such that the effects of the Earth's rotation, ellipticity, and lateral heterogeneity in shear and compression velocity, density, undulations in mantle and core discontinuities, and anisotropy all act to distort the shape and frequency of the normal modes from their ideal form. This distortion is termed "splitting" and the degree of splitting reflects the above features of the Earth filtered through the Chapter 7, page 623 individual sensitivity of each normal mode. The splitting due to the Earth's rotation and ellipticity may be calculated for a given reference seismic model. The remaining signal represents the affects of the Earth's 3D internal velocity and density heterogeneity, boundary structure, and anisotropy on the particular mode. The normal modes vary in their sensitivity as a function of depth to the S- and P-wave, and density heterogeneity, the undulations in mantle discontinuities, (and anisotropy) such that some modes are predominantly sensitive to perturbations in shear velocity, while others are largely sensitive to both compression and density perturbations. Likewise, some free oscillations are only sensitive to upper mantle perturbations with their depth resolution falling off rapidly well before reaching the lower mantle, while others effectively extend into the inner core. The component of the normal mode which reflects the Earth's 3D internal heterogeneity is mathematically described by a set of individual, complex coefficients termed aspherical structure coefficients, kc's (e.g. Ritzwoller et al., 1986), or just simply "structure coefficients" (e.g. Giardini et al., 1987), or "interaction coefficients" by Ritzwoller et al. (1988). Hereafter, I use structure coefficients). The subscript k identifies the particular multiplet or peak in the free oscillation spectrum while the subscript/superscript notation are the spherical harmonic indicies and refer to the degree s and order t of the spherical harmonic expansion). This set of structure coefficients, when multiplied by the corresponding spherical harmonics and summed, result in a function termed the "splitting function" (e.g. Giardini et al. 1987; 1988; Ritzwoller et al., 1988; Ritzwoller and Lavely, 1995) defined as: Chapter 7, page 624 Where Y' (9, cp) is the spherical harmonic coefficients as a function of latitude and longitude. Ft(9,cp) is a function which represents at a given location, the local radial average of the Earth's internal velocity and density structure for that particular free oscillation. When plotted over the Earth's entire surface, the splitting function portrays a global image of the average 3D structure sampled by the particular normal mode. The structure coefficients are commonly derived by interative spectral fitting where the estimates of the individual coefficients are iteratively adjusted to minimize the difference between a synthetic and the observed normal mode spectrum (e.g. Ritzwoller et al., 1988; L i et al., 1991a; He and Tromp, 1996). The derived set of structure coefficients represent "data" similar to seismic travel times in that they allow the Earth's 3D internal structure to be further deduced. The normal mode structure coefficients may in turn, be linearly related to the spherical harmonic components of the Earth's 3D velocity structure (of the same order and degree) that is recovered in seismic tomographic models (Ritzwoller and Lavely, 1995): kcs = kCs + kCs where kc's represents the component due solely to volumetric structure while kc's represents the component from undulations on boundary structure. These two terms may themselves be expanded to emphasize the number of potential influences via: surface ,=1 (hVAr)) (oVJr))' (8p(r))' dr Vs(r) Vs(r) p(r) where kSs(r), kPs(r),and ^s(r) 3 1 6 m e sensitivity kernels as a function of radius for the relative perturbations in shear velocity, compression velocity, and density, respectively; Chapter 7, page 625 (&VS(r))'s, (8V,,(r))'x, and (8p(r))', represent the spherical harmonic coefficients of the perturbations in P- and S-velocity, and density, respectively; VP (r), Vs (r), and p(r) represent the reference P- and S-velocity and density profiles, taken from seismic reference models such as akl35 (the affects of anisotropy are not included in the above expression, see L i et al. (1991a) for the additional terms). For boundary structure, the structure coefficient is somewhat less involved and is expressed as: *c;=2>.;.5A' d where the summation is over all internal mantle discontinuities, d, kD's is the boundary kernel for boundary d, and Bdh's represents the spherical harmonic coefficients of undulations in the dh mantle discontinuity normalized by its reference radius. As expressed above, the structure coefficients are sensitive to both perturbations in both shear and compression velocity and density, but also to perturbations to the radius of the mantle discontinuities, such as the moho, the core-mantle boundary, and the 410, 520, and 660 km discontinuities. In spite of the large number of affects which influence free oscillations, the relationship between the structure coefficients, derived from spectral fitting, and 3D velocity and density heterogeneity is a linear one, and thus, permits a relatively straightforward comparison between synthetic structure coefficients predicted from tomographic models and observed structure coefficients. However, most tomographic models are simply either shear (or compression) wave models and consequently, equivalent perturbations in density and Chapter 7, page 626 compression (or shear) velocity must be inferred through the use of scaling factors. Assuming that the tomographic model is a shear wave model, the necessary relationships are: VP(r) dlnVs) Vs(r) and (6p(0); ( dlnp) (6FS(0); p(r) d\nVsJ Vs(r) ' where the shear wave heterogeneity has been converted to equivalent compression wave and density heterogeneities. In normal mode seismology, the scaling factors have often assumed to be constant with depth. With these scaling factors the volumetric structure coefficient may be written as: ^ ^ surface 'v = 1 Vs(r) d\nVs; (5^,(0): vs(r) ^ainp^ dlnK sj Vs(r) dr While in theory, with sufficient number of high quality observations, normal mode free oscillation seismology has the potential to directly solve for simultaneous perturbations of shear velocity, compression velocity, and density, in practice, there are insufficient observations to do so. Indeed because free-oscillation seismology requires digital records of very long period seismograms produced by large, deep earthquakes, it is only after 1976 that analysis of real data has been possible (Giardini et al., 1987). Inspite of these limitations, a major advantage of free oscillations is that these seismic phases sample the entire mantle, and Chapter 7, page 627 hence, provide true global coverage. This contrasts with body waves (i.e. direct P-and S-wave phases), which suffer from an uneven global distribution of receivers and earthquakes. In addition, because normal mode data of the same frequency is used to derive estimates of (d\nVs/dlnVP)p and (din p/dln J^) (or (5 In p/dlnVP) ), possible probl ems that exist when tomographic models of widely different frequency are compared, such as in the initial estimates of Dziewonski and Woodhouse (1987), are not an issue. Lastly, inspite of the statement above that normal mode observations are presently insufficient to simultaneously constrain bV$, bVp, and bp, Tromp (1995a) and He and Tromp (1996) point out that the two 1994 large magnitude earthquakes in Bolivia and the Kurils have been recorded on over 80 digital instruments with excellent global distribution. This has resulted in a huge increase in the quantity and quality of normal mode observations (for example Resovsky and Ritzwoller (1998) report greater than 3100 derived structure coefficients compared to only 27 in Ritzwoller et al. (1988)). An immediate result of this new data set is that the latest free-oscillation studies (Ishii and Tromp, 1997; 1998) have begun to consider depth dependent profiles for (d\nVs / d \nVP)p and (d\npld\nVs)p (or (dlnp/dlnVp) p). Masters et al., (1982) adopted constant values of (dlnFv/3lnVp)p = 1.25 and (Slnp/dlnJ^)^ = 0.4 ((5In p/dln Vp)p = 0-5) based on extrapolating the high temperature, but room pressure experimental mineral physics values (Anderson et al., 1968) across the whole mantle. Subsequent studies by the same group continued with these values (e.g. Ritzwoller et al., 1986; 1988) as have others (e.g. Hara, et al., 1996). Giardini et al. (1987) were the first group to question this choice, arguing instead that the level of lower mantle P-wave heterogeneity, as inferred using the V3 tomographic model, was better satisfied with Chapter 7, page 628 (d\nVs/dlnVP)p = 2.0 and (d in p/51n VP) = 0.5. In a follow up article, Giardini et al. (1988) discussed their results in detail and using the combined upper S + lower P tomographic model of M84A + V3 to predict structure coefficients, argued that the optimal value for (d\\\Vs /d\nVp)p lies in the range 2.5 - 3.2 with preferred values of {d\nVs/d\nVp)p = 2.8 and (dinp/dlnV P ) p =1.1 (see figure 7.34). This figure plots the variance reduction achieved for various choices of (d In p/d In VP) and (d lnVs fd lnVP )p as measured by: ( / \ observed [ / \ predicted k Cs ) \k Cs ) x2(k<) = Z A=1 where (A c\ yrLd,atil j s the predicted structure coefficient for a particular tomographic model, ( t c | )" f c ' " " ' is the observed structure coefficient, ka's is the uncertainty estimated for the observed coefficient, and K is the number of coefficients. Note that the green dot in figure 7.34 represents the high temperature but room pressure experimental estimates ((dlnVs/d\nVp)p = 1.25 and (91np/51nFp) = 0.5), values favoured by Masters et al. (1982), but which result in a relatively poor variance reduction. Note too that the particular structure coefficients are relatively insensitive to the choice of (d\np/dlnVp)p at least for large values (compare the curves for (dlnp/SlnF,,^ =1.5 and 2.5). As noted above, Giardini et al. (1988) interpreted these results to favour relatively high values of (dlnVs/d\nVp)p = 2.8 and ( d l n p / S l n F ^ =1.1. Nevertheless, it should be stressed that such high values are based upon a "spliced" S- and P-wave tomographic model that is less Chapter 7, page 629 than ideal. M84A (Woodward and Dziewonski, 1984) is a pure S-wave, upper mantle tomographic model which does not include any correction for known crustal effects (topographic perturbations to the free surface, ocean crustal thickness, Continental Conrad and Moho discontinuities and perturbations of S, P, and density in the two continental layers separated by the Conrad discontinuity). As noted by Ritzwoller and Lavely (1995), the details of the crustal correction have a relatively large affect on the velocity amplitudes of the tomographic models. They note that half of the difference in rms velocity amplitude exhibited between the upper mantle parts of SH12WM13 (a whole mantle, shear wave tomographic model from the Harvard group, based in part on M84A) and SH.10c.17 (a whole mantle shear wave tomographic model constructed by the Scripps group) is due to entirely to differences in the two crustal models adopted by the two groups. They further note that when they compare the combined S + P whole mantle M84C + L02.56 against SH12WM13, the combined model exhibits anomalously large rms velocity amplitudes near the Earth's surface and at the top of the lower mantle (670-800 km), immediately below where the two models are "spliced" (M84C differs from M84A in that the former has a crustal correction, while the latter does not). Consequently, the use of M84A + V3 by Giardini et al. (1987, 1988) in forward calculating structure coefficients is less than ideal because the anomalous amplitudes will in turn, propagate through to affect the inferred values of (d\nVs/dlnV,,)p and ( a i n p / a i n ^ ) p . Ritzwoller and Lavely (1995) also note that a poor prediction of structure coefficients does not distinguish i f the misfit is due to an error in the rms velocity amplitude of the tomographic model or due to a spatial error (i.e. the spatial or radial placement of the velocity Chapter 7, page 630 perturbation in the tomographic model). They conclude that most of the misfit between observed and predicted structure coefficients for the particular tomographic models they evaluated (SH12WM13, SH.10c.17, M84C + L02.56, MDLSH) predominantly reflects the combined affects of amplitude errors and errors in the radial distribution of velocity anomalies, but not geographic spatial error. That both amplitude and radial distribution errors may be affecting the results of Giardini et al. (1988) is suggested by the significant difference between the lower mantle estimate of (d \nVs /d \nVp ) p = 1.80, based on a statistical analysis of the variance in ISC S and P wave travel time residuals (Davies et al., 1992) and the preferred value of Giardini et al. (1998; (d lnVs /d lnVP ) p = 2.80) (see figure 7.34). A n additional argument against the high values preferred by Giardini et al. (1988) was advanced by Ritzwoller et al. (1988) who demonstrated that by allowing up to ± 3 km of topography on the core-mantle boundary combined with (<9 lnl^./d lnVp ) p = 1.25 and ( S l n p / d l n J 7 ^ = 0.5 gave as good, or better, fit to the observed structure coefficients than the M84A + L02.56 combined model that utilized a higher value of (d lnVs /d lnVp ) p =2.5 (and (d In p/d lnVp ) = 0.5), but with no topography on the core-mantle boundary. In a further study by the Harvard group, L i et al. (1991a) adopt intermediate values of (dlnVs/8\nVP)p = 2.0 and (d\np/d\nVp)p = 0.5, somewhat lower than the values advocated in their earlier study (2.8 and 1.1, respectively). They also treat the topography on the core-mantle boundary as an unknown in the retrieval of observed structure coefficients, although they acknowledge that the amplitude of the topography trades off strongly with the adopted value of (d \nVs /d \nVP ) p . Their choices for (d lnVs /d lnVp ) p and Chapter 7, page 631 (din p/d InK,) were based on the results of L i et al. (1991b) who attempted to determine confidence limits on these scaling factors by a clever forward modeling study which is outlined briefly below. To negate the sensitivity to topography on the core-mantle boundary, L i et al. (1991b) combined a number of specific mantle-sensitive normal modes into a set of hybrid modes that eliminate any sensitivity to core-mantle boundary topography (thus the observed structure coefficients and associated differential sensitivity kernels used by L i et al. (1991b) represent linear combinations of observed structure coefficients and their corresponding kernels in L i et al. (1991a)). Having removed sensitivity to C M B topography, L i et al. (1991b) focused next on placing bounds on (d \nVs /d \nVp ) p by utilizing hybrid normal modes which are dominantly sensitive to either shear or compression velocity with only minor sensitivity to density. They recast the observed structure coefficients into components of upper mantle, lower mantle, and error: / \v k k - i I .S-sensilive . .upper I rl 1 y _ I Vower mantle , I I \manlle I \ k C s ) ~ \ k C s ) + \ k C s ) + £ . v ' where {kc's)S hyb"d are the hybrid observed Vs sensitive structure coefficient, . .S-sensitive \kc's)''""""'e ^ ^ e predicted lower mantle structure coefficients that are predominantly upper sensitive to Vs structure, [k c's f'a""e are the predicted upper mantle structure coefficients, Ripper and s'v are error terms. To account for [k c's J""""" , L i et al. (1991b) either utilized the S-wave upper mantle tomography model M84A together with assumed values of Chapter 7, page 632 (d \nVs Id \VLVP ) p =2.0 and (d In p/d lnVp) = 0.5, or ignored this term altogether, under the assumption that it would be absorbed into the error term s'.. A further simplification adopted by L i et al. (1991b) was to ignore any contributions due to density heterogeneity in the lower mantle ((d In p/d \nVP) =0.0). Thus, the predicted lower mantle S-sensitive structure coefficients were recast in terms of perturbations to a single data type: S-sensitive ( t \ower mantle (oVJr))' (oT„(r))' (op(r))' *S,<r) ~ + Mr) K ' r + Mr) v5ir) Vs(r) P(r) dr ( .S—sensitive t vower mantle P Mr) (&Vs(r)l Vs(r) P-wave + Mr)\ + Mr)-dlnVs dlnVP i&Vp(r)lV VP(r) dinp d]nVP VP(r) dr ( . S-sensitive t Vower mantle r k C ° > JZMB Mr) P-wave , a inK p J? VP(r) V3 dr In the above expression, L i et al. (1991b) used the spherical harmonic coefficients of the P-wave tomographic model V3 (Morelli and Dziewonski, 1987) for (bVp(r))'x and then adjusted the value of P-wave (Q \nys JQ \nyp ) p t 0 determine the probability distribution of this term Chapter 7, page 633 while comparing the predicted sum of S-sensitive tower mantle + upper mantle ^ ^ / against the observed hybrid structure coefficients. This initial estimate of P'wave(d\nVs/dlnVp)p might be biased i f the velocity amplitudes in the tomographic model V3 over- or underestimates the "true" amplitude. To account for this, they switch from S-sensitive to P-sensitive hybrid structure coefficients and expand the lower mantle terms via: C«:rw-Ur P-wave wer mantle ( .S-wave , .upper t yower mantle . ( f ynantle . t k C s ) + \ k C s ) Ss where the relatively minor contribution from the predicted lower mantle shear wave heterogeneity is calculated via: . S-wave I yower mantle \ •Ss(r) \sw and x /•*- wave ( t \ower mantle k C ° > CMB <Ps(r){F] Vs(r) \*VP(r)l dr \V3 V,,(r) dr The term {F} represents a constant used to decrease (or increase) the velocity amplitudes in the tomographic model V3 and, in turn, may be used to estimate an unbiased estimate of the scaling factor via: unbiased P-wave ( 5 \nVs/d\nVP)p = {F} P-wave (d lnVs / d lnVP )p . In a similar fashion, parallel expressions relating the S-wave heterogeneity of the lower mantle tomographic model SW (Woodhouse and Dziewonski, 1986; 1989) to P-hybrid structure coefficients may be constructed: Chapter 7, page 634 / Al'-hyhrid ( , V P- sensitive h>wer mantle + U) : upper \mantle . t where the predicted lower mantle, i^-wave sensitive structure coefficients are given by: , P-sensitive ( I \lower mantle f*' •Ps(r) S-wave / . N ' d\nVs A Vs(r) dr Again, to determine if the resulting S-wave estimate, S-w a v e (d lnVs /d \nVP ) p , is biased by the velocity amplitudes of the tomographic model SW, L i et al. (1991b) switched to S-wave hybrid structure coefficients and again introduced the {F} factor: / , \S-hybrid ^ ( , \ o w e r mcmtle ( I Vower mantle , ( I \« \k Cs ) ~ \k C.v ) + \k Cs j + \k Cs ) P-wave 'ower mantle where the predicted lower mantle P-wave component is given by: .upper ynantle ^ t . P-wave ( t \lower mantle f*^® Mr) V3 dr and the predicted S-wave component is given by: S-wave 'ower mantle 60 M i >S,(r){F} SW vs(r) dr The resulting two unbiased probability distributions of (d\nVs /d\nVp)p were then averaged and these are plotted in figure 7.35 (note that they choose to plot their inferences as (d\nVP /d\nVs)p , which is the inverse of the form used herein, (d\nVs/dlnVp)p ). The upper panel shows the probability distribution when upper mantle heterogeneity is explicitly accounted for using M84A, while the lower panel shows the distribution when upper mantle Chapter 7, page 635 heterogeneity is absorbed by the error term, e's . Also plotted is the lower mantle estimate of Davies et al. (1992; (d\nVs/dloVp)? =1.80) based on a statistical analysis of the ISC S- and P-wave travel time residuals. L i et al. (1991b) recommended the values when M84A was utilized to account explicitly for upper mantle heterogeneity, which result in an optimum value of (d lnVs /d lnVP ) p = 2.27 ranging between 1.66 and 2.56 (75% confidence limits). In contrast, it is clear from the bottom panel that when no upper mantle correction is explicitly included, the resulting optimum value is substantially lower ((dlnVs/8\nVP)p « 1.81 with 75% confidence limits of 1.42 to 2.38) and virtually indistinguishable from the independent lower mantle estimate of Davies et al. (1992). In light of the above discussion concerning the problems of the uncertain amplitude of velocity heterogeneity in M84A and the large discrepancy between the inferred value for (d lnVs /d lnVp ) p when this upper mantle correction is used and the statistical value of Davies et al.(1992), I prefer the values where no explicit upper mantle correction was made. As mentioned earlier, Ritzwoller and Lavely (1995) have undertaken a recent review of some of the global tomographic models and compared the respective predicted structure coefficients for the tomographic models to observed coefficients taken from Smith and Masters (1989) and Ritzwoller et al. (1988). They point out that within the 5VS, 8VP, 5p representation of heterogeneity, the structure coefficients are virtually insensitive to the value of the density scaling factor, (d lnp/5 lnVP ) , and consequently, allow their study to focus on the affects of {d lnVs /8 lnVP ) p in comparisons between observed and predicted structure coefficients (however, they note that the sensitivity to density is substantially increased when Chapter 7, page 636 the structure coefficients are recast in terms of perturbations in adiabatic bulk and shear moduli, and density, 8p, 5KS, 8p ). The tomographic models they studied are listed in table 7.3 together with the adopted values of (d\nVs/dlnV,,)p and (d In p/d In Vs ) originally used in their construction. Table 7.3. Original values for the scaling factors adopted in construction of the tomographic models evaluated by Ritzwoller and Lavely (1995). Model Year Region {d\nVs/d\nVP)p {dlnp/dlnVs)p SH12WM13 (S-wave) 1993 Whole mantle 1.25 0.4 SH. 10c. 17 (S-wave) 1992 Whole mantle 1.25 0.4 M D L S H (S-wave) 1990 Whole mantle 0.0 0.0 L02.56 (P-wave) 1984 Lower mantle 2.0 0.4 M84A (S-wave) 1984 Upper mantle 0.0 0.0 M84C (S-wave) 1984 Upper mantle 0.0 0.0 In evaluating the adopted values for (d \nVs /d lnVp ) p , Ritzwoller and Lavely (1995) focus on the degree 5 multiplets (5S) because these structure coefficients are insensitive to core-mantle boundary topography and nearly insensitive to shear wave heterogeneity. Thus, these particular coefficients highlight the success (or failure) of (d]nVs/d\nV,,)pm converting the shear wave models into a "pseudo" P-wave model with which to calculate structure coefficients. They find that for SH12WM13, SH.10c.17, and the combined model M84C + L02.56, the predicted structure coefficients are better fit when the value of (d\nVs/d\nVP)p is increased from 1.25 to « 2.0. This value is lower than that advocated by either Giardini et al. 1988; (d\nVs/d\nVP)p = 2.8) or L i et al. (1991b; (dlnVs/d\nVP)p = 2.27) but very near the value estimated by Davies et al. (1992; (d\nVs/dlnVP)p = 1.80), a Chapter 7, page 637 result which strongly suggests that the initial claims for relatively high values of (<3 lnVs Id \nVP ) p are incorrect. A l l of the free oscillation estimates discussed above are plotted in figure 7.36. It is clear from casual inspection of this figure that although a wide range of values have been recommended, the recent values are reasonably consistent at « 1.80-2.00 (Li et al., 1991b; Ritzwoller and Lavely, 1995). Tromp (1995a), He and Tromp (1996), and Resovsky and Ritzwoller (1998) stress the large impact that the two large deep earthquakes in 1994 have had on free-oscillation seismology. In addition to providing a much larger data set of observations, the expanded data set allows consideration of depth dependent radial profiles of (d lnVs jd lnVp ) p and (d In p/d In Vp ) . Ishii and Tromp (1997; 1998) have used this data set to directly infer S-, P-, and density mantle heterogeneity and corresponding correlation and scaling factors between the different expressions of heterogeneity. The two stage steps where observed structure coefficients are first derived and then forward modeled by tomographic velocity heterogeneity is bi-passed, and instead, models of mantle heterogeneity are directly sought which optimally fit the observed normal mode spectrum. Their model, termed SPRD6, consists of S-, P-, and density models of mantle heterogeneity (bVs/Vs ,8VP/VP ,6p/p) from which they estimate the (d lnVs /d lnVP ) p scaling factor by scaling the rms amplitude ratio with the correlation between the S and P models (Ishii, personal communication) via: Chapter 7, page 638 0 = KrmsVSJ f8lnV^ 8lnVv + (r) ((dlnVP){dlnVs)) {dlnVpf) ^((dlnVs) ({dlnVP){dlnVs)) ( dlnVf dlnVp Jp (r) ^((dlnVpf) ^((dlnVj r8lnVf dlnVp)p (r) ^ rms Vs ^ rms Vp where ^ rms Vp ^ rms Vs represents the ratio of root mean squared amplitude of the Vp and Vs velocity models, r8\nVs^ dlnVp ( r ) Jp represents the depth dependent scaling factor, and ((51n^)(ainFs,)) (dlnVpf) PlnVsf represents the correlation between the Vp and Vs velocity models and the chevron brackets represent the average over the unit sphere. When they recast their model in terms of shear and compression velocity and solve for a depth dependent profile of (d \nVs /8 lnVp ) p , their 1997 resulting curve is shown in figure 7.37 as the yellow curve. However, in their 1998 study, the preferred curve (see figure 7.37, the gray curve) had substantially decreased in magnitude and was now, near-vertical. Also plotted in this figure is the upper mantle estimate of Woodward and Masters (1991a) and Robertson and Woodhouse (1998) and the lower mantle, depth-independent estimates from Ritzwoller and Lavely (1995) and L i et al. (1991a), the latter for which no upper mantle tomographic model is adopted. It is clear from this figure that the 1998 free-oscillation, depth dependent curve of Ishii and Tromp (1998) is in good agreement with the upper mantle seismic estimates with the average upper mantle and transition zone value of 1.48 being within error of the Woodward and Masters (1991a) "oceanic" value of 1.55 ± 0.10. In the Chapter 7, page 639 lower mantle, the 1998 depth dependent curve of Ishii and Tromp (1998) shows no systematic increase with depth and instead oscillates around (d\nVs /d\nVp)p «1.55 (the lower mantle arithmetic average is 1.46). In figure 7.38 the 1997 and 1998 depth dependent profiles of Ishii and Tromp are compared to the "100%-(5lnJ^/5lnVP) p profiles deduced by Robertson and Woodhouse (1996) and Bolton (1996) and the rms-ratio- (d \nVs/d \nVP )p profiles deduced by Bolton (1996) and Vasco and Johnson (1998). It is immediately clear from this figure that the 1998 free-oscillation profile is mimics the to rms-ratio (d lnVs /d lnVp ) p profiles, but is in strong disagreement with the (d lnVs /d lnVp ) p profiles that forced a 100% spatial correlation between the S- and P-wave structure when simultaneously solving for a single P-wave model and a radial profile of (dlnVs/d\nVp)p . However, the 1997 profile acts in essentially the opposite manner and provides an excellent fit to the "high" (d lnVs /d lnVP ) p profiles. Thus, a critical question is which normal mode profile is correct? Unfortunately, no consensus has emerged in the free oscillation community that any of the depth dependent (d \nVs Id \nVp ) p profiles derived from normal mode data alone are robust. Resovsky and Ritzwoller (1998) has recently established a new and expanded, high-quality catalogue of normal mode structure coefficients (3100) and used this data set, together with published shear wave tomographic models (S16B30 and SKS12WM13), to derive a new degree 8 shear wave tomographic model, named MM2L12D8 (Resovsky and Ritzwoller, 1999a). This model was constrained to lie roughly between existing tomographic models that were largely constructed using other types of seismic data, but was free to maximize the fit to the new data set of normal mode coefficients. They also constructed associated scaled 3D Vp and density Chapter 7, page 640 models where it was assumed that the lateral variations in Vp and density were perfectly correlated with Vs (as would be expected for a thermal origin) and adopted constant values for the scaling factors of [(dlnVs/d\nVP)p , (ainp/51nF s) p ] = [1.25, 0.30] in the upper mantle and [2.00, 0.20] in the lower mantle. Although they found that a small subset of their normal mode coefficients preferred Vp and density to be decorrelated from the Vs model in the lower mantle, they noted that the amplitudes among the decorrelated Vp and density models differ by more than 100% throughout the mantle. From this they concluded that it is not possible to derive robust 3D models of Vp and density through inversions of existing normal mode data. From the perspective of constraining a depth dependent (5 l n F s / 5 InF/, ) p profile, the data set is still too limited to robustly constrain a depth dependent profile (Resovsky, personal communication). Resovsky and Ritzwoller (1999b) have also performed inversions where additional geoid data was combined with normal mode observations for inversions for Vp and density structure, but found that strong tradeoffs between topography on the internal mantle boundaries and the 3D density model rendered the resulting density models highly non-unique. In this study they explored a wider range of possible decoupling between Vs and Vp 3D models during the inversions of the normal mode data but still concluded that the normal mode observations are insufficient to constrain the particular depth interval where a decorrelation might occur between Vp and density and the Vs model. To make further advances, and from the perspective of constraining (d\nVs/dlnVp)p (and (d\np/d\nVs)p ), they conclude that new structure coefficients are required which have high sensitivity to upper mantle structure. If this region could be tightly Chapter 7, page 641 and well constrained, then the tradeoff between density models at different depths across the mantle could be broken. Thus, it is not at possible to favour either the 1997 or 1998 free-oscillation curves of Ishii and Tromp plotted in figure 7.38. However, before leaving this section it is noteworthy that Masters (1999) has recently presented results of incorporating the new Resovsky and Ritzwoller (1998) normal mode structure coefficients in joint S and P wave tomographic models. In contrast to MM2L12D8, which was not constructed by inverting all of the different types of seismic data (instead the shear wave model was constrained to stay roughly between existing shear wave models), these new, joint 3D Vs and Vp tomographic models are inverted to satisfy all of the data sets that went in to the Bolton (1996) S16B30 and P16B30 models (augmented by the new and expanded structure coefficients). From these joint S and P-wave models he determined a new radial (51nF s ./SlnJ / / J) p profile which is substantially reduced compared to the preferred best fitting profile of Bolton (1996). The new profile is essentially indistinguishable across the lower mantle from the Vasco and Johnson (1997) profile. This is an exciting result since these joint tomographic models are likely to be the best constrained 3D seismic models to date, and hence the resulting (d \nVs /d lnVp ) p profile should be robust. It is significant that when the normal mode data is combined with many different types of seismic data sets (absolute travel times, surface waves, see page 611 for a more complete description), the resulting amplitude of the shear to compression wave models is consistent with a thermal origin (as will be shown in greater detail below in section 7.20). Chapter 7, page 642 7.11 (a In Vs/d In KP) in the D" region from PKP(ab-df) differential travel times? Thus far the seismic estimates have been concerned to large extent with estimates for (d lnVs /d \nVP ) p that reflect mantle values without explicit concern for the lowermost part of the lower mantle, the D" layer. Song and Helmberger (1997) utilize PKP(ab-df) differential travel times to probe the velocity heterogeneity in this region. The PKPdf raypath, schematically shown in figure 7.39, penetrates the core-mantle boundary nearly vertically and intersects the solid, inner core. In contrast, the PKPah phase only grazes the core-mantle boundary and never intersects the inner core. Because the raypaths are so similar in the upper mantle and portions of the lower mantle, Song and Helmberger (1997) argue that most of signal in the PKP(ab-df) differential time reflects P-wave velocity heterogeneity accumulated in the lowermost parts of the mantle. They compare their PKP differential travel time residuals to predictions from published S-wave tomographic models (Grand et al., 1997; Su et al., 1994)) to examine the proportionality of P to S in the lowermost mantle assuming that S- and P-wave heterogeneity is correlated. They determine a range of estimates for (d InV,, /d \nVs ) p (note they choose the inverse of the expression used herein) by determining the variance reduction for the tomographic models, where the variance reduction is the difference between the observed PKP residual and the product of the S-wave model and the (d InV,,/d\nVs)p factor. Their results are re-plotted in figure 7.40. Note that for SH12WM13, the variance reduction peaks a negative value, while Grand's (1997) model achieves only a modest variance reduction (7%) with an inferred scaling factor Chapter 7, page 643 of (d \nVP/d \nVs)p = 0.2 ((d lnK, ) p = 5.0). Also plotted in this figure is the range of values for (d lnVs /d \nVp ) p discussed thus far, which extend from 0.59 (1/1.70, free-oscillation seismology, Ishii and Tromp, 1998) to 0.28 (1/3.50; ratio or rms velocity amplitudes of joint S- and P-wave tomographic models (Bolton, 1996)). Song and Helmberger (1997) note that for "typical" values of (d lnVs /d lnVP ) p = 2.0, the resulting predicted variance reduction is increased (i.e. worsens) by -7% for Grand's (1997) tomographic model, while for SH12WM13 (Su et al., 1994), the increase is -70%. Note that while Grand's (1997) model incorporates SKS seismic phases to obtain lower mantle sensitivity, the SH12WM13 model does not include any "deep" seismic phases, and consequently is likely to have poor resolution in the D " layer (recall the large change in rms velocity across the D" layer between SH12WM13 and SKS12WM13 in figure 7.16). Thus, the very poor variance reduction exhibited by SH12WM13 is not unexpected. At face value, the results of Song and Helmberger (1997) suggest that S and P-wave heterogeneity is very poorly correlated in the D " layer, implying that thermal effects are not the dominant driving force in this region of the mantle. However, before accepting this conclusion, we note that the PKPdf branch is known to exhibit anomalous travel times which reflect the effects of anisotropy within the inner core (Poupinet et al., 1983; Morelli et al., 1986; Woodhouse et a l , 1986; Shearer et al., 1988; Shearer and Toy, 1991; Creager, 1992; Song and Helmberger, 1993, Tromp, 1993; Vinnik et al., 1994; Su and Dziewonski, 1995; Song, 1996). Indeed, Rodgers and Wahr (1994) in a study of core-mantle boundary topography using ISC PcP and PKPa0, o c , and df absolute and differential travel times, argue that the PKPdftravel times are contaminated by inner core anisotropy (raypaths along Chapter 7, page 644 the Earth's spin axis are fast and those along the equator are slow) and hence of little use in their study. Song and Helmberger (1997) claim that inner core anisotropy is not a significant factor contributing to their differential travel time anomalies and consequently, do not make any correction for this feature. In contrast, Su and Dziewonski (1997) claim the effect of inner core anisotropy is not negligible on the PKPdf phase and correct for this effect, using the empirical relationship of Su and Dziewonski (1995), when including this phase in their joint shear, compression, and bulk sound velocity tomographic model MK12WM13. Although not considered by Song and Helmberger (1997), it is widely acknowledged that topography on the core-mantle boundary trades off with the amplitude of velocity heterogeneity directly above the C M B (Ritzwoller et al., 1988; L i et al., 1991a; Rogers and Wahr, 1993; Stark and Hengartner, 1993; Pulliam and Stark, 1993; Vasco and Johnson, 1998). Rekdal and Doornbos (1992) demonstrate that an undulating core-mantle boundary can bias travel times of PcP, PKPa0 and PXP^phases. Vasco and Johnson (1998) include both core-mantle boundary and inner core boundary topography and note that the inferred magnitude of ICB topography trades off with velocity heterogeneity directly below in the inner core as deduced by PKPdfdata while the C M B topography trades off with the velocity heterogeneity directly above in the D" layer. Thus, the poor correlation of PKP(ab-dj) differential travel time anomalies with predictions from S-wave tomography models that Song and Helmberger (1997) find is likely to reflect a number of different processes acting in the D" region (anisotropy, presence of a melt phase, presence of chemical heterogeneities, shear and bulk attenuation, thermal effects, core-mantle boundary topography) and within the inner core (anisotropy, inner core boundary topography), which all together, combine to degrade the P-to-S correlation. Lastly, the high values may also be an artifact of comparing Chapter 7, page 645 independent models. Recall the anomalously large values estimated by Ritzwoller and Lavely (1995) when they calculated lower mantle (d\nVs /d\nVp)p profiles via the ratio of rms velocity amplitudes from independent S and P wave tomographic models (see figure 7.18). Therefore, it may be premature to accept the extreme value inferred by Song and Helmberger (1997; (d lnVs /d \nVP ) p = 5.0) as an accurate estimate. For instance, the radial profile of (dlnVs /d\nVp)p calculated by the ratio of rms velocity amplitudes from the joint S- and P-wave tomographic models WEI997 (Vasco and Johnson, 1998) only reaches a maximum value of 2.10 at the base of the D" region, and this model includes a number of "deep" seismic phases. Also note that the depth dependent, normal mode estimate of Ishii and Tromp (1998), which is based on seismic phases that have true global sensitivity, is relatively constant across the D" region at roughly 1.70. In contrast, the ratio of rms velocity amplitudes from the joint S- and P-wave tomographic models of Bolton (1996) reach somewhat higher values of 3.40 directly above the core-mantle boundary. However, Bolton (1996) notes that this high value reflects anomalous S-wave travel times which are geographically restricted to the central Pacific, south east of Hawaii. When these particular travel times are ignored, the resulting value for (d lnVs /d lnVp ) p decreases to 1.70, in excellent agreement with the results estimated independently by Vasco and Johnson (1998) and Ishii and Tromp (1998). The main point is that studies which have much better spatial coverage and for which (SlnFj /Sln^,) , , is based on self-consistent joint S- and P-wave models give much lower values than that inferred by Song and Helmberger (1997). Consequently, I believe that their large value reflects the fact that they are comparing independent S- and P-wave models Chapter 7, page 646 (recall the anomalously high values of 4.0-7.0 calculated by Ritzwoller and Lavely (1995) when they estimate (d\nVs/dlnV,,)p using the ratio of rms velocity from independent tomographic models; see figure 7.19). 7.12 Summary of Seismic estimates of (dlnVs /dlnV,,)p Although it is often stated that the parameter (d lnVs /d InV,, ) p in the mantle is high (2.0-2.5), it is clear from this review of the various seismological estimates, that in fact, this is not the case, with the most recent and well constrained estimates clustering about lower values (see figure 7.41). In the upper mantle, early studies were quite scattered (see figure 7.7) such that inferred values of (dlnVs /d\nVP)p ranged from as low as 0.99 to as great as 2.59 ± 0.54. However, the ratio of co-located, cap averaged SS-S and PP-P differential travel time residuals (&tss_s /&tPP_p) for oceanic upper mantle (Woodward and Masters, 1991a), based on analysis of long-period digital data, gives an upper mantle value of (d\nVs/dlnVP)p = 1.55 ±0.10. Because, oceanic lithosphere is not plagued by the numerous complications that result from seismic raypaths which traverse continental crust, this value represents a robust estimate for the upper mantle. On land, the recent study of Robertson and Woodhouse (1998), using ISC S and P station corrections, finds a nearly identical result of (d \nVs /d lnVp ) p = 1.56 ± 0.10. Lastly, the subtraction of predicted crustal S- and P-wave signals using CRUST 5.1 (Mooney et al., 1997) from mean travel time residuals at the global set of digital broad-band stations results in a strong global correlation Chapter 7, page 647 of S- to P-wave travel time residuals. The slope of the correlation line translates into (d \nVs 18 lnVP ) p = 1.64, a value within error of the digital long-period "oceanic" value of Woodward and Masters (1991a) and the short-period, ISC station correction value of Robertson and Woodhouse (1998). Progressing deeper, the regional studies of Jordan and Lynn (1974) and Bokelmann and Silver (1983), which sample the top of the lower mantle below the Caribbean, find a slight increase relative to the upper mantle with both of their studies inferring (dhiVs/d]nVP)r = 1.70 ± 0.20 for the depth interval of 660 - 1300 km. This value is in agreement with that independently estimated by Bolton (1996) from comparing co-located, cap-averaged long-period, absolute S and P travel time residuals, (8ts/8tp) in the depth interval 650-1100 km. The regional Caribbean estimate is within error of the statistical lower mantle average calculated by analyzing the variance of the ISC S- and P-wave travel time residuals (Davies et al., 1992; (dlnVs/8lnVp)p - 1.80). The implication is that the mineralogy of subducting slabs, assuming the Caribbean anomaly is representative, does not result in unusual perturbations in the relative magnitude between S and P-wave velocities anomalies. Because the S-wave arrivals in the ISC data base are contaminated by SKS and ScS arrivals at roughly 80° epicentral distance, this latter estimate is applicable from 660 to only 2450 km in depth, and thus is not representative of the lower most part of the lower mantle. At the base of the lower mantle there exist somewhat conflicting results that appear to be sensitive to the geographical areas that are sampled. Pulver and Masters (1990) compared a preliminary data base of co-located, cap averaged differential travel time Chapter 7, page 648 residuals for ScS-S and PcP-P, ($tScS_s, &tPcP_p) and determined the resultant scaling factor (d \nVs/d lnVp ) p = 1.70. This value is both in agreement with, and in conflict with, the various results of Bolton (1996). He used co-located, cap averaged ratios of absolute S and P-wave travel time residuals in 4 depth bins across the lower mantle and found (d lnVs fd h\Vp)p to progressively increase with depth from 1.70 (650-1100 km) to 3.40 (2300-2890 km). The latter value is in strong disagreement with Pulver and Masters estimate. However, Bolton (1996) notes that within this deepest depth bin, most of the increase in (d lnVs /d lnVp ) p reflects anomalous arrival times whose raypaths bottom out in the basal 300 km of the lower mantle, with the upper 300 km of this bin having a relatively lower (d lnVs /d lnVp ) p value. Furthermore, Bolton (1996) noted that when anomalous S-wave travel time residuals that originate in a geographically restricted area southeast of Hawaii are removed from consideration, the resulting (d lnVs /d \nVp ) p value in the lowermost layer (2300-2890 km) decrease from 3.40 to 1.70. This value is identical to that of Pulver and Masters (1990). Indeed, when the line (fit by least squares) that represents the global correlation of absolute S-wave residuals to P-wave residuals is compared to the line required to maintain (d \nVs jd lnF ; J ) p = 1.70, it is clear that only a slight amount of counter-clockwise rotation has occurred for the intermediate depth bins, implying that the progressive increase discovered by Bolton (1996) reflects the effects of only a few anomalous cap-averages. Because the anomalous area recognized by Bolton (1996) connects with a large-scale "superplume" like feature which rises from the core-mantle boundary to just below the transition zone in the central Pacific, there exists the possibility that the progressive increase Chapter 7, page 649 in the two intermediate depth bins also reflects geographically restricted anomalous travel time residuals. Additional evidence that the progressive increase m(dkiVs/d\nVp)p with depth, as deduced by the 4 depth bins, is not a robust feature of the lower mantle comes from radial (d lnVs /d lnVp ) p profiles derived from the ratio of rms velocity amplitudes of joint, whole mantle S and P-wave tomographic models. Two of the most recent joint whole mantle models, WE1997 (Vasco and Johnson, 1997) and S16B3G7P16B30 (Bolton, 1996) are in excellent agreement with one another across the whole mantle, differing significantly only in D " region. The similarity between the (d lnVs /d lnVr ) p radial profiles from these two joint, whole mantle models should not be taken lightly. WE 1997 is based on a large data base of short period ( 1 - 4 second) ISC arrival times (P, PP, PcP, PKPa0, PKPDC, PKPdf S, SS, ScS, SKSac) and a preliminary data set of long-period differential precursor times (otss_s s and otss_S4wS (Shearer, 1993)). In contrast, S16B30 (Masters et al., 1996) and P16B30 (Bolton, 1996) are constructed using a large data base (30,000 each) of long-period (20-30 seconds) absolute S and P-wave travel time residuals, 5000 PP-P, 10,000 SS-S (extended sets from Woodward and Masters, 1991), and 5000 ScS-S and PcP-P (extended sets from Woodward and Masters, 1991b) long period, differential travel time residuals, 2034 spheroidal normal mode structure coefficients (Smith and Masters, 1989; Ritzwoller et al., 1986, 1988) and 10,000 Rayleigh and Love wave phase and amplitude velocity measurements of various periods between 70 and 250 seconds (Laske and Masters, 1996). The later two data sets have their greatest sensitivity in the upper 1000 km of the mantle, and hence substantially aid in constraining the amplitude and geographic position of the velocity Chapter 7, page 650 structure in the upper mantle and transition zone (in constructing the joint tomographic models, Bolton (1996) adopted (d]nVs/dhiVP)p = 1.70 and (dlnp/dlnJ^) p = 0.68 to the structure coefficients and Rayleigh wave data in the inversion algorithm for the P-wave tomographic model. Note that the resulting (dlaVs/d\nVp)p profile based on the ratio of rms velocity amplitudes is not dependent upon this input value as indicated by the profile which oscillates near 1.60). Thus, the data sets that went into constructing these joint models differ substantially (as does the model parameterization and inversion technique), yet the relative amplitude of S to P-wave velocity heterogeneity, as measured by the radial profile of the (d inVs /d InV,, ) p calculated from rms velocity amplitudes from the respective joint models, is very similar in overall shape and absolute value. This similarity argues strongly that these two independent radial profiles are converging to that of the Earth's mantle. Lastly, the radial depth dependent(d\nVs/d\nVp)p profile based on free-oscillation seismology (Ishii and Tromp, 1998) is very similar to the rms ratio based profiles of Bolton (1996) and Vasco and Johnson (1998). It is interesting to note that this profile, the first free-oscillation estimate to utilize the digital records for the two 1994 deep large earthquakes, and the first normal mode estimate to explicitly include depth dependence, predicts a nearly constant value of « 1.70 across the basal 700 km of the lower mantle. This value agrees with that of Pulver and Masters (1990) and with the "filtered" depth bin value of Bolton (1996) when anomalous S-wave residuals are removed. That the free-oscillation profile differ from the two rms ratio profiles (Bolton, 1996; Vasco and Johnson, 1998) may be due to the latter Chapter 7, page 651 two profiles uneven sampling of the lower most mantle such that they exhibit an increased sensitivity to the anomalously slow S-wave anomaly in the south-central Pacific. The only discrepancy among the recent seismic estimates are the (d lnVs /d lnVp )p profiles which are based upon the assumption that the joint S- and P-wave tomographic models are 100% spatially correlated. When Robertson and Woodhouse (1996a) and Bolton (1996) invoke this assumption, the resulting (d lnVs/d\nVp ) p profiles exhibit a progressive increase across the lower mantle that systematically deviates away from the (d\nVs /dlnVP)p profiles based on the ratio of rms velocity amplitudes (see figure 7.30). Robertson and Woodhouse (1996a) argue that assuming a 100% spatial correlation between the joint S-and P-wave models and then inverting the combined shear and compression wave data sets to calculate (d lnVs /d lnVp ) p as a function of depth is to be preferred over simply taking the ratio of rms velocity amplitudes. However, they demonstrate, by filtering their data set to include only observations where both P - and S-wave arrivals from the same earthquake and recorded on the same seismometer are used in the numerical inversion, that damping in the inversion process is not a factor affecting the rms ratio based (dlnVs /d\nVp)p profiles (see figure 7.23). Therefore, concerns about different levels of damping in deriving the joint S- and P-wave models is not a valid reason to dismiss rms-ratio derive (d lnVs /8 lnVp ) p profiles. In summary, inspection of figure 7.41 reveals that the whole mantle is characterized by radial (d lnVs /d lnVp )p profiles which are nearly constant across the full depth extent of the mantle and which, in general, oscillate around «1.55 ± 0 . 3 0 , where the latter error estimate is simply visually inferred from the extremal bounds in this figure. It is encouraging Chapter 7, page 652 < that a number of different workers, using different data sets and techniques are finding relatively consistent results. 7.13 Previous estimates of (d lnVs /d lnVP )p from Mineral Physics. In this section we briefly review the mineral physics studies which have focussed on constraining (d \nVs/d \nVp)p. First, I discuss theoretical studies and then turn to more limited number of experimental studies. While in the previous section it was concluded that the seismic estimates are not unusually high, with recent estimates giving relatively constant values of roughly 1.55 ± 0.30 across the whole mantle, it should be stated at the outset of this section that the theoretical studies reviewed below were motivated to explain the "high" values of 2.0-2.5 in the lower mantle advocated by Dziewonski and Woodhouse (1987). Thus, these mineral physics studies have been attempting to justify high values which are likely artifacts (recall that Dziewonski and Woodhouse (1987) used the ratio of rms velocity from independent, rather than joint, S- and P-wave tomographic models in calculating the(3 lnVs/d lnVP)p . Subsequent studies which compare joint, whole mantle models have derived lower values using this particular method). While it is still not possible to experimentally measure shear and compression velocities at temperature and pressure conditions of the lower mantle, recent advances in experimental technique do allow these properties to be measured at upper mantle (Li et al., 1998). Because the experimental advances are very recent, the number of relevant mantle Chapter 7, page 653 minerals studied to date is small; nevertheless, these studies provide the first direct experimental measurements with which to compare the seismic and theoretical estimates to. 7.14 Theoretical Mineral Physics estimates; molecular dynamics simulations To reconcile the high seismic estimates of Dziewonski and Woodhouse (1987) with the low pressure experimental estimates of (d lnVs /d lnVP )p , a number of theoretical studies have been made to estimate the affects of high pressure on the elastic properties of lower mantle minerals. The ratio (d \nVs /d lnVp )p may be dissected into a combination of dimensionless thermoelastic parameters (e.g. Isaak et al., 1992); dlnVPjp ( r - i ) l + 4 P 3K s J \KSJ r -v 3K s J In this form, the ratio (d \nVs /d lnVp )p is dependent upon three parameters; 85 the adiabatic Anderson-Gruneisen parameter, F which is the corresponding shear modulus parameter, and (\JL/KS) , the ratio of the shear to adiabatic bulk modulus, where p is the shear modulus and ^ s is the adiabatic bulk modulus. In turn, 85 and F are defined as (e.g. Anderson, 1967): S 5 =-| [dT j and f 1 A r = v a p y Chapter 7, page 654 where a is the coefficient of thermal expansion. Inspection of the above relationship for (d lnVs /d InV,, ) p reveals that it will increase i f 85 decreases with increasing pressure (assuming that both F and (yi/Ks) are relatively insensitive to pressure). Radial profiles of both the shear and adiabatic bulk moduli are available across the lower mantle from seismic reference Earth models (e.g. PREM, akl35) and show that (n/Ks) is relatively constant at « 0.50 (see figure 7.42). Thus, whether or not the logarithmic ratio {d\nVs/d\nVp)f increases with pressure is reduced to determining the pressure dependence of the two dimensionless parameters a n d T- The room pressure values for 85 range from 3 to 6 (Agnon and Bukowinski, 1990) which must drop to values of 1.0 to 1.8 (assuming that F is constant at roughly room pressure values of 5.8 - 7.0) to cause (d \nVs /d \nVP ) p to increase to seismic estimates (Anderson, 1987a). Anderson (1987a) estimated these values from lateral variations in some of the earliest seismic tomographic models and the density model of Hager et al. (1985) under the assumption that the lower mantle is adiabatic and that the lateral variations reflect only variations in temperature. As noted by Agnon and Bukowinski (1990), the amplitude of the lateral density anomalies in the Hager et al., (1984) model depend upon both the viscosity model and the value of the scaling factor, (51np/91nF s ) p used to convert the velocity anomalies into equivalent density models. Increasing the amplitude of the density anomalies requires that a smaller value for F be inferred (within the modeling framework of Anderson, 1987). To determine i f pressure will cause 85 to decrease, but leave F relatively unaffected, as Anderson (1987) infers, a number of molecular dynamics simulations have been performed and these will be reviewed here. Chapter 7, page 655 Agnon and Bukowinski (1990) used molecular dynamics computer simulations to model the behavior of the adiabatic Anderson-Gruneisen parameter, ds for MgO as a function of pressure and temperature of the lower mantle (MgO, the Mg end member of magnesiowustite, is one of three minerals comprising the lower mantle). Because simple cubic oxides are relatively straightforward to model in terms of molecular dynamics and because a large high temperature and moderate pressure experimental data base exists with which to compare theoretical results to, the thermoelastic properties of MgO have often been the mineral of choice when calculating predicted mineral properties in the lower mantle. They calculated the variation of ds as a function of pressure along moderate (500 K) and high temperature (1500 K) isotherms and their results are re-plotted in figure 7.43. It is clear that OS decreases with increasing pressure, and hence together with an assumption of near constant T, indicates that the ratio (dlnVs /d\nVP)p should increase to high values in the lower mantle (Agnon and Bukowinski (1990) did not model Y directly, and instead only estimated lower bounds on this parameter of Y > 5). Of course implicit in this is that MgO is a good proxy for the thermoelastic properties of Mg-perovskite, the predominant mineral by volume (70-77 vol%) in the lower mantle. Parker and Wall (1991) also used molecular dynamics to estimate the constant temperature logarithmic ratio (d\nVs /<31np)T for both MgO and Mg-perovskite. This ratio is related to the constant pressure logarithmic ratio (the ratio of interest) via the thermodynamic relationship: ( a imya in P ) p {d\nVP/d\np\ ' dlnVs S l n F Chapter 7, page 6 5 6 and 1 ( mnVs ] { 5 1 n p J n I 31np J T aT I D L N T J Thus, Parker and Wall (1991) estimated the first term on the right hand side of the second equation (they admitted their molecular dynamics simulations were incapable of accurately predicting the remaining parameters of the second term on the right hand side). They predicted radial profiles of (d lnVs /d lnp)T and (51nF p/31np)T , both at constant temperature, and combined these to obtain (dlnVs/dlnVr ) T . They find that for both MgO and Mg-perovskite, this isothermal ratio decreases with increasing pressure across the lower mantle to reach values of 0 . 4 0 at the core-mantle boundary (see figure 7 . 4 4 ) . Both their absolute values and the negative trend are in sharp disagreement with the seismic estimates, but it should be stressed that the logarithmic ratio they calculate is not directly comparable since they did not calculate and include the term — (dlnVs/dlnT) . Consequently, it a T may be premature to assign too much significance to this particular result since the discrepancy between their predicted values and the seismic results may simply reflect unaccounted terms. Isaak et al. (1992) have undertaken the most complete molecular dynamics simulation to date concerning the possible effects of high temperature and pressure on (d \nVs /d \nVr )p for MgO. They modeled T as a function of both high temperature and pressure and found that after an initial decrease from high ambient values at the surface, T was nearly constant across the lower mantle at « 5 . 0 (see figure 7 . 4 5 ) . Combined with values for ds, which they find Chapter 7, page 657 decreases across the lower mantle, and (\±/Ks) for MgO, they calculated (d \nVs/d lnVp)p across the mantle for two isotherms and these are re-plotted in figure 7.46. It is clear from this figure that for MgO, the combined affects of high temperature and pressure result in Nevertheless, it should be noted that MgO is only a relatively minor constituent (<15 vol%) of the mineralogy of the lower mantle, and therefore, an implicit assumption in comparing periclase molecular dynamics predictions results to those inferred from seismic tomography is that the thermoelastic characteristics of MgO closely approximate Mg-perovksite. Because the ambient adiabatic bulk and shear moduli of MgO is significantly different from Mg-perovskite, it is not obvious that this assumption is necessarily a good one. Robertson and Woodhouse (1996b) combined estimates for density to velocity scaling factors used in viscous flow studies with some of the molecular dynamics results discussed above to interpret their "100%-(51nF s/51nF /,) p profiles. They noted that the expression for a (dlnVs/d\nVp)p profile which is in excellent agreement with the seismic results. (d ]nVs /8 lnVP ) p given by Isaak et al., (1992): 4 p 3 K s could be simplified slightly by substituting the following expression for T: where the parameter (dlnp/8lnVs)p is the density to S-wave velocity scaling factor. The resulting expression for (d lnVs /8 lnVP ) p is: Chapter 7, page 658 dlnV^ ydlnVp y P 1 51np ( 6 s - l ) - 4 t l y P 3 K s dlnVs Robertson and Woodhouse (1996b) note that because the ratio \i/Ks is nearly constant across the lower mantle (« 0.50), the ratio (d lnVs jd lnF ; ) ) p is only dependent upon the function (31np/31nFs.)p (8S -1) across the lower mantle. They utilize a number of different estimates of (d\npjdlnVs\ from viscous flow studies which combine seismic and geodynamic results (e.g. Forte et al., 1993; King and Masters, 1992) or theoretical mineral physics studies (Karato, 1993) together with 8S from the literature. However, it should be noted that none of the viscous flow studies undertaken to date have properly constrained the (31np/91nK s ) p profile; a (dlnp/SlnJ^. ) p profile, a radial viscosity profile, and the 3D velocity structure from a seismic tomographic model are utilized in viscous flow studies to model the long wavelength geoid field. The viscosity profile is usually held fixed and the (dlnp/dlnVs ) p profile, which converts the velocity anomalies into density anomalies, is perturbed to maximize the fit to the observed geoid or free-air gravity field. Because the radial viscosity profile of the Earth's mantle is still a controversial subject, the resulting (dlnp/dlnVs\ profiles are highly non-unique. A few studies have attempted to solve simultaneously for both the (d lnp/3 lnVs ) p and viscosity profiles, but concluded that the inversion is very poorly constrained, such that the resulting profiles are only weakly constrained (Corrieau et al., 1994). In addition, recent studies have introduced chemical scaling factors ((91np/51nF s ^ h e m ), in addition to the conventional thermal scaling factor Chapter 7, page 659 (dlnp/3lnVs \ ,to convert seismic velocity anomalies into density (Forte et al., 1995a, b). It is argued that this additional contribution is needed to reflect the anomalous chemical composition of the sub-crustal lithosphere relative to the composition of normal, ambient upper mantle. Thus, it appears that Robertson and Woodhouse (1996b) have effectively converted the expression for (d lnVs /3 lnVP ) p based on two uncertain mineral physics parameters (T and 8S) into an equivalent one, also based on two unknown parameters ((d lnp/3 In Vs ) p and 8S)- While they conclude mineral physics estimates are in agreement with their high seismic value derived on assuming a 100% spatial correlation of S- and P-wave anomalies, I concluded in the previous section, which reviewed the seismic inferences of (d lnVs I3 \nVp ) p , that their profile was likely to be an artifact of forcing a 100% correlation. Lastly, I note that only when (d lnp/3 In Vs ) p from viscous flow models was used in estimating (d \nVs /3 InV,, ) p , did the mineral physics estimates approximate their results -the mineral physics estimates of (3 lnp/3 In F s ) p resulted in no agreement. Interestingly, both of the (3 InVjd lnV,,)p profiles from Isaak et a l , (1992) and Karato (1993) are in sharp disagreement with the Robertson and Woodhouse (1996a) tomographic profile, yet both of these agree very well with the preferred seismic results discussed above. 7.15 (3 InVjd \nVP)r: hydrous Partial Melts in the Lower Mantle? The theoretical mineral physics studies reviewed above evaluated the possibility that the combined effects of high temperature and pressure on the dry bulk mineralogy would be Chapter 7, page 660 sufficient to result in an increase in (d \nVs/dlnVr)p to values equal of the seismic estimates of Dziewonski and Woodhouse (1987). Anderson et al., (1987) suggested partial melt as one possible explanation of the high values of (d\nVs/dlnVP)p in the lower mantle since it is widely accepted that small amounts of partial melt will affect the shear velocity to a much greater degree than the compression velocity, and consequently, will result in larger perturbations in shear than compression velocity (e.g. Anderson and Sammis, 1970). The hypothesis that the high values of Dziewonski and Woodhouse (1987) reflects partial melt has been explored in greater detail by Duffy and Ahrens (1992b) who considered a variety of possible melt geometry's and their related affect on (d lnVs /8 lnVr )p . If the lateral velocity variations solely reflect variations in the shear modulus (//), the parameter (dlnVs /8lnVp)p reduces to (Anderson, 1987): r8lnVs) _ 5p f l / 2 ^ 8\nV„ V p j v 5Ks+^b[i Xi i , \ 3 V P {melt} => -4*7 Duffy and Ahrens (1992b) point out that for the lower mantle, the ratio of compression to shear velocity, V,,/Vs «1.8 , resulting in (d lnVs /d InV,, ) p « 2.4. I have re-evaluated (d lnVs 18 \nVp)p = (3>V}/4V^) throughout the lower mantle using the velocities from the akl35 global reference earth model (Kennett et al., 1995) and the (d \nVs /d lnVP )P>artial melt profile is plotted in figure 7.47. Inspection of this figure shows that a partial melt results in (5 lnVs/8 lnVp) profile which smoothly increases with increasing depth from « 2.4 to « 2.7 across the lower mantle. Indeed, the melt derived profile actually appears to be too high, even with respect to the early seismic estimate of Dziewonski and Woodhouse (1987). Chapter 7, page 661 When compared to recent seismic estimates, also plotted in this figure, it is clear that the melt-derived profile does not provide a good match to these recent, and more robust, estimates. It is interesting to note that in the D " region, the (d lnVs jd \xsVP )^a r t i a l m e " profile is less than the seismic profile of Bolton (1996) based on the ratio of rms velocity amplitudes from his joint, whole mantle S- and P-wave tomographic models. Taken at face value, this discrepancy implies that the high values he derives for the D" region cannot be solely explained by the presence of temperature and partial melt, and instead, might require either a change in chemistry or strong seismic attenuation effects. Alternatively, the (3 lnVsjd I n p r o f i l e of Vasco and Johnson (1998), also based on the ratio of rms velocity amplitudes from joint, whole mantle S- and P-wave tomographic models, does not undergo the same degree of increase in the D" region as Bolton's estimate, and consequently, implies that partial melt is not necessarily required to explain the relative perturbations in velocity. Recall that Vasco and Johnson (1998) included a number of deep seismic phases which penetrate the outer and inner core and which result in very good sensitivity to D" velocity structure. In addition, in their numerical inversion for the joint whole mantle, they solved simultaneously for both velocity heterogeneity and core-mantle boundary topography (along with topography on the 410 and 660 km mantle discontinuities and inner-outer core boundary topography, and inner core anisotropy). In contrast, the joint S- and P-wave tomographic models constructed by Bolton (1996) are purely volumetric models in that no consideration of mantle discontinuity topography or core-mantle boundary topography was made. Thus, in the lowermost mantle, it is likely that {d lnVsjd l n F ; J ) p profile of Vasco and Johnson (1998) is more robust than Bolton's. Chapter 7, page 662 In figure 7.48 I compare the (d \nVs /8 \nVP ) p a r t i a l m e , t profile against the seismic (d\nVs/d\nVP)p profiles that were calculated assuming a 100% spatial correlation between the velocity anomalies in the joint S- and P-wave tomographic models (Robertson and Woodhouse, 1996a; Bolton, 1996). While I have argued previously that these particular profiles are not robust I nevertheless, compare them against the melt-derived profile. It is clear that while the melt-derived and seismic profiles intersect in the lower third of the mantle, the respective curves possess distinctly different slopes, and in addition, for the whole mantle profile of Bolton (1996), the partial melt-derived profile is incapable of explaining the high values in the lower most 600 km of the lower mantle. The discrepancy between these seismic profiles and the partial melt profile demonstrates that inspite of the gradual increase with depth exhibited by both the seismic profiles and the partial melt profile, it is unlikely that these particular seismic results can be simply explained by invoking the presence of partial melt. Although one could envision a situation where the volume or geometry of partial melt changed progressively with increasing depth in the lower mantle such that the final profile equals the shape and absolute values of the 100%-(<9 In Vs/8\nVp)p profile, this situation would appear to require some special pleading. Lastly, in figure 7.49 I compare the melt-derived (d lnVs/d lnVP)p profile against the seismic profiles of Robertson and Woodhouse (1995) which are based on the ratio of the rms velocity amplitudes of their lower mantle joint S- and P-wave tomographic models. Note that the very high values (>3.0) characterizing the "hump" of the their rms-ration (5 \nVs/d \nVp) profiles can not be easily explained by the presence of a partial melt, since their values substantially exceed the partial melt profile. Chapter 7, page 663 Thus far, in the melt-derived profile it has been implicitly assumed that sufficient partial melt is present to drive the "dry" (d \nVs/d lnV,,)p profile completely to its equivalent "wet" (d \nVs/d lnVP) profile. The question on what effect relatively small amounts of partial melt, randomly distributed throughout the lower mantle, has on dry (3 In Vs/d In Vp) profile been investigated in detail by Duffy and Ahrens (1992b). They modeled the effects of a variety of possible melt geometry's together with various amounts of partial melt on (3 \nVs/d \nVP)p using the methodology of Watt et al. (1976), for partial melt distributed in either tubes and spheres, and of Walsh (1969), for partial melt distributed in penny-shaped inclusions. These techniques predict the effect of a prescribed melt geometry and volume on the shear and adiabatic bulk modulus, where Duffy and Anderson (1992b) assumed that the melt-free solid properties were adequately represented by the seismic reference model P R E M (Dziewonski and Anderson, 1981). In addition, they adopted {dVP/dT)p =0.2 m / sec AT , estimated on the basis of bulk sound velocity systematics (Duffy and Ahrens, 1992a) and assumed that the shear velocity temperature derivative was related to the compression velocity one via: (dVs/dT)p = 0J5{dVP/8T)p. Together, these assumptions result in their melt-free estimate for (3 lnVs/d \nVP)p via the relationship: rd\nVs) VP(dVs/dT)p (vp) 0.75 (dVP/8T)p d\nVp Vs(dVP/dT)p [Vs ),„<,,., (SVP/dT) Chapter 7, page 664. One of their plots is shown in figure 7.50. The curve in this figure labeled 0% melt represents their calculated melt free lower mantle (5 l n ^ / d l n F / ) ) p profile, while the other curves represent the effect of progressively greater amounts of melt (melt fractions 0.5, 1, and 2%) distributed randomly in elongate tubes. Also plotted is the seismic range inferred by Dziewonski and Woodhouse (1987). Taking their melt-free (d lnVs/d lnVp)p profile at face value, then it is clear from this figure that some amount of partial melt is required to satisfy the Dziewonski and Woodhouse (1987) tomographic estimate. However, in the previous sections it has been clearly shown that recent, and more robust seismic estimates for the lower mantle give (d \nVs/d \nVP)p profiles which are substantially lower than this early estimate. Indeed, this is clearly illustrated in figure 7.51 where the recent seismic observations are compared to Duffy and Ahrens (1992) results. While the melt-free estimate is slightly on the low side of the seismic estimates, this likely reflects the uncertain assumptions that Duffy and Ahrens (1992a) made for the Vs and Vp temperature derivatives. Nevertheless, the resulting melt-free (d \nVs/d \nVp)p profile is very similar to the recent seismic inferences and suggests that with better constraints on the (dVs/8T)p and (dVp/dT)p , the slight discrepancy between the melt free and seismic estimates may be removed. A second feature which is illustrated in this figure is the large discrepancy between the partial melt curves calculated by Duffy and Ahrens (1992a) and the seismic estimates. Note that even the (d lnVs /d \nVP )pw t i a l m e l t for 0.5% randomly oriented partial melt (distributed in tubes) is significantly greater than the seismic estimates. This discrepancy Chapter 7, page 665 would increase i f the same melt volume was distributed in thin films, but would stay roughly similar for a spherical melt geometry. Thus, i f one must invoke the presence of partial melt to explain the seismic derived (d l n F s / 5 In F p ) p profiles, then these results suggest that the melt volume is very small. While I note that because the bulk modulus of a lower mantle partial melt is unknown, the above calculations were done assuming that K'!!e" = K™LM , an assumption that is very likely to be wrong given that experimental studies have concluded that the bulk moduli of silicate melts is well below that of solids (see Herzberg, 1987 for a reveiw; Miller et al. (1991) experimentally determined that for a komatiite melt, the room pressure adiabatic bulk modulus was Kg = 27.0 GPa. Recall that for Mg-perovskite the equivalent parameter is Kg « 260.0 GPa). Duffy and Ahrens (1992a) considered the effects on (d lnVs/d lnF^ ) p a r t , a l m e l t for different assumed values of K'™" using the shock-wave derived bulk moduli for the solid brucite (Mg(OH)2) and for solid serpentine (Mg 3Si 20 5(OH) 4). The adiabatic bulk modulus and its pressure derivative are Ks = 51 ± 4 GPa and {dKs/8P)T = 5.0 ± 0.4 for brucite (Duffy et a l , 1991) and 220 + 71 GPa and 5.16 ± 2.81 for serpentine (Tyburczy et al., 1991). At high pressures, Duffy and Ahrens (1992a) note that the resulting Ks of brucite is 40-80% of P R E M while that of serpentine is equal to or greater than P R E M . While the (d lnVs /d lnVP ) ' a r t i a l m e U profile with K™" = brucite was much lower than that calculated with K™" = KpsmM at the top of the lower mantle, this profile converged towards the "melt = P R E M " (d \nVs /d lnVp ) p a r t i a l m e l t profile with increasing depth. For K'™" = serpentine, the effect on the (d \nVs /d \nVp ) p a r t i a l m e l t profile was modest with only a slight increase. These calculations can only indicate general trends Chapter 7, page 666 because, unfortunately, the composition of a lower-mantle partial melt is unknown, and hence, its Ks and (dKs/8P)T remain unmeasured. Before leaving this section I emphasize two points. First, it is evident from a comparison between the seismic (3 \nVs/d InVP) profiles and both the (dlnVs/dlnV,,)^0 profile, derived from molecular dynamics calculations (Isaak et al., 1992), and the melt-free (3 h\Vs/d I n p r o f i l e , estimated by Duffy and Ahrens (1992a), that there is no large discrepancy between mineral physics estimates and seismic inferences. What discrepancy that does exist is very slight and may disappear i f better mineral physics constraints are applied (see below). Furthermore, while the calculations of Duffy and Ahrens (1992a) clearly demonstrate that widespread partial melt can increase the melt free (3 \nVs/d In J ^ p profile to higher values, I note that all of the seismological effects of invoking partial melt across the full depth extent of the lower mantle have not been fully considered. It is widely accepted on the basis of experimental work together with regional tomographic studies on back arc basins and mid-ocean ridges, that widespread partial melt will significantly perturb the attenuation properties of melt-bearing mantle. If the lower mantle did in fact possess widespread partial melt, then this should clearly be reflected in the radial reference models of shear attenuation through the seismic Qs parameter, with the lower mantle having Qs values similar to that of the shallow upper mantle (Qs = 50-70). However, all of the attenuation models constructed to satisfy normal mode attenuation observations, (e.g. Q M U (Sailor and Dziewonski, 1978); SL8 (Anderson & Hart, 1978); PREM (Dziewonski and Anderson, 1981); QM1 (Widmer, Masters, & Gilbert, 1991); QL6 (Durek & Ekstrom, 1996); akl35-Q and akl35-F (Montagner and Kennett, 1996)) have, the Chapter 7, page 667 highest Qs values in the lower mantle, strongly implying that the lower mantle is melt-free (see figure 7.52). Therefore, it appears that the hypothesis of widespread partial melt within the lower mantle is actually not required by seismic (d lnVs/d lnVp)p inferences on one hand, and is in strong conflict with seismically inferred Qs values on the other. Hence, the hypothesis that widespread partial melt within the lower mantle is responsible for "large" seismic (5 In Vs/d In VP)p inferences is not a viable one. I qualify this statement with one caveat; the D" layer at the base of the lower mantle does exhibit extreme velocity heterogeneity (± 3-4% 8 ^ , 8 ^ ), with some studies inferring extreme velocity decreases in shear waves in a relatively thin, basal layer (-5-10% dVs ). These anomalies been interpreted by some to reflect the effects of a thin zone of partial melt (e.g. Garnero et al., 1998; in press; Lay et al., in press; Williams and Garnero, 1996). Returning to the topic of this chapter, it is tempting to ascribe the increase near the D " layer in the rms-ratio (5 In Vs/dlnVp)p profiles of Vasco and Johnson (1998) and Bolton (1996) to this effect, but I caution that the effects of strong decreases in seismic attenuation may result in a similar feature in the (5 lnVs/d \nVp) profile. I also point out that virtually all of the interpretations that favour a thin layer of partial melt are usually based on a single data type (e.g. 6VS ) rather than a complete characterization (e.g. 8VS,8VP, Sp, Qs, Q,,,h , where p is density, Qs and Qp are shear and compression seismic attenuation, and h is layer thickness). Those D" layer studies which have attempted to interpret their seismic observations have admitted that the magnitude of Chapter 7, page 668 the inferred seismic velocity drop across the basal layer trades off with the layer thickness, such that a very thin layer (e.g. 5 km) must possess a very large velocity drop (e.g. - 10% 8VS ) while a thick layer (e.g. 50 km) is characterized by a modest drop (e.g. -5%; Garnero et al., in press). In addition, the density structure of the D" layer itself, and of the thin basal layer is also of critical importance (recall that Vs = ^/p/p , Vp = S](KS + | p)/p ) with some advocating a density increase across the D" layer (Kumagai et al., 1992). In addition, it should be recalled that the anomalies are inferred relative to a reference velocity profile, which in the D" seismological studies, has been P R E M . A subsequent global reference velocity model, SP6, constructed to fit travel times of P, PcP-P, PKPao, PKPbc, and PKP df and S, SKS, and SKKS-SKS phases by the Harvard group (Morelli and Dziewonski, 1993) has negative V$ and Vp gradients in the D" layer and absolute velocities which are lower than those in P R E M (see figure 7.53). They state that with the thickness of D " layer held fixed, the velocity gradients in the D " layer had to be negative to reproduce the traveltime observations. They stress that their velocity structure is to be taken as a global average, because regional studies have resolved considerable velocity heterogeneity in the D" layer. Also plotted in this figure are the results of Kumagai et al., (1992) who used a set of normal modes which are sensitive to deep mantle velocity and density structure to refine these properties in the D" layer. They found that when the they constrained the relative perturbations of velocity to be of the same sign (&VS/VS = &VP/VP , with the velocity structure above the D " layer equal to P R E M , while the velocity structure within the D " layer assumed to be simple linear gradients), the resulting density structure had to be positive (see figure 7.53). Because free-oscillations provide good mantle averages of structure, the Chapter 7, page 669 resulting density structure may be considered a global average. Thus, the velocity structure of SP6 and the combined velocity and density model of Kumagai et al. (1992) imply that P R E M velocities are too high, while the density structure is too low. Changing both of these features will then modify the magnitude of the inferred velocity heterogeneity inferred for the D " layer. Another consideration is the possible effects of topography on the core mantle boundary. Recall that in the joint, whole mantle tomographic models of Vasco and Johnson (1998), where they solved for both core-mantle boundary topography and mantle velocity heterogeneity, they noted that the magnitude of the inferred topography traded off against the magnitude of the velocity heterogeneity in the D" layer which sits directly above the C M B . This is important, because all of the regional seismic studies which have probed the D" velocity structure, have done so, assuming zero topography on the C M B . Lastly, the D " layer is currently interpreted to represent both a thermal and chemical boundary layer with the temperature structure rising rapidly with increasing depth in the D " layer, from the mantle adiabatic geotherm to link up with the much higher core geotherm (e.g. Loper and Lay, 1995; Boehler et al., 1995). The magnitude of the temperature jump across the D" layer is at least 1500°K based on the offset between the mantle and core geotherms and such a temperature increase should result in rapidly decreasing seismic Qs and Qp structure. Garnero et al. (in press) undertook some preliminary modeling with low Q values and stated with respect to very low Q values for the D" region that "such Q effects could easily be miss-mapped into ultra-low velocity zone velocity structure". Chapter 7, page 670 While a full consideration of the affects of attenuation on seismic velocities will be covered elsewhere, Karato (1993) has made a preliminary attempt to incorporate anelasticity effects in to density scaling factors and this study is reviewed next. 7.16 The effects of Anelasticity Karato (1993) argued that the temperature dependence of both S- and P-wave velocities should be strongly dependent upon both the purely elastic and anelastic properties of the minerals. Purely elastic effects are insensitive to the frequency of the elastic waves and are equivalent to the "temperature" effects that have been considered thus far in this thesis. In contrast, anelastic effects are associated with energy loss dependent upon the frequency of the elastic wave. For a weakly frequency dependent seismic attenuation model: where co is the angular frequency and a controls the frequency dependence, commonly assumed to be a constant value lying between 0.1 and 0.3 (e.g. Karato and Spetzler, 1990). For such a model, the dependence of seismic velocity on frequency is (Minster and Anderson, 1981): V{(*,T) = V0{T) 1-1 1 2 tan 'cwO Q{(o,T) v ^ J Taking the derivative with respect to temperature results in: ainK dT J? ainF0 dT (an/2) 1- A i / 'an} Q{(O,T)RT2 tan\ \ * J 7T Chapter 7, page 671 where (dlnV0 /dT)p represents the purely elastic temperature derivative, AH is the activation enthalpy, R is the gas constant, and the second term reflects anelastic effects. In the upper mantle Karato (1983) adopted the high temperature experimental value for olivine (Isaak, 1992) for (dlnV0 /dT)p whereas in the lower mantle he estimated this on systematics advocated in Duffy and Anderson (1989) while for the activation volume, he adopted 500 kJ/mole for the upper mantle, based on experimental results of Jackson et al. (1992) and in the lower mantle used the empirical relationship AH = gRTmell, where g is an empirical non-dimensional constant, commonly assumed to be equal 30 but with an uncertainty of at least ± 10, and Tmelt is the melting temperature of the lower mantle. For the mantle profile of Q Karato adopted the QM1 Qg and Qp profiles of Widmer et al. (1991) and admitted that his conclusions were dependent upon this particular profile (see figure 7.52), such that different Q profiles would result in different (dlnV/8T)p profiles. Karato (1993) then converted the logarithmic temperature derivatives into the dimensionless logarithmic ratio of density to velocity perturbations via the thermodynamic relationship: where in this expression, a is the coefficient of thermal expansion which Karato (1993) took from Chopelas and Boehler (1989). The latter study modeled the density structure of a two-component mixture of Mg-perovskite and magnesiowustite across the lower mantle and concluded with the data then at hand that density profiles alone could not be used to distinguish different proposed bulk chemical compositions of the lower mantle. One of the Chapter 7, page 672 steps in this study resulted in a profile of a(T, P), which has been used by a number of studies (Yuen et al., 1993; 1994; Matyska et al., 1994) in addition to Karato (1993). The resultant depth profiles of (dlnp/31nF s.) p and (51np/51nF /,)p are plotted in figure 7.54. Karato (1993) states that the large humps in the mid mantle directly reflect the hump in the adopted Q model. These two profiles may be combined to give (d In Vs/d In Vp) via the ratio: ' 51np ^ (d lnF s /d lmv) P = d\x\VP chip and this is shown in figure 7.55. While the similarity between the various preferred seismic profiles and Karato's is, at first glance, impressive, I stress that this is fortuitous and reflects the combination of a number of questionable assumptions adopted by Karato (1993) in deriving the purely elastic and anelastic temperature derivatives. For example, he noted that uncertainty in the constant g will result in at least a 30% uncertainty in the (dlnV/dT)p profiles. A n additional source of error, albeit not quantified, arises from the large uncertainty as to the appropriate lower mantle melting curve (e.g. Heinz and Jeanloz (1987) vs. Zerr and Boehler, 1993) which Karato (1993) admits will have a large, but unstated, effect on the calculated (dlnV/dT)p profiles (it is not even stated what particular melting curve is actually used for Tmelt in calculating AH in the lower mantle). A further source of uncertainty arises from the construction of the purely elastic temperature derivatives, (dlnV/8T)P . Karato (1993) stated he adopted temperature derivatives from Duffy and Anderson (1989) for deep mantle Chapter 7, page 673 mineral phases. However, virtually all of the thermoelastic parameters for Mg-perovskite, Ca-perovskite, and magnesiowustite listed in this particular study are "guesses" based on a controversial procedure, advocated by Anderson (1988), of predicting the material properties of unmeasured minerals based on a set of measured compounds, many of which are not mantle minerals, and consequently, have little relevance to geophysics. I have shown in previous chapters that nearly all of these parameters are incorrect when compared to subsequent experimental measurements. Furthermore, to use the temperature derivatives of Duffy and Anderson (1989), a mantle geotherm is required to correct the reference adiabatic and shear moduli, at 298 K , up to high temperature, e.g.: In a fashion similar to the lower mantle melting temperature, Karato (1993) does not tabulate or plot the mantle geotherm he used, nor does he provide a reference for it. Finally, I note that by adopting the QM1 seismic attenuation model, Karato (1993) is ignoring the known temperature dependence of seismic Q (e.g. Berckhemer et al., 1979; 1982a; Minster, 1980; Gueguen et al., 1989; Jackson, 1993). From experiments on mantle silicates seismic Qs is known to follow the Arrhenius relationship via: and p y geolherm geolherm 298). f A£ Q + PAK(r)) e; 1(co,r, JP) = e o co- a exp - a RT J Chapter 7, page 674 where co is the angular frequency, a, the coefficient of the frequency dependency, AEQ is the activation energy of attenuation, AV(r) is the activation volume of attenuation and may or may not be assumed to be a function of pressure, Q0 is a pre-exponential constant, P is pressure (GPa), T is absolute temperature (°K), and R is the gas constant. Thus, there exist quite a number of troubling aspects with Karato's (1993) study, which when considered in total, renders the resultant (d \nVs/d lnF, , ) p profile of dubious merit. I also point out that it is unclear from his study, what exactly are the effects of anelasticity on (d In p/d In Vp ) p , and hence (5 In Vs /d In VP) , because no calculated purely elastic profiles were provided with which to compare the combined purely elastic + anelastic profiles against. To correct this omission, in figure 7.56 I re-plot his calculated logarithmic purely elastic temperature derivatives, (dlnV/dT)p for shear and compression waves, and combine these, via the following relationship, to calculate the purely elastic (d\nVs/dlnVP)p profile. { ST J p (dlnVs/dlnVP)p = , dT This curve is plotted in figure 7.57 and it is clear that this profile is a worse fit to the preferred seismic estimates; nevertheless, the purely elastic curve does give an indication of the relative effect of seismic Q on the (d \nVsld l n F / ) ) p profile, albeit, I contend, only a qualitative one, in light of the number of uncertainties on how the purely elastic and anelastic {d\nV/dT)p profiles were constructed. Interestingly, the purely elastic profile is very near Chapter 7, page 675 the high temperature, room pressure value of 1.25 adopted by Masters et al. (1982) in free-oscillation studies, but less than that estimated by Duffy and Ahrens (1992b) for their melt-free purely elastic profile. Both purely elastic profiles are considerably less than the canonical lower mantle range of (d lnVs/d InV,,)p = 2.0 - 2.5 (Dziewonski and Woodhouse, 1987). 7.17 (d In Vs /d In VP)p from experimental mineral physics As noted earlier, limitations in experimental apparatus do not allow measurements at sufficiently high temperature and pressure so that the parameter (d \nVs/d \r\Vp)p may be directly measured at lower mantle conditions. However, recent advances have enabled researchers to measure the room temperature, shear modulus pressure derivative, (d\i/dP)T to pressure conditions approaching the top of the transition zone, and consequently, when combined with ambient pressure, high temperature experimental measurements of the shear modulus temperature derivative, (<3p/dT)p allow high temperature and pressure profiles of Vs and Vp to be constructed, which may be combined to give a (3 \nVs/8 \nVp) profile. Zaug et al. (1993) measured the room temperature values for both the shear and bulk moduli pressure derivatives for San Carlos olivine, (Mg 0 9 Fe 0 , )Si0 4 and combined these with independently measured, room pressure, but high temperature estimates of the shear and bulk moduli temperature derivatives to calculate (d InVjd lnVP)p at 0 GPa, 1100 °C and 13 GPa and 1400 °C. The former approximates the Chapter 7, page 676 value near the Earth's surface, while the latter approximates conditions near the 410 km seismic discontinuity ("approximate" in that these particular temperatures are somewhat below what the self-consistent adiabatic pyrolite geotherm predicts). These values are plotted in figure 7.58 together with the upper mantle estimate derived from the oceanic data of Woodward and Masters (1991a), the ISC station correction derived value of Robertson and Woodhouse (1998), the continental broadband "crustal" correction of Mooney et al., (1997), and finally, the estimate of Dziewonski and Woodhouse (1987). The calculated values of Zaug et al. (1993) cut across the average upper mantle estimates, being slightly lower at zero pressure and slightly higher at high pressure. Indeed, the arithmetic average of the Zaug et al. (1993) values is 1.55 in excellent agreement with that based on Woodward and Masters (1991a; (dlnVs/d]nVP)p = 1.55 ± 0.10). While it is tempting to extrapolate the trend exhibited by the Zaug et al. (1993) data to higher pressure (the trend projects to intersect the Dziewonski and Woodhouse (1987) inference at the top of the lower mantle), note that olivine converts to its P-polymorph at 410 km depth, and consequently, such an extrapolation is invalid. L i et al., (1998) describe preliminary results for polycrystalline olivine where the ultrasonic velocities were measured while the sample was subjected to simultaneous high temperature and pressure conditions (up 10 GPa and 1000°C; they plot some of their results but defer to a future publication to give the raw data and its interpretation). The major appeal to such studies is that it decreases the ambiguity in correcting up room temperature and pressure shear and bulk moduli to mantle conditions. Conventionally, the temperature derivatives are often measured on a sample at room pressure by one group (e.g. olivine Chapter 7, page 677 temperature derivatives of Isaak et al., 1992), while the pressure derivatives are measured at room temperature (but high pressure) by another group (e.g. olivine pressure derivatives from Duffy et al., 1995; Zha et al., 1996; L i et a l , 1998) on a different sample. Thus, there exists the potential that material properties measured for one sample may not be precisely applicable to the other due to minor differences in composition or physical properties (e.g. for synthetic crystals the degree of porosity), or lastly, inter-laboratory systematic biases. Therefore, measuring velocities at simultaneous high temperature and pressure will allow both the pressure and temperature derivatives to be extracted from the same sample under identical conditions. 7.18 Summary of Mineral physics estimates The mineral physics estimates, both theoretical and experimental, are plotted in figure 7.59. It is evident that there is no large discrepancy between the theoretical and experimental mineral physics inferences on one hand and the preferred seismic profiles on the other, although admittedly, the melt-free and purely elastic profiles lie on the low side of the seismic inferences. I caution, however, that the profiles of Karato (1993) and Duffy and Ahrens (1992b) are quite uncertain given the large number of approximations and assumptions that were made in constructing these particular (a lnJ^ /5 In Vp~) profiles. In contrast, the profile from the MgO molecular dynamics study (Isaak et al., 1992) suffers from the implicit assumption that the material properties of periclase are very similar to Mg-perovskite, the mineral which dominates by volume (70-77 vol%) the lower mantle mineralogy. Such an assumption is not supported by the large difference between the bulk Chapter 7, page 678 and shear moduli (at ambient conditions) for these two minerals. Therefore, to determine i f the preferred seismic ( d lnVs/d h\VP)p profiles may indeed be explained simply by lateral variations in a melt-free pyrolite mantle, I use the pyrolite mineral physics model described in the previous chapters to calculate a robust whole mantle (3 lnVs/d In Vp) profile. 7.19 Methodology I calculate the (d lnVs/d lnF^) profile via the relationship (Isaak, 1992): 'dlnVA = VP (dVs/dT\ {dlnVP)p Vs {dVp/8T\ and hence, require depth profiles of the shear, V$ and compression, Vp velocity across the mantle together with their associated temperature derivatives ({dVs/dT)pand(dVp /dT\ ). Rather than adopt the velocity profiles from a seismic reference models, I utilize the predicted V$ and Vp profiles for the pyrolite bulk composition, which provide an excellent fit across the whole mantle (see figure 7.60). Recall that this mineral physics model was first constructed by modeling bulk sound velocity (V®) and density (p) profiles, calculated along a self-consistent adiabatic geotherm. The temperature at the foot of the geotherm was chosen to be consistent with the MORB mantle potential temperature, determined independently from theoretical models of decompression melting at mid-ocean spreading ridges (e.g. McKenzie and Bickle, 1988; White et al., 1992; Brown and White, 1994). The mineral physics model was then extended to model Vs and Vp throughout the mantle by inclusion of shear moduli temperature and pressure terms. Chapter 7, page 679 To determine profiles for the two velocity derivatives I simply re- calculated the mineral physics model 100°K above and below the reference adiabat (see figure 7.61) which entails only increasing (or decreasing) the anchor temperatures at 100 km and 661 km respectively. By re-running the pyrolite mineral physics model at temperatures slightly above and below the reference model, I approximate the temperature derivatives by taking the average of the difference between the hot and cold profiles and the reference velocity profile. For example, for Vp : V dTj (AVA v AT, ((v ref - J/ Hl" \ (if ref - v C M V V? -V" Vp -V\, + rpref rpHot J ^ 'J'ref rpCold The resultant profiles of (d Vs/dT\ and^K,, /dT)p are combined with the pyrolite Vs and Vp profiles to calculate a self-consistent profile of (6 In Vs /8 In Vp ) throughout the mantle. Recall that the dimensionless thermoelastic parameters, Ss a*10" T may be recast in terms of the a, coefficient of thermal expansion, velocity, and the temperature derivative of velocity via: 1 dT Jp and r = --a p where p and Ks are the shear and adiabatic bulk moduli, respectively. The Anderson-Gruneisen parameter, 5s an& gamma, T may be combined to give; Chapter 7, page 680 rdlnVs^ dlnVP ( r - i ) 1 + i i L 3K s J s 3 r - i + 4 p 3 £ s J Recall that Agnon and Bukowinski (1990) and Isaak et a l , (1992) had used molecular dynamic computer simulations to determine that the Anderson-Gruneisen parameter for MgO decreases in an exponential-like fashion across the depth extent of the mantle (see figure 7.43) while T for MgO remains near constant. When these results are combined, the resulting (dlnVs /dlnVP )p profile (Isaak et al., 1992) provides a good match to the preferred seismic profiles, implying that there is no discrepancy between the seismic and mineral physics inferences. Again, I repeat that this conclusion implicitly assumes that MgO is a good proxy for the lower mantle mineralogy of Mg-perovskite, Ca-perovskite, and magnesiowustite. In a similar fashion to (dVs/dT)p, I calculate approximate, average pyrolite temperature derivatives for the adiabatic bulk and shear moduli ((dKs/dT)p, {d\i/dT\, ) and thus, calculate predicted pyrolite profiles for h$ and Y. These profiles include the thermoelastic properties of all of the minerals in the pyrolite assemblage, and thereby allow a more complete evaluation of {dlnVs /dlnVp )p based on expressions involving ds and T. 7.20 Results and Discussion Inspection of figure 7.62 shows that the calculated Pyrolite (5 lnVs/d l n F^p profile is relatively constant at « 1.25 in the upper mantle and transition zone. This lies below the "oceanic" average seismic estimate derived from the Woodward and Masters (1991b) Chapter 7, page 681 observations and that found by Mooney et al., (1998), but is bracketed by the tomographic rms ratio profiles of Vasco and Johnson (1998) and Bolton (1996). At the top of the lower mantle the pyrolite ( 9 lnVs/d lnVP)p profile increases abruptly to « 1.52 and then increases smoothly in a near linear fashion to « 1.82 at the base of the lower mantle (note that this profile does not include any chemical or attenuation affects which are to expected to affect the thermal/chemical boundary layer that forms the shallow-most upper mantle and D" layer). When the predicted ( 9 \nVs/d \nVP)p profile is compared to the preferred seismic inferences reviewed earlier, it is evident that there is good-to-excellent agreement across the whole mantle (see figure 7.63). The Pyrolite profile lies just within the regional seismic estimate from the Caribbean (Jordan and Lynn, 1974; Bokelmann and Silver, 1993) in the top of the lower mantle, but are in excellent agreement with the whole mantle, rms-ratio ( 9 InVjd lnVP)p profiles of Bolton (1996) and Vasco and Johnson (1998), and the depth dependent free-oscillation ( 9 lnVs/d \nVP)p profile of Ishii and Tromp (1998). Nevertheless, i f the minimum error estimates, that Bolton (1996) calculated for the 100% (d \nVs/d lnVp)p profile, are considered equally applicable to his rms-ratio ( 9 \nVs/d lnVp)p profile, then the pyrolite mineral physics estimate falls within the error envelope of this seismic estimate. In the depth interval where the statistical estimate of Davies et al. (1992) is applicable (660 - 2450 km), the arithmetic average of the pyrolite value is 1.59 in reasonable agreement with their inference ( ( 9 \nVs/d \nVP)p = 1.80) based on the variance of the ISC S and P-wave arrivals. In the D" layer, the predicted pyrolite Chapter 7, page 682 (3 \nVs/d lnVp) profile is in very good agreement with the Pulver and Masters (1990) inference and the Vasco and Johnson (1998) profile, but substantially less than calculated by Bolton (1996). As discussed earlier, the addition of many "core" seismic phases and the parameterization of core-mantle boundary topography in the tomographic inversion scheme of Vasco and Johnson (1998) suggest that their tomographic models are likely to have better resolution in the D" layer than the Bolton (1996) joint models. Hence, it is encouraging that of the two rms-ratio (d \a.Vs/d h\Vp)v profiles, the pyrolite (d lnVs/d \nVp)p profile is closer agreement to the tomographic profile (WEI997). In figure 7.64 I compare the pyrolite mineral physics prediction to the theoretical mineral physics estimates of Karato (1993), Duffy and Ahrens (1992b), and Isaak et al. (1992). Because I do not incorporate attenuation effects, the calculated Pyrolite profile is purely elastic and hence, should be compared to Karato's purely elastic profile and Duffy and Ahrens (1992b) melt-free profile. Inspection of this figure reveals that the predicted pyrolite profile is significantly greater than either the melt-free or purely elastic profiles, but slightly less than the isothermal MgO profile of Isaak et al. (1992). Both Karato (1993) and Duffy and Ahrens (1992) argued that the discrepancy between their purely elastic and melt-free profiles, respectively, and the seismic estimate of Dziewonski and Anderson (1987), required the incorporation of additional non-thermal mechanisms. However, It is evident from figure 7.64 that at least one source of uncertainty leading to the purported discrepancy was the low mineral physics values estimated by these authors. Thus, there is, in actuality, no large discrepancy between the seismic and mineral physics inferences. On one hand, the predicted pyrolite profile is greater than both the predicted purely elastic and melt free profiles of Chapter 7, page 683 Karato (1993) and Duffy and Ahrens (1992) respectively, and on the other, the recent seismic profiles to which I compare against, are lower. Taken together, these results indicate that there is, in fact, no compelling requirement to appeal to other mechanism than temperature perturbations, when interpreting velocity anomalies recovered in tomographic models. Recall that the Pyrolite mineral physics model has already been tested by comparing the predicted profiles of density and bulk sound velocity in one test, and the Vs and Vp profiles in another, against the seismic observations. These comparisons, discussed in the previous chapters, demonstrate that a melt-free, purely elastic, uniform-whole mantle, Pyrolite bulk composition provides an excellent match to the seismic observations. While the Pyrolite model is non-unique, and I admit that other, "pyrolite-like" mineral assemblages would like fit the seismic observations, the match between the predicted and seismic Vs and Vp profiles was apriori evidence that the mechanisms invoked by Karato (1993) and Duffy and Ahrens (1992) are not required (or alternatively, if these processes operate, then their effects are minor). The conclusions determined in previous chapters based on a comparison between predicted and seismic p and V® profiles on one hand, and Vs and Vp profiles on the other, is supported by the excellent agreement between the predicted Pyrolite (9 In Vsjd In VP)p profile and the recent seismic inferences found here. In terms of anelastic effects it is interesting to note that the predicted pyrolite(9 lnVs/d \nVp)p profile lies intermediate between the purely purely elastic and the combined purely elastic + anelastic profiles of Karato (1993) across most of the mantle. While the difference between Karato's purely elastic and anelastic profiles demonstrates that anelasticity will shift the (9 lnVs/d \nVp) profile to higher values (anelasticity will have a Chapter 7, page 684 greater effect on the shear, rather than the bulk, moduli, and consequently, all other things being equal, a perturbation in temperature will cause a greater perturbation in S- than P-wave velocity), the magnitude of the shift indicated by Karato (1993) is rather high, but, as emphasized earlier, also highly uncertain. To correctly incorporate the effects of anelasticity into the existing purely elastic mineral physics model will require a fully frequency, temperature, and pressure dependent seismic Q model for both shear and compression waves (Qs(a>,T,P) and Qp(us,T,P)). Inspite of the interest in attenuation by the seismological community, and consequently, the construction of radial Q profiles, this type of model does not, as of yet, exist. In figure 7.65 I compare the pyrolite (d\n.Vsld\x\.Vp) profile with the profiles estimated by Robertson and Woodhouse (1995; 1996a). I also show the rms-ratio profiles of Bolton (1996) and Vasco and Johnson (1998), the former plotted with the minimum error estimates taken from Bolton (1996) profile where he assumed a 100% spatial correlation between the S- and P-wave anomalies. While simply shifting the error estimates from one profile is not rigorously justified, this gives a crude idea of the possible errors one may infer for the whole tomographic profile of Bolton (1996). It is clear that across the upper 800 km of the lower mantle, the two different profiles of Robertson and Woodhouse (1995; 1996a) are in good agreement with the pyrolite profile. As discussed earlier, both the large "hump" in their rms-ratio derived(3 lnVs/d In Vp) profile and the large and abrupt increase in their 100%-correlation {d\nVsld\xiVP) profile are likely to be artifacts resulting from the progressive loss of resolution with increasing depth of the S-wave tomographic model relative to its sister P-wave model. This interpretation is strengthened by the predicted Chapter 7, page 685 ( 9 l n ^ / 9 l n F ^ p profile which demonstrates no abrupt or strong mid-mantle peak. With respect to the Bolton (1996) rms ratio profile, the predicted pyrolite profile lies outside the error estimates for the bulk of the upper mantle. This is significant, at least from the point of view of the mineral physics inference, since of the various depth intervals of the mantle, the elastic properties for shallow upper mantle minerals is by far, the best constrained. Thus, it may in this region that anelasticity and/or the effects of partial melt, are required to obtain better agreement between the seismic and mineral physics profiles. Now I evaluate the behaviour of 5 S and F as a function of high temperature and pressure using the pyrolite mineral physics model. Recall that (9 \nVs/d InY,,) may be transformed into a expression depending upon only three variables, (\i/Ks) , 5 S and F (Isaak et al., 1992; Anderson et al., 1992; Robertson and Woodhouse, 1996b); dlnV,, ( r - i ) l + 4 fi 3K s J Jv 1 + 4 \i 3K s J Figure 7.42, presented earlier, shows the (\i/Ks) ratio estimated from the P R E M seismic reference model together with the lower mantle ratio calculated from the shear and adiabatic bulk moduli of the pyrolite mineral physics model. Two points are worth noting. First, the pyrolite mineral physics ratio gives an excellent match across the full extent of the lower mantle, and consequently, this parameter is not going to result in a significant error in evaluating (9 \nVs/d \nVj,)p from its dimensionless components. Second, over the lower mantle, the (\i/Ks) ratio is effectively constant at 0.50, indicating that the depth dependence Chapter 7, page 686 of (d In Vs/d In Vp)p is largely controlled by the high temperature and pressure behaviour of only 5 S and F . I evaluate 5 S and T via their thermodynamic definitions (e.g. Anderson et al., 1992): aKs dT and a p From the pyrolite mineral physics model I calculate the lower mantle coefficient of thermal expansion following the expression of Ita and Stixrude (1992; their expression #18) and this result is shown in figure 7.66. My result is consistent with previous studies which, for simplified lower mantle mineral assemblages of only Mg-perovskite and magnesiowustite (e.g. Chopelas and Boehler, 1992), found that the coefficient of thermal expansion decreases with increasing depth (in this study, a decreases from « 2.5 x 10"5 K"1 to 1.2 x 10"5 K"1 across the lower mantle). The effective temperature derivatives of the shear (<3p/6T)p and adiabatic bulk moduli (d Ks /d T)p for the pyrolite mineralogy are approximated in the same way that the velocity temperature derivatives were estimated (e.g.); "* reI T Hoi ( nref -\icM ^ Figure 7.67 shows the calculated Pyrolite T profile and compares it with the estimated range of 5.80-7.00 of Anderson (1987a). His estimate was constructed by adopting the Chapter 7, page 687 seismic (9 \nVs/d lnVP)p range of Dziewonski and Woodhouse (1987; 2.0-2.5) and combining this with the logarithmic velocity to density scaling factor, (91np/91nFs, ) p = 1/(1.2) = 0.83, calculated from the geoid-tomography study of Hager et al., (1984). For a preferred value of (d\nVs/d\nVP)p = 2.0, Anderson (1987a) predicted T = 5.80. Also shown if figure 7.67 are the high temperature, but room pressure, experimental values of O.L. Anderson and Isaak (1995) where I have plotted only values determined from observations > 1300°C (or above the Debye temperature). While Anderson (1987a) argued that T is constant across the lower mantle, the predicted pyrolite profile shows a slight depth dependence where it first increases very slightly up to 1200 km depth and then smoothly decreases to a value near 5.0 at the core-mantle boundary. Nevertheless, this depth dependence is modest, and hence, to first order, T may be taken as a constant roughly equal to 6.2. In contrast to the modest agreement between the predicted pyrolite T and that inferred by Anderson (1987a), figure 7.68 shows that a large discrepancy does exist between the predicted Anderson-Gruneisen parameter, 5 S for the pyrolite mantle and the Anderson (1987a) estimates. As argued by Anderson (1987a) and Agnon and Bukowinski (1990), to increase (dlnVs/dlnVP)p to "high" seismic values requires that 8S decrease from the relatively high values at low pressure (compare the high temperature experimental results for some geophysically relevant minerals, taken from O.L. Anderson and Isaak (1995)) to values of < 2.0 in the lower mantle (note that these studies were adopting the lower mantle seismic values of (9 lnVs/d \nVp) = 2.0-2.5 from Dziewonski and Woodhouse (1987) as the seismic reference). For his preferred Y value, Anderson (1987a) determined that 5 S = 1.80 Chapter 7, page 688 would result in (3 lnVs/d \nVp) = 2.0. In contrast, while the pyrolite mineral physics 8S curve does indeed decrease over the lower mantle, it does not decrease below 2.0. However, recall that in reviewing the seismic results I concluded that the early estimate of Dziewonski and Woodhouse (1987) is likely to be too high because they did not compare the rms velocity amplitudes from joint tomographic models in calculating (3 lnVs/d ]nVp)p. Those studies that have used joint S- and P-wave models have found much lower values. Thus, in spite of the predicted pyrolite S s curve not decreasing to values inferred in earlier studies, this is not a critical issue. A last point to draw for the predicted pyrolite F and 8S curves is the implication for the very high (3 \nVs/d In Kp) p values determined from the seismic studies when the S- and P-wave models are assumed to be 100% spatially correlated (Bolton, 1996; Robertson and Woodhouse, 1996a). In figure 7.30 I plotted these required (3 \nVs/d lnVP) curves together with associated profiles derived by the ratio of rms velocity amplitudes. In attempting to explain the high values in the "assumed 100%" profiles in terms of thermal perturbations in a melt-free, chemically homogeneous mantle, Bolton (1996) noted that to reach a value of (d lnVs/d \nVP)p = 3.0, F would have to increase from 6 to 11 across the lower mantle, while the 8S curve would have to decrease from 3 to -1 (where F = 6 and 8S = 3 represent his preferred values at the top of the lower mantle). These required curves are plotted in figure 7.69 and 7.70 and it is immediately clear from these figures that such changes in either F or 8S are not consistent with the pyrolite mineral physics model. I should stress that all of the parameters to calculate 8S are experimentally measured for all of the lower mantle mineral phases, and consequently, the large discrepancy between the predicted Chapter 7, page 689 pyrolite curve and that required to explain Bolton's inferred (d lnVs/d In Vr) curve is significant. Although Bolton (1996) recognized that the required Tor 8S values are highly anomalous, and thus, the high (5 lnVs/d lnVP)p values cannot be explained in terms of purely thermal perturbations, he still accepted the "assumed 100%" (d ]nVs/d \nVP) profile as valid, and to explain the high values, invoked either compositional variations or the presence of partial melt. The mineral physics modeling in the previous chapters has shown that no such compositional variations are required to fit the seismic p, V0, Vs, and Vp radial profiles across the lower mantle. I concluded in these chapters, that while not unique, the uniform pyrolite bulk composition provides an excellent fit to all of the seismic observations routinely used to discriminate between various compositional models (magnitude of the seismic jumps across the 410, 520, and 660 km discontinuities, P- and S-wave normal incidence reflectivity of the seismic discontinuities, velocity gradients in the transition zone, absolute velocities and density profiles across the whole mantle). Consequently, I can confidently reject systematic, compositional variations as a possible explanation for the high (d XnV^/d In Vp) values in the profile constructed under the assumption of a 100% spatial correlation between the S- and P-wave models. Likewise, in a previous section, I reviewed the effects of widespread partial melt in the lower mantle and found that studies advocating this process to explain "high" seismic values had not fully considered the associated attenuation effects which would accompany widespread partial melt. Because in all of the seismic attenuation models published to date, the lower mantle is characterized by very high seismic Qs (low attenuation), and because very low seismic Qs values are characteristic of Chapter 7, page 690 zones of partial melting (back arc basins, mid-ocean ridges), the seismic observations argue strongly that widespread partial melt does not exist in the lower mantle. Indeed, when I compare the predicted partial melt ( 9 \n.Vs/d lnF, , ) p profiles against the "assumed 100%" ( 9 h\Vs/d Yo.Vp) profiles, it is clear the two sets of curves are discrepant, with the slope of the partial melt profiles too steep with respect the "assumed 100%" profiles. Bolton (1996) provides an additional compelling argument against the partial melt hypothesis as a plausible explanation of the high values. He notes that if partial melt (and compositional variations) are the explanation, then one would expect that in the mantle beneath the "Pacific ring of fire", where slabs traverse down to the core mantle boundary, that this "ring" should contain the most anomalous (d\nVs/d\nVP)p values (assuming that subducting slabs are cycling volatiles and compositional variations deep into the mantle). Recall that with his co-located, cap averaged 5*- and P-wave travel time anomalies, Bolton (1996) was able to calculate individual ( 9 In Vs / 9 In VP) values for his caps at the turning depths for the raypaths across the lower mantle. These individual ( 9 lnVs/d lnVp) values were combined in the four depth bins to which a line was fit (see figure 7.15). In contrast, to what is expected i f slabs are cycling compositional variations and volatiles into the deep mantle, he found that the most anomalous ( 9 \nVs/d ]nVP) values occur in the middle of the Pacific, south east of Hawaii, in the center of the "Pacific superplume", and not where the slabs intersect the core mantle boundary around the perimeter of the Pacific. Thus, these seismic observations do not support the hypothesis that the high values characteristic of the "assumed 100%" ( 9 \nVs/d lnVp) profiles can be easily explained by a slab-derived partial melt. The results Chapter 7, page 691 presented in figure 7.69 and 7.70, together with the difficulties in appealing to either systematic compositional variations or widespread partial melt lead me to conclude that the (9 \nVs/d \nVp)p profiles which are constructed by forcing a 100% spatial correlation between the S- and P-wave models (e.g. Bolton, 1996; Robertson and Woodhouse, 1996a) are numerical artifacts. What then is the cause of the high, individual ( 9 lnVs/d In Vp) values in the central Pacific, recognized by Bolton (1996) in constructing the co-located, cap-averaged depth bins? Assuming these values are real, one is forced to appeal to either localized chemical heterogeneities, localized partial melt, or attenuation effects. In this case, the partial melt would not reflect a slab-derived volatile melt, but more likely, partial melting of one of the exotic high pressure mineral phases unique to former oceanic crust at lower mantle conditions (Kesson et al., 1994). The modeling of these effects on the D" velocity profiles are beyond the scope of this chapter. Alternatively, there is the possibility that the anomalous (d \nVs/d \r\VP)p values of Bolton (1996) are numerical artifacts which reflect a localized loss of resolution in either the 5*- or P-wave model of his joint tomographic models. As noted earlier, WE 1997, the joint, whole mantle S- and P-wave models of Vasco and Johnson (1998), are likely to possess much better resolution in the lower most mantle than Bolton's because they incorporate many core-penetrating seismic phases and allow for topography on the core-mantle boundary. The WE 1997 models do not exhibit the very large shear wave anomalies relative to P-wave anomalies in the D" layer (see figure 7.27), and consequently, the WEI997 rms-ratio derived(9 \nVs/d lnVP)p profile has much lower values in the D" layer (~2.1) than that Chapter 7, page 692 estimated from the rms ratio of the S16B30/P16B30 profiles («3.5). Figure 7.63 clearly shows that a value of 2.1 is only slightly greater than that calculated herein for a pyrolite mantle (1.82) and this difference may not be significant. Alternatively, this difference may be explained in terms of attenuation effects, since anelasticity will should decrease rapidly across the thermal boundary layer in the D" region, and hence, act to increase the purely elastic profile calculated here. In terms of the effect of seismic attenuation, the study by Karato (1993) indicates that incorporating this effect will increase likely the (d l n ^ / 5 \nVp) profile calculated here. However, the largest increase will occur where seismic Q is lowest, and hence has the largest effect on velocities. This would imply that the upper mantle (d In Vs/d In V,,) profile, where traditional radial models of Qs are lowest (see figure 7.52), will be affected the most by the addition of anelastic effects while the lower mantle will be relatively unchanged. However, to incorporate seismic Q into the mineral physics model correctly, the attenuation model must be temperature, pressure and frequency dependent, which the existing seismic models are not. To remedy this situation, I have constructed a Qs((o,T, P) and Qp(a>,T, P) models (Calderwood, 1998) which will be combined with the mineral physics model, but this is beyond the scope of this chapter. 7.21 Conclusions The purpose of this research is to assess the discrepancy between seismic and mineral physics estimates for the parameter {d\v¥gld\riVp)p. Previous studies have recognized an apparent discrepancy between low values of mantle minerals experimentally measured under Chapter 7, page 693 high temperature, but room pressure conditions, and high values estimated from seismic observations that span the whole mantle. This discrepancy between mineral physics estimates on one hand, and seismological on the other, has encouraged hypothesis that dismiss temperature perturbations as the dominant driving force for velocity heterogeneity in the mantle, and instead, invoke the presence of widespread partial melt, or alternatively, chemical anomalies. To address this question I calculate a whole mantle profile of (SlnJ^./SlnF/,) ;, for a uniform pyrolite composition mantle by re-running a self-consistent mineral physics model at higher and lower temperatures to derive self-consistent estimates of the velocity derivatives ((dVs/dT)p , (dVp/8T)F ). These profiles are then combined to obtain an purely elastic (dlnVs /dlnVp )p profile across the whole mantle. I find that for a uniform pyrolite model, the predicted whole mantle profile of (9 InVjd \nVP)p agrees very well with the latest, high resolution estimates from seismology. In addition, the pyrolite mantle is also used to predict lower mantle profiles of the dimensionless parameters T and 5S. These profiles strongly conflict with those required to explain the very high values from seismic (9 \nVs/d l n F / ) ) p profiles constructed assuming a 100% spatial correlation between S- and P-wave anomalies, indicating that such high values (Bolton, 1996; Robertson and Woodhouse, 1996a) are not likely to be real. Hypothesis which argue for a systematic increase in (9 In Vs/d lnVP)p with increasing depth, reflecting either the presence of a widespread partial melt, or chemical variations within the lower mantle, can be confidently rejected on the basis of prior mineral physics modeling and observations of seismic Q$. Nevertheless, the geographically restricted and anomalously high Chapter 7, page 694 (8 \nVs/8 kiVP)p values recognized by Bolton (1996) may reflect either the differentiated dregs of former subducted slabs, namely heavy residues comprised largely of oceanic crust, or small amounts of partial melt existing in the source regions of mantle plumes. These two interpretations are consistent with recent seismic observations that subducting slabs traverse the whole mantle (van der Hilst et al., 1997) and with preliminary experimental mineral physics studies which demonstrate that oceanic crust is slightly heavier, and hence, chemically different, than the ambient pyrolite mantle at core-mantle boundary conditions (Kesson et al., 1994). However, I caution that the high (5 lnVs/8 lnVP)p values of 3.5 are still very difficult to explain in terms of a partial melt since the highest value expected for a melt is only 2.65. One caveat should be noted concerning these interpretations. The mineral physics models presented here do not account for the effects of seismic attenuation, which Karato (1993) shows semi-quantitatively, will act to increase the predicted purely elastic (d \nVs/d \nV,,)p profile. However, to fully account for such effects, models of seismic Q$ and Qp, which are fully frequency, temperature, and pressure dependent, must be constructed before seismic attenuation can be correctly incorporated into predictions of (d\nVs/d \nVP)p. These two interpretations of the high (d \nVs/d hxV,,)p values implicitly assume that the high seismic values in the D" layer are, in fact, real. However, there exists circumstantial evidence that this might not be the case, since the raypath coverage at the core-mantle boundary in the central Pacific and in South Africa, the two regions which possess anomalously slow velocities, is relatively sparse. This poor coverage may allow the spherical Chapter 7, page 695 harmonic function, which is used to parameterized the lateral variations in relative velocity, to produce numerical artifacts in these two regions, with the magnitude of the inferred anomalies in either the S- or P-wave tomographic model being over or under predicted. That this situation might explain the anomalous value of Bolton (1996) is suggested by a comparison between the rms-ratio (5 lnVs/d \nVp)p profile calculated from the joint S- or P-wave tomographic models of Vasco and Johnson (1998) and Bolton's. The Vasco and Johnson (1998) models incorporated many core seismic phases (PcP, ScS, PKPab, PKPbc, PKPdf SKSac), and furthermore, also solved for core-mantle boundary topography in their inversion for joint S- or P- models. Therefore, the spherical harmonic expansions of lateral heterogeneity in the D" region is likely to be well constrained. In contrast, Bolton (1996) did not incorporate any core penetrating phases and did not account for any topography on the core mantle boundary (nor transition zone discontinuities). Thus, it is likely that the Vasco and Johnson (1998) models have better resolution in the D" layer than either S16B30 or P16B30. A close inspection of figure 7.42 clearly shows that in the D" layer, the rms ratio (d \nVs/d l n ^ ) p profile for WE 1997 only exhibits a modest increase to values of 2.1, a value which is far less than that calculated for Bolton's joint tomographic models (3.5). A value of (d \nVs/d l nF / , ) p =2.1 is only slightly higher than that calculated here from the pyrolite mineral physics model. Chapter 7, page 696 7.22 References Agnon, A. , and Bukowinski, M.S.T., 1990. 5S at high pressure and dlnVs/dlnVp in the lower mantle. Geophysical Research Letters, vol., 17, 1149-1152. Anderson, D.L., 1975. Chemical plumes in the mantle. Geological Society of America Bulletin, vol., 86, 1593-1600. Anderson, D.L., 1987. A seismic equation of state 2. Shear properties and thermodynamics of the lower mantle. Physics of the Earth and Planetary Interiors, vol., 45, 307-323. Anderson, D.L., 1987b. 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Geophysical Journal International, vol., 127, 1-16. 0 100 200 300 400 500 600 700 800 900 1000 1100 ^ 1200 J2 1300 ^ 1 4 0 0 S 1500 Q 1700 1800 1900 2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 f" Dziewonski & Woodhouse (1987) | rms velocity amplitude ratio 2.0-2.5 I I I I I I frtr Chapter 7, page 713 T T T . . J I I I I I I I I I | I I I I | I I I I | I I II high Temperature but room pressure experimental mineral physics estimates mmm region of reduced — velocity gradients p~ D" Layer I I I ' I i ' ' I » ' ' ' ' ' ' ' ' • I ' ' ' t C O 0.0 0.5 1.0 1.5 2.0 2.5 3.0 {din Vjdln tf) 3.5 4.0 Figure 7.1 Summary figure of illustrating the discrepancy between seismic estimates and room pressure experimental values. Chapter 7, page 714 Figure 7.2. Schematic diagram illustrating the SS and S raypaths through the Earth's mantle. Chapter 7, page 715 Q 2 ^2 1 03 0 !< CO -3 Young Oceans/+~ slope of line —2.2 (dlnVs ldlnVPX= L18 Phanerozoic Orogenic Zones 4. intermediate Oceans Old Oceans Phanerozoic Platforms Precambrian Shields 1 1 - 2 - 1 0 1 median of PP-P residuals (seconds) Figure 7.3. Plot of SS-S travel time residuals versus PP-P travel time residuals averaged by tectonic province (after Woodward and Masters, 1991a). Chapter 7, page 716 SS Bounce Points 0 50 100 150 200 A g e ( M y r ) Figure 7.4 Schematic diagram illustrating the effect of cooling and thickening oceanic lithosphere with respect to the reflected bounce point of SS raypaths. Chapter 7, page 717 •0.51 ± 0.01 sec/(Myr) -\ point — mean of 100 observations-^ J I I L in 0 50 100 150 A g e o f S e a f l o o r ( M y r ) 3 2 1 O 1 0 *** -1 S3 £- 3 1 1 1 1 1 1 - A _ A I | l I l I | i i A 1/2-A -0.18±0.01 sec/(Myr[_ A A A * ^ Z ^ r ^ ~-A — i i i i 1 i i l i t i i l i i 3 50 100 150 t cn ri -a 5 " D O O A g e o f S e a f l o o r ( M y r ) Figure 7.5 Plot of SS-S (top) and PP-P (bottom) travel time residuals as a function of seafloor age at the SS or PP bounce point (after Woodward and Masters, 1991 a). 0 I I i i i i 1 1 1 100 200 300 rn 400 P H © Q 500 600 700 800 Woodward & Masters (1991b) oceanic areas 1.55 ±0.10 Chapter 7, page 718 I I I I I I I I I I I I I I I I ' I I I I l l l I I I I I Dziewonski & Woodhouse (1987) I I I I I I I ai I 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 (din Vs Id In VP\ Figure 7.6. Comparison of the long-period, oceanic upper mantle estimate derived from Woodward and Masters (1991a) SS-S and PP-P residuals as a function of age with the lower mantle estimate of Dziewonski and Woodhouse (1987). 0 I i I I I 100 200 300 C H 400 Q 500 600 700 800 Woodward & Masters (1991a) oceanic areas 1.55 ±0.10 Robertson & Woodhouse (1997\ JSCS to P ratio " 1.56 ±0.10 Souriau ct Woodhouse (1985) 1S(' S to P ratio 1.38 b 0.11 Wickens & Buchbinder (1980) world wide average 1.31 ±0.06 ' Poupinet (1977) 0.99 Romanowicz & Car a (1980) central USA 1.27 ±0.60 Western USA 1.39 ±0.43 Cl I I I I I I I I Chapter 7, page 719 I I I I I I I I I - I Doyh <x Ilaics (1967) 2.03 -0.24 "Jeffreys & Singh (1973) Europe 1.64 to 2.52 Wickens & Buchbinder (1980) Canadian Shield 2.05 ± 0.25 Souriau <$ Woodhouse (1985) preferred 2.02 ± 0.0-r-5~^>—. Hales A Roberts (1970) 2.32 Roiuaiuiw u." A Cara (1980) ; s ; 2 59 0.55 Dziewonski & Woodhouse (1987) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 (din Vs Id In VP\ 3.5 4.0 Figure 7.7. Summary of upper mantle estimates from continental station corrections. Also plotted is the "oceanic" estimate derived from Woodward and Masters (1991a). 0 Ll I I I I I t I 100 200 300 ^ 4 0 0 O H Q 500 600 700 800 Woodward & Masters (1991a) oceanic areas ' 1.55 ±0.10 Robertson & Woodhouse (1997) ISC S to P ratio - 1.56 ±0.10 ri ' ' ' i • ' • Chapter 7, page 720 I I I I I I I I I I I I I I I I I I l-i Mooney et al., 1997 CRUST 5.1 correction to global travel time residuals from broad-band digital stations 1.64 I l l l l l l l l Dziewonski & Woodhouse (1987) I I I I J_L I I I 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 (din Vs Id In Figure 7.8. Summary of the preferred upper mantle estimates. Al l of these estimates are based on comparing self-consistent S and P-wave observations to derive the upper mantle average (8lnVs/dlnlf)pvalue. Chapter 7, page 721 0 L 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 « . 500 ^ 0 0 0 O H Q1500 a 2000 3 H 2500 3000 P-waves S-waves I . I • I • I • I • I • I • I . I • I •• —|— Caribbean anomaly! -dordan & Lynn (1974Jjj -4-Bokelmann & Silver Dziewonski & |Woodhouse(19&¥| 1 t CD CO fe CO c\i c E o CD 0 2 4 6 8 10 0 Travel time anomaly (seconds) 1 2 3 (din Vjdln %) Figure 7.9. (left) Maximum variation of the S and P-wave travel time residuals as a funciton of turning depth in the lower mantle beneath the Caribbean, (right) The related (dlnVsldln\[,)f values for the two depth intervals. Chapter 7, page 722 Figure 7.10. Schematic diagram illustrating raypaths for the core reflected ScS phase relative to surface reflected SS phase. ScS-S differential travel time residuals are primarily sensitive to lowermost velocity structure, while SS-S differential residuals reflect the velocity heterogeneity below the surface bounce point. Chapter 7, page 723 earthquake Lower Mantle\ Outer Core t CO Figure 7.11. Schematic diagram illustrating raypaths for S-waves bottoming in the lower mantle. Boxes schematically represent the depth bins adopted by Bolton (1996) for plotting the co-located, cap-averaged S- versus P-wave travel time residuals. J£ 8 8 * 3 2 * 3 o • 00 , w -4 0 3 -6 cj.8 8 C 6 C O 4 ve u C« 2 ed eu 0 on i B -2 to > -4 C3 C L , -6 ca -8 C/5 -o c o CJ 4> cu co OQ C/5 £ co -to 0 cd -2 l " 4 S-8 e 2 i ; i 1 r (dlnVs IdlnV^Y = 1.70 \\(dbiVs ldlnVP) = 2.30 J I I cu 0 -10 -8 -6 - 4 -2 0 2 4 6 8 10 P-wave cap averages (seconds) Figure 7.12. Scatter plots for the 4 depth bins in the lower mantle where Bolton (1996) compared co-located, cap-averaged S- and P-wave travel time residuals. Chapter7, page 724 depth 650 - 1100 km depth = 1100- 1700 km c o • -j depth = 1700-2300 km depth = 2300 - 2890 km 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 {din VJd In K F ) Figure 7.13. The scaling factor (dlnVsldlnV,)p plotted as vertical bars over the 4 depth intervals considered by Bolton (1996). Also shown are the preferred upper mantle mean value and the lower mantle inference from the Caribbean anomaly. Note that when the anomalous values in the lowermost bin are not considered, the new estimate decreases substantially, and agrees with the earlier Pulver & Masters (1990) inference. Chapter 7. page 726 positive S-wave cap averages (2300-2891 km) with > 25 hits per cap -10 -8 -6 -4 -2 0 2 4 6 8 10 P -wave cap averages (seconds) Figure 7.14. Scatter plot of S- and P-wave residuals for those cap-averages which contain at least 25 observations in each cap (the plots in figure 6.12 only contain points which have a minimum cut off of 5 observations per cap). Figure after Bolton (1996). c o ii V w 2 I S o « J -2 8 t 3 C 6 o o 4 ve (se 2 o 0 ? Oi) 1 CS •~ -2 > -4 re -6 ca -8 Chapter 7, page 727 depth = 6 5 0 - 1100 km depth = 1100- 1700 km depth = 1700-2300 km depth = 2300 - 2890 km -10-8 -6 -4 -2 0 2 4 6 8 10 P-wave cap averages (seconds) Figure 7.15. Scatter plot of S- and P-wave residuals showing hypothetical correlation lines for a constant value of (dlnVsl&ny, )p = 1.70 throughout the mantle (in red) compared to the least squares regression lines determined by Bolton (1996; blue). 0 1 0 0 — 200 — 300 — 400 500 600 700 800 900 1000 1100 ^ 2 0 0 § 1 3 0 0 O 1 4 0 0 ^ 1 5 0 0 <L>1700 Q1800 1900 2000 2100 2200 2300 2 4 0 0 2500 2600 2700 2800 2900 3000 1 1 Chapter 7, page 728 I I 1 I I I I I I I I I j I I I j I I I I M J I I I I I I I I I I I I I I I I j I I I P16B30 (Bolton, 1996) WE1997 (Vasco & Johnson (1998) 11 i •JLM4P6 (Robertson & Woodhouse, 1995) V3 (Morelli & Dziewonski, 1987) I ASP 3D P (Vasco el al., 1994) I I I 1 1 1 1 M 1 I 1 1 1 1 1 1 1 1 i 1 t 1 1 t 1 I 1 t 1 I 1 1 1 I 1 n 1 1 1 t 'X> 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 rms amplitude of the relative velocity perturbation P-wave tomographic models Figure 7.16. The rms amplitude of selected P-wave tomographic models discussed in the text. Chapter 7, page 729 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2 .2 2.4 rms amplitude of the relative velocity perturbation S-wave tomographic models Figure 7.17. The rms amplitude of selected S-wave tomographic models discussed in the text. Q o 100 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 Chapter 7, page 730 JJ1 • 1 •11• 1 • 11 • 1 • 1 ••111 • • 1 • 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1M1 j 1M 11 i 111111 l | l l l l | IMM _ Dziewonski & Woodhouse (1987) all even and odd degrees (2</<6). rmsrSH.10c.171 rms[L02.56] rms[MDLSH] rms[L02.56] rms[SH12WM131 rms[L02.56] i 11 • 11 • • • 11 • • 11 • • i • I • i • • t • i i • t • • 111111T t CD 00 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 (din Vs/d In \fyt Figure 7.18. Profiles of the ratio of rms velocity for recent Vs global tomographic models (Ritzwoller and Lavely, 1995) where L02.56 is the Vp tomographic model. Note the expanded scale. X L 7.5 0 100 200 h 300 F -400 500 600 700 800 900 1000 1100 ^ 1 2 0 0 J2 1300 w 1 4 0 0 *S 1500 & 1 6 0 0 p 1700 1800 1900 2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 rm Chapter 7, page 731 |i"ii|Mi"|i"i"i«i"|ii"i|Mii|iiii|iiii|iiii|iiii|iiii|ini|irif|iiii even degree 2 terms only r m s [ S H . l Q c . l 7 ] rms [L02 .56 ] rms[MDLSH] rms[L02.56] rms[S12_WM13j j rms[L02.56] -\ t CO (6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 (din Vs/d In \§ Figure 7.19. The depth profile of the ratio of rms amplitudes of Vs tomographic models to the Vp tomographic model L02.56 but for only even degree 2 terms of the spherical harmonic expansion for which the tomographic models are parameterized laterally (after figure 23a of Ritzwoller and Lavely, 1995). 0 1500 gl600 Q1700 1800 1900 2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 T T T Chapter 7, page 732 upper mantle and transition zone structure not explicitly modeled, but accounted for by station corrections. ML depth interval unreliable due to leakage of upper mantle signal the correlation coefficient between the joint S- and P-wave tomographic models for different parameterizations of the models (Robertson and Woodhouse, 1996). The velocity perturbations are expanded laterally in terms of spherical harmonics to degree 6, 8, or 12. depth interval unreliable due to lack of S-wave da, and SKS contamination 1 = 6 reduced velocity gradienls~\ above D" layer D" layer 1 CMB 0.00 0.20 0.40 0.60 0.80 1.00 Correlation Coefficient of S to P models Figure 7.20. Correlation of joint S- to P-wave tomographic models across the lower mantle (Robertson and Woodhouse, 1995). Also plotted are common mantle phase boundaries and the depth intervals where the tomographic models are likely to be unreliable. 500 Number of S arrivals 1000 1500 2000 i i | i i i i leakage of upper mantle signal into the lower mantle due to the adopted parameterization where only a lower mantle tomographic signal is extracted, rather than a whole mantle model. Upper mantle velocity structure is assumed to be accounted for by the use of station corrections. No. of S-wave arrivals (blue bars) Chapter 7, page 733 2500 3000 i i | i i i i depth interval unreliable due Joj leakage of upper mantle signal 1270- 1470 km = Onset of degraded j S-wave resolution (Vasco et al, 1994) dep th i n te r va l un re l i ab le due to l a c k o f d a t a a n d c o n t a m i n a t i o n by SKS phase. Only 4 % of the summary S ray data set penetrates to depths greater than 2000 km in contrast to 24% of the P data set. Thus, the rms amplitude of the JLM4S6 S-wave tomographic model is poorly constrained below 2000 km depth. ' I ' ' Figure 7.21. Distribution of S-wave summary rays as a function of bottoming depth (Robertson and Woodhouse, 1996). Also shown are two regions in the lower mantle where they admit the resultant ratio of S to P scaling factor is unreliable. Chapter 7, page 734 1.50 2.00 2.50 (din VsBln VP\ Figure 7.22. Ratio of S- to P-wave rms velocity amplitudes from joint lower mantle tomographic models JLM4S6 and JLM4P6 (Robertson and Woodhouse, 1995). To assess the potential effect of damping during the inversion, the data set was filtered to included only S- and P-wave data that are common to the same seismogram. Chapter 7, >e735 4.00 (din Vs/dln VP\ Figure 7.23. Ratio of S- to P-wave heterogeneity from explicitly solving for the ( ^ ln V /^ln V ) profile by inverting both P and S data sets for a single Vp tomographic modef and the associated proportionality profile that maximizes the fit of a scaled-Vs model to the S data. Also shown are the profiles based on the ratio of rms velocity amplitudes. Chapter 7, page 736 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 C o r r e l a t i o n c o e f f i c i e n t Figure 7.24. Correlation of joint S- and P-wave tomographic models WE 1997 (Vasco and Johnson, 1998) and S16B30 to P16B30 (Bolton, 1996). Also shown is the correlation between the lower mantle joint models of Robertson & Woodhouse (1995). Chapter 7, page 737 sl6b30 70 km 170 km 0.03 0.0225 0.015 0.0075 0 •0.0075 -0.015 -0.0225 -0.03 Figure 7.25 Model S16B30 of Masters et al. (1996) showing the relative S-wave velocity perturbations at 12 depths through the mantle. Figure from Bolton (1996). The amplitude scale is dVs/Vs. Chapter 7, page 738 p!6b30 70 km 170 km Figure 7.26 Model PI6630 of Bolton (1996) showing the relative P-wave velocity perturbations at 12 depths through the mantle. Figure from Bolton (1996). The amplitude scale is dVp/Vp. 0.2 0.4 0.6 0.8 1.0 1.2 1.4 r m s v e l o c i t y a m p l i t u d e ( % ) Figure 7 .27. Radial profiles of the rms velocity amplitudes from the joint, whole mantle S - and P-wave tomographic models of Bolton (1996) and Vasco and Johnson (1998). Note the discrepancy between the relative S - and P-wave amplitudes in the lowermost mantle. 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 (din Vsldln V)e Figure 7.28. Profiles of the rms-derived (dlnVsldln\PT) factor for the two whole mantle, joint tomographic models are compared to independent estimates. Note that the joint lower mantle models of Robertson and Woodhouse (1995) result in a large peak in the middle of the lower mantle, a feature absent in both whole mantle models. 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Figure 7.29. A comparison of the rms-ratio profiles to the 4 global, depth estimates of Bolton (1996) that are based only on the ratio of absolute S- to P- wave residuals. Chapter 7, page 742 I I I | I I I I | I I I I Bolton (1996) rms S to P ratio Vasco & Johnson (1997) j rms Sto P ratio* assumed 100% S- to P-wave ~ spatial correlation '(Robertson & Woodhouse, 1996a). assumed 100% spatial ~ H correlation of S- to P-wave __"] anomalies (Bolton, 1996) — 1 \ \ -~l 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I 1 \ ISA—r i 11 i i i i 11 i i 11 i i i>l i i i r 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 (din Vs/8ln %)? Figure 7.30. A comparison of the rms-ratio derived profiles to those calculated assuming 100% spatial correlation between the S- and P-wave velocity anomalies in the joint, whole mantle tomgraphic models. Chapter 7, page 743 0 500 1 0 0 0 r n 1500 a, Q 2 0 0 0 2500 3000 -~I—F ISCP I I 1 Gudmunl.grf 1 I I I 111 I I I I I I I I I I I I I I I ' ' ' ' 1 1 l 1 l l l l 0.0 2.0 4.0 600 1000 2000 Slowness (10" 4 sec/km) correlation ha l f width (km) Figure 7.31. (left) The profile of slowness derived from a statistical analysis of the ISC P-wave data (after Gudmunsson et al. 1990). (right) The associated profile of the correlation half width. Chapter 7, page 744 0 ~T— r uses i—r 1000 h Q 2000 3000 0.0 CD 1 - L 4.0 .-4 800 2000 4000 6000 Slowness (10 sec/km) Correlation half width (km) Figure 7.32. (left) the profile of rms slowness perturbations in the mantle derived from a statistical analysis of the ISC S-wave arrival times, (right) The associated profile of the correlation half width for the perturbations. i i i i I 111 Pi t 660 km Davies, Gudmundsson, & Clayton (1992) statistical analysis of ISC S to P variance Vasco & Johnson (1998) ratio of rms velocity for joint tomographic models Bolton (1996) ratio of rms amplitudes for joint tomographic models •region of reduced velocity gradients upper mantle average (Woodward & Masters, 1991a; Robertson & Woodhouse, 1998) f~ D" Layer ' ' ' ' I I ' I i I ' ' ' ' ' ' ' ' I Dziewonski & Woodhouse (1987) —j ratio of rms velocity for **] independent tomographic models I Chapter 7, page 745 I I I | I I I I I I I I .0 0.5 1.0 1.5 2.0 2.5 3.0 (din md In J f ) 3.5 4.0 Figure 7.33. The statistical inference of Davies et al. (1992) based on the variance of ISC S- and P-wave arrival times, is compared against the profiles discussed in the text. Chapter 7, page 746 1.00 0.90 0.80 O .2 0.70 > 0.60 0.50 T —i—|—i—i—i—|—i—r (din pi d i n 0 = 0.0 Masters etaL (1982) Ritzwoller et al (1988) M84A + V3 0.40 j i L • prefered range Giardini et al, (1988) • • • I t a CO CO "O CD CD 1.0 2.0 3.0 4.0 ( d / w Vsldln K) Figure 7 . 3 4 . The variance reduction obtained in comparing predicted to observed free-oscillation structure coefficients for various combinations of the density-to-Vp and shear velocity-to-Vp scaling factors (after Giardini et al., 1988). Chapter 7, page 747 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 (din V / d l n t y p Figure 7.35. The probability distribution of the S- to P-wave scaling factor in the lower mantle (assuming a constant value applies across the lower mantle) derived by free-oscillation observations (after Li et al., 1991). 0 100 200 300 400 500 600 700 800 900 1000 1100 ^ 1 2 0 0 J2 1300 w 1 4 0 0 * £ 1500 §"1600 Q 1700 1800 1900 2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 . extrapolated room pressure value ' Masters el al. (1982), .Ritzwoller et ai, (1988) 1.25 I Stochastic mantle ave - Davies, Gudmundsson, & Clayton. (1992) 1.80 reduced velocity gradients \ I ~ in D" seismic models = top \ f__ of thermal boundary layer (?) (_ D" layer (chemical and thermal I boundary layer) ' ' ' ' 1 i ' ' ' I ' i Chapter 7, page 748 I I | I I I I | I I I I referred value' "1 2.80 wfjfoj^I estimate with M8~^2 ^^permantle correction-end 75% eonfidence limits' ' ft al., 1991b) ~ \ 2.27 Optimal estimate with nd~\ yy^pam upper mantle yy^irreetion and 75% • ^K^^dence limits (Lietal, 1991b) ~_1 1.81 -I I I I I I I cn > 0.0 0.5 1.0 1.5 2.0 2.5 (dim Vs/8 In $p 3.0 3.5 4.0 Figure 7.36. Summary of free-oscillation estimates the most recent estimates (e.g. Li et al., values of 1.81-2.00. where a constant lower mantle value was assumed. Note that 1991b; Ritzwoller and Lavely, 1995) favour relatively low 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 (din Vsldln VP) p Figure 7.37. A comparison of the depth-dependent profiles of Ishii and Tromp (1997; 1998) against the preferred lower mantle mean value of Li et al. (1991b). The 1997 profile of Ishii & Tromp is not reliable. Chapter 7, page 750 (din Vsldln VP)? Figure 7.38. Comparison of the depth-dependent profile of Ishii and Tromp (1998) to the rms-ratio derived profiles determined from the whole mantle, joint S- and P-wave tomographic models. Their preliminary 1997 profile is also plotted and led them to argue in favour of the profiles which assume a 100% spatial correlation between the S- and P-wave anomalies. In marked contrast, their 1998 profile strongly agrees with the rms-ratio derived profiles. Chapter 7, page 751 earthquake PKPdf Figure 7.39. Schematic diagram illustrating raypaths for the core reflected PcP phase and core penetrating PKP phases. Chapter 7, page 752 •0.5-0.4-0.3-0.2-0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 (din VPldln Vs\ Figure 7.40. Variance reduction in the lowermost mantle for various values of the (dlnVs/dlnlf,) scaling factor and shear wave tomographic models (after Song and Helmberger, 1997). The yellow band represents likely values based on this work. o 11 it i •* Chapter 7 , page 7 5 3 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 {din Vs/dln Vr) Figure 7.41. Summary of the preferred seismic estimates reviewed in the text. Chapter 7, page 7 5 4 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 '1600 1700 1800 1900 2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 0 L ' 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 •_-pyrolite mineralphysicsZ — ^ model ~Z I ^ P R E M — — I lower mantle min = 0.45 ~ — 1 lower mantle max = 0.55 1 r , 1 , 1 , 1 , 1 1 1 — , 1 , 1 , 1 , 1 " CD to i E 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 U/K,. Figure 7.42. The radial profile of the shear to adiabatic bulk moduli ratio from the seismic reference model PREM and the Pyrolite mineral physics model. Chapter 7, page 756 0.00 1.00 2.00 3.00 4.00 (din Vjdln %\ Figure 7.44. Profiles of the isothermal (din Vs/8ln fp\ (after Parker and Wall, 1991). Note that these profiles are not directly comparable to the adiabitic value, which is of interest here. Chapter 7, page 758 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 (din Vjdln VP)p Figure 7.46. Profiles of the theoretical scaling factor for periclase (Isaak et al., 1992) compared to some of the seismic estimates reviewed in the text. 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 '1600 1700 1800 1900 2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 _i i i i | i f i i | i i W Chapter 7, page 759 I I I I I I | I I I I | I I I I p~ Caribbean anomaly ~ Jordan & Lynn, 1974 Bokelmann and Silver, 1993 (1.70+0.2) Woodward & Masters, 1991a; H Robertson & Woodhouse, 1998 Dziewonski & Woodhouse, 1987 ratio solely _ due to melt _2 akl35 seismic model I— ratio of rms amplitudes \frem joint S & P tomographricJ_ models. " Vasco & Johnson, 1998 Bolton, 1996 |— statistical lower mantle average Davies et al., (1992) 1.80 I I I I I I I I I I I I I I I onset of reduced velocity gradients D" layer | I I I I t cn cb > 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 (din Vjdln %) p Figure 7.47. Comparison of the predicted melt-bearing S- to P-wave scaling factor to some of the seismic estimates discussed in the text. 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 (din Vs/dln VP)p Figure 7.48. Comparison of the melt-bearing scaling factor to the seismic estimates which assumed a perfect 100% spatial correlation between the S- and P-wave velocity anomalies (Robertson and Woodhouse, 1996a; Bolton, 1996). 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 (din Vjdln VF)f Figure 7.49. Comparison of the melt-bearing scaling factor with the rms-ratio derived profiles of Robertson and Woodhouse (1996a) and other seismic profiles discussed in the text. Chapter 7, page 762 (din Vjd In $ „ Figure 7.50. Comparison between predicted lower mantle melt-free and melt-bearing scaling factors as calculated by Duffy and Ahrens (1992). Also shown is the Dziewonski and Woodhouse (1987) lower mantle estimate. 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 (din Vsldln VP) Figure 7.51. Comparison of theoretical melt-free and melt-bearing profiles (Duffy and Ahrens, 1992) to the preferred seismic profiles discussed in the text. Note the very good agreement between the melt-free profile and the rms-ratio derived profiles. 43 O H Q 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500 2600 2700 2800 I ' Ir4—* ri= Chapter 7, page 764 T SI PREM QM1-A akl35-Q SL8 1 0 100 200 300 400 500 600 700 s h e a r a t t e n u a t i o n , Q , Figure 7.52. Radial profiles of the shear wave quality factor Qs taken from seismic studies. Note the high values in the lower mantle relative to the shallow most 100-200 km. The low values at shallow depths are interpreted to reflect the presence of partial melt. If correct, then the high values in the lower mantle argue against the presence of partial melt in this region. Chapter 7, page 765 2200 2300 2400 2500 &2600 2700 2800 E constraint inversion I 1 I 1 I 1 I VP\ -1 PREM velocities above 200 km from CMB D" layer = 200 km thick (assumed) Kugmagai etal. (1992) = 150 km thick (assumed) Morelli & Dziewonski, 1993; Dzeiwonski & Anderson, 1981 constrained! inversion t CO Q Q CO E 3 5.0 6.0 7.0 8.0 9.0 10.0 11.0 Velocity (km/sec) density (g/cmA3) 12.0 13.0 14.0 Figure 7.53. A comparison of velocity and density profiles from the recent seismic reference model SP6 (Morelli and Dziewonski, 1993) with the PREM model (Dziewonski and Anderson (1981). Also shown is the free-oscillation derived profiles advocated by Kumagai et al. (1992). Chapter 7, page 766 0.00 0.10 0.20 0.30 0.40 0.50 0.60 (dlnp/d In V)r Figure 7.54. The density to velocity scaling factor profiles estimated by Karato (1993). The mid-mantle peaks dirictly reflect the use of the QM1 shear attenuation profile. (din Vsldln Vp)? Figure 7.55. A comparison of the predicted S- to P-wave scaling factor derived from the density to velocity profiles o f Karato (1993) to the preferred seismic profiles discussed in the text. 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 -(din VldT\ Figure 7.56. Profiles of elastic logarithmic shear and compression velocity temperature derivatives (after Karato, 1993). 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 (din Vsldln VP\ Figure 7.57. A comparison of the elastic and anelastic profiles derived from Karato (1993) with the melt-free profile of Duffy and Ahrens (1992b) and the preferred seismic profiles discussed in the text. Chapter 7, page 770 0 L l I I I I 111 100 200 300 ^400 O H Q 500 600 700 800 Woodward & Masters (1991a) oceanic areas 1.55 ±0.10 Robertson & Woodhouse (1997) ISC S to P ratio ' 1.56 ±0.10 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 m p-rrrr -I I I I i I I I I I I I I I I I I I I •Mooney et al., 1997 CRUST 5.1 correction to global travel time residuals from broad-band digital stations 1.64 Olivine Zaug et al, (1993) mean value = 1.55 Dziewonski & Woodhouse (1987) i i i M i i i i I i i i r i g - 1 _ > 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 (din Vs Id In VP\ Figure 7.58. A comparison of the experimental inference of Zaug et al. (1993) with the upper mantle seismic estimates discussed in the text. 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 (din Vs/dln VP\ Figure 7.59. A summary of the mineral physics estimates and the preferred seismic profiles. Chapter 7, page 772 Q 100 200 300 400 500 fez 600 P 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 4 5 6 7 8 9 10 11 12 13 14 V e l o c i t y ( k m / s e c ) Figure 7.60. A comparison of the calculated S- and P-wave velocity profiles for a uniform Pyrolite mantle with the reference seismic profiles of akl35 (Kennett et al., 1995). Chapter 7, page 773 0 100 200 300 400 &500 Q 600 700 800 900 1 I « Mid-Ocean Ridge mantle potential temperature 1330-1350 C (1603-1623 K) Hot-Spot mantle potential temperature upper mantle anchor temperature at 100 km depth." Adjusting this single temperature results in shifting the upper mantle geotherm to higher or lower temperatures. Reference Pyrolite geotherm from modeling density and Cold Model + -WOK Hot Model z + 100K ~-lower mantle anchor temperature —3 1 1 J _ J 1200 1400 1600 1800 2000 2200 2400 T e m p e r a t u r e ( K ) Figure 7.61. The upper and lower mantle adiabatic geotherms for the Pyrolite mineral physics model. Re-running the mineral physics model involves only adjusting the two anchor temperature values at 100 and 661 km depth. 0 100 200 300 400 500 600 700 800 900 1000 1100 ^ 1200 j § 1300 w 1 4 0 0 F-iS 1500 &1600 Q 1700 1800 1900 2000 h~ 2100 2200 h-2300 2500 2600 2700 2900 i i i i l i i I I l i ui i l i i i i I i i i FT Chapter 7, page 774 I I I | I I I I | I I I I Pyrolite mineral physics — — "I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 • 1 1 t C D CO 0.0 0.5 1.0 1.5 2.0 2.5 (din Vsldln VP) 3.0 3.5 4.0 Figure 7.62. The predicted Pyrolite anharmonic scaling factor. 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 (din Vsldln VP)^ Figure 7.63. A comparison of the predicted Pyrolite anharmonic scaling factor with the preferred seismic estimates which are discussed in the text. 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 I i i i j 111 " Chapter . I I i | I I I I | I I I anharmonic |- Karato (1993) • \~~Qnharmonic *• anelastic Karato (1993) melt-free r Duffy & Ahrens , (1992b) onset of reduced •locity gradients I—D" layer • (chemical and thermal boundary layer) r " i l l l l l l l l l l l 7, page rp-r 776 T T mineral physics anharmonic Isaak et al. (1992) I I I I I I I I I I I I I I t O) o 0.0 0.5 1.0 1.5 2.0 2.5 3.0 (din Vsldln VP\ 3.5 4.0 Figure 7.64. A comparison of the predicted Pyrolite anharmonic scaling factor with the mineral physics estimates discussed in the text. Chapter 7, page 777 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 (din Vs/din VP) Figure 7.65. A comparison of the predicted Pyrolite anharmonic scaling factor with the lower mantle seismic inferences of Robertson and Woodhouse (1995; 1996a). Chapter 7, page 778 I I I I I 1 I I I I I I I 1 I 1 I I I I I I I I I I I I I I I I I rj 5.0E-6 l.OE-5 1.5E-5 2.0E-5 2.5E-5 3.0E-5 3.5E-5 4.0E-5 thermal expansion coefficient a(T, P) (1/K) Figure 7.66. Profile of the predicted Pyrolite coefficient of thermal expansion.The cusp in the profile between 420 and 490 km is likely to be an artifact of the adopted mineral assemblage. Chapter 7, page 779 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 ^ 1 4 0 0 1500 Q 1700 1800 1900 2000 2100 2200 2300 h-2400 -2500 -2600 -2700 -2800 h 2900 high temperature experimental results O.L. Andeson and Isaak (1995) predicted range and preferred value (5.80) of Anderson (1987) assuming: V(dlnVpld lnp)=\2 from geoid modeling of Hageretal. (1984) 2) {din V/dln Fpp=2.0-2.5 from Dziewonski & Woodhouse (1987) pyrolite mineral physics model *1 i 1 1 1 1 1 1 1 1 1 1 1 1 1 *1 1 • ' ' < 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 Figure 7.67. Predicted profile of the dimensionless parameter, f for a Pyrolite mantle. Chapter 7, page 780 Q o 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 I i i i I I I I I eg 4 0 O ^ 1 I l+l I r T 1>. C High temperature experimental results O.L. Anderson and Isaak (1995) ~predicted range and preferred value (1.80) -of Anderson (1987) I ' ' ' »-* -I-t-pyrolite mineral physics • ' ' ' i ' ' ' ' i ' ' i ' i ' » i 1t c 3 1— o c < 0.0 1.0 2.0 3.0 4.0 5.0 6.0 Figure 7.68. The predicted Pyrolite profile of the Anderson-Gruneisen parameter compared with the inferences from Anderson (1987). Chapter 7, page 781 ^ <ss & / $4 ^ 1 ^ T T T high temperature experimental results O.L. Andeson and Isaak (1995) "predicted range and preferred value (5.80) of Anderson (1987) assuming^ '\)(dln\fldlnp)=\2 ^ S j s J from geoid modeling of Hager etai. (1984) .2)(dln Vs!cln Vp ) p = 2.0 - 2.5 from Dziewonski & Woodhouse (1987) r profile required to satisfy-j the 100% spatial correlatioffH (din VIdin Vp). profile of J Bolton (1996) pyrolite mineral physics model F r = —gfcidwdT> J J I 1 I I I 1 I I I I I I I 1 I I 1 1 1 1 t cn CV E ro a 0 1 2 3 4 5 6 7 r 8 9 10 11 12 Figure 7.69. A comparison of the required lower mantle profile of rto satisfy the calculated (dlnV;/dlnl£)p profile assuming a 100% spatial correlation between S- and P-wave anomalies in joint, whole mantle tomographic models of Bolton (1996) and the predicted Pyrolite profile. Q 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 -2. i i i i i i i i | i i i i | i i i i | i i i i j i Chapter 7, page 782 r r r % c7 e.3 I T T T T High temperature experimental results O.L. Anderson and Isaak (1995) predicted range and preferred value (1.80) of Anderson (1987) I I I I 8S profile required to satisfy the 100% spatial correlation (Bin V.IB In f£ p profile of Bolton (1996). 11 I I t c E O c < 0 -1.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 Figure 7.70. A comparison between the required 85 profile to satisfy the calculated (dlnVsldln%)p profile assuming a perfect 100% spatial correlation between the S- and P-wave velocity anomalies (Bolton, 1996) and the predicted Pyrolite profile. Chapter 8, page 783 Chapter 8 A Thermal Origin for Seismic Anomalies from Mineral Physics modeling of a Pyrolite mantle and Seismic Tomography. Chapter 8, page 784 8.1 Abstract A major question of geodynamics is the driving force of mantle convection. While it has been commonly believed that thermal buoyancy is largely driving convection in the Earth's mantle, the validity of this assumption has recently been questioned in studies which calculated temperature anomalies from seismic anomalies recovered in tomographic models. In these studies, recent laboratory mineral physics results (Chopelas, 1992) are combined with seismic tomography to calculate extremely large temperature anomalies, 8 7" in the lower mantle on the order of +2500°K to -2000°K (Yuen et al., 1993; 1994; Cadek et al., 1994). The extreme magnitude of these temperature anomalies has caused these researchers to reject a purely thermal origin for lower mantle seismic anomalies, 5Vs and, instead, to invoke chemical anomalies in the lower mantle, implying that chemical, rather than thermal, buoyancy is primarily driving lower mantle convection. However, these studies employed the isothermal scaling factor for MgO, rather than the required adiabatic one, to convert the seismic anomalies to associated temperature anomalies. They argued the use of the incorrect scaling factor probably amounted to an error of only 30%. In addition, since magnesiowustite comprises only a relatively small amount by volume (<12%) of the lower mantle mineralogy, it is not clear that its properties are representative of the lower mantle. The inference of chemical anomalies in the lower mantle is in conflict with the conclusions drawn from the mineral physics modeling of p and F 0 , V$ and Vp, and finally, (<3 \nVs Id lnVF )p profiles for a uniform pyrolite composition, In the later study I am able to reconcile recent seismic estimates of the ratio (dlnF^/dlnF^),, with mineral physics estimates of (d lnVs /d lnVp )p at high T and P and thereby conclude lateral seismic variations are thermal in origin. This latter result is in conflict with the inference, noted above, that the lower mantle is dominated by chemical anomalies. To resolve this discrepancy I use the pyrolite mineral physics model to calculate the Vs velocity temperature derivative {dVs/d l)p throughout the mantle and use this to re-calculate the inferred temperature anomalies of Yuen et al. (1993). I find that the magnitude of the lateral temperature anomalies are significantly reduced compared to the above studies that invoked chemical anomalies such that 5T now ranges from » ± 100 °K at 660 km to « ± 480 °K at the top of the D" layer. As an additional check, I compile and re-calculate, using updated parameters, independent constraints on mantle temperature variations and find that these estimates range from « ± 50 °K beneath mid-ocean ridges (Shen & Forsyth, 1995) to « ± 65 °K at 410 km and « ± 85 °K 660 km depth (Revenaugh & Jordan, 1991 re-calculated; Flanagan and Shearer, 1998 re-calculated) to » ± 500 °K at the top of D"(Wysession et al., 1992). The agreement between the mineral physics interpretation of seismic tomographic velocity anomalies and the re-calculated independent estimates on lateral temperature variations demonstrates that lower mantle seismic velocity anomalies are indeed due to temperature fluctuations. Furthermore, when the rms velocity amplitudes for recent high resolution, whole mantle S-wave models are converted to temperature, there is no large temperature perturbation at 660 km depth, as would be expected if the 660 phase change acts to significantly impede mantle flow as some convection models have recently suggested. Therefore, away from chemical Chapter 8, page 785 and thermal boundary layers that exist at the surface and base of the Earth's mantle, I conclude that, 1) the lateral seismic anomalies resolved in tomographic studies are largely thermal in origin and consequently, 2) the dominant force driving mantle convection is indeed thermal buoyancy. Chapter 8, page 786 8.2 Introduction This chapter reports and interprets mineral physics estimates of the absolute magnitude of lateral temperature variations in the mantle. In a previous chapter I demonstrated that for a uniform pyrolite composition at the high temperature and pressure conditions within the mantle, it is possible to reconcile mineral physics estimates of (d l n F s / d InFp )p , a parameter that represents the ratio of relative Vs and Vp velocity heterogeneity within the mantle, with values derived independently from seismic studies. Early studies noted that seismic estimates of (dlnVs /8lnVr)p tended to be « 2.0, which contrasted with mineral physics estimates, derived largely from room pressure, experimental measurements for mantle silicates which gave (d lnVs /d lnVp )p « 1.0. This discrepancy led some workers to postulate that the seismic anomalies observed within the deep mantle do not reflect lateral perturbations in temperature and consequently, advanced a number of alternative mechanisms to reconcile the two inferences. However, the discrepancy disappeared when a high temperature and pressure mineral physics estimate of (dlnVs /d\nVp)p , calculated using the pyrolite model, was compared to the most recent seismic inferences. Thus, to first order, the relative magnitude of lateral variations in Vs and Vp inferred from seismic tomography are consistent with that predicted from a uniform composition mantle at high temperature and pressure. Indeed, lateral variations in Vs and Vp are expected to be proportional and spatially correlated i f they result from lateral temperature variations associated with thermally driven mantle convection. Chapter 8, page 787 In this chapter I place constraints on the magnitude of the lateral temperature variations which are responsible for the velocity anomalies. Essentially, the question addressed herein is "how hot (or cold) are the lateral seismic anomalies?" This study is a largely a synthesis of geophysical observations that provide constraints on the lateral temperature variation in the mantle, but where possible, I re-calculate the temperature estimates using updated parameters to ensure self-consistent estimates are compared to one another. Our major contribution occurs in the lower mantle, where in contrast to recent studies, which estimated lateral temperature anomalies of « ± 2500°K in the lower mantle, I find that the lateral variations are rather modest, ranging from « ± 100 °K at 660 km to « ± 480 °K at the core-mantle boundary. 8 . 3 Previous Work The Earth's temperature distribution is of fundamental importance to geophysics and central to the correct interpretation of data from solid-earth geophysics, petrology, and geochemistry. In this section I summarize a number of independent techniques for estimating the lateral temperature anomalies within the mantle with the goal of presenting a coherent picture of the mantle's thermal structure. I begin at the Earth's surface and move progressively deeper into the mantle, concentrating on oceanic, rather than continental, regions since these are, from a chemical view point, the least complicated. Temperatures in the mantle may be estimated by using two techniques (e.g. Solomon, 1976): 1) the measurement of physical properties which are strongly dependent upon temperature (MORB chemistry, ocean crustal thickness, viscosity, electrical conductivity, seismic attenuation, Chapter 8, page 788 RMS velocity heterogeneity), and 2) the topography of seismic discontinuities that can be correlated to known phase transitions that are well calibrated experimentally (e.g. 410-, 520-, and 660-km discontinuities). Below I summarize results using both techniques. 8.4 Lava eruption temperatures Although the bulk of the constraints on the lateral temperature variations within the mantle are indirect observations, I begin by noting an often overlooked constraint based on direct measurement of the temperature of erupting lava. As summarized by Solomon (1976), measured temperatures in lava fountains and lava lakes in Hawaii range between 1060 and 1190 °C (1333-1463 °K) which under the assumption that only adiabatic decompression has affected the lava during magma segregation and eruption, implies a temperature at the source region of roughly 1200 ±100 °C. While I will return to melt generation and the associated shallow mantle temperature perturbations when decompression melt studies are reviewed, in passing I note that petrologists had long recognized the global, near-uniform maximum magma eruption temperature of « 1200 °C (1473 °K; Carmichael et al., 1974, p. 359). 8.5 Oceanic heat flow and bathymetry The variation of oceanic heat flow and bathymetry as a function of sea floor age is typically described in one of two different models describing the cooling of oceanic lithosphere. The simplest model is that both subsidence and heat flow reflect cooling of a simple thermal boundary layer at the Earth's surface (Turcotte and Oxburgh, 1967; Parker and Oldenburg, 1973; Davis and Lister, 1974). In this model, a uniform half space with an Chapter 8, page 789 initially uniform internal temperature and constant basal temperature is invoked to describe cooling oceanic lithosphere. The initial temperature structure is created at the ridge and the thermal boundary layer, taken as the oceanic lithosphere, thickens progressively away from the mid-ocean ridge. The variation of temperature as a function of depth (z) and age within the half space, the conductive geotherm, may be described by (e.g. Carlson and Johnson, 1994): T{t,z) = Tmerf[zJA^j) where Tm (°C) is the initial mantle temperature of the half space, t is age, and z is the depth measured down from the surface, and K is the thermal diffusivity of the mantle (m2/sec and equal to k/{pm CP) where k is the mantle thermal conductivity (W/mK), pm is the mantle density at temperature Tm, and C p is the heat capacity at constant pressure (J/kg K)). The associated heat flux q (mW/m2) as a function of age is described by: =«;•-=!= Subsidence is assumed to occur by Airy isostatic compensation such that the top of the oceanic crust may be described as a function of time by: d(t) = dl ridge + '2pma TmdV/l^ ft (p»-Pff 2o) where c i r i d g e is the mean depth to the mid-ocean ridge crest (meters), a is the mantle volumetric thermal coefficient of expansion (1/K), and pH^Q is the density of water (kg/m3). Typically, in fitting the observed heat flow and subsidence, the above expressions are often simplified to: Chapter 8, page 790 1 q(t) = a-=, •sit and d{t) = dridge + by/T where a and b are constants to be determined by fitting the equations to observations. In employing these equations it is commonly assumed that some of the parameters are taken as known (e.g. pHiQ, dM^ a, k, C p) which allows one to determine a common mantle temperature (Tm) from both heat flux and subsidence data. Inspection of the above equations reveals that i f no process retards or disrupts the cooling of the thermal boundary layer, the predicted heat flux and subsidence for oceanic lithosphere is predicted to continue indefinitely as a function of the square root of lithospheric age (see figure 8.1). Carlson and Johnson (1994) have fit the half-space cooling model to ODP and DSDP depths to basements and found that the depth versus age data for seafloor younger than 80 Myr results in basal mantle temperatures in the range of 1300-1370 °C with a best fitting value of 1335°C. However, early observations, dominated from sites located in the western Pacific plate, reveal that for lithosphere older than « 70-80 Myr, neither heat flux nor bathymetry follow the predictions of the cooling half space model and instead tend to "flatten" beyond this particular age (Parsons and Sclater, 1977; Sclater et al., 1981). To account for this "flattening", an alternative to the halfspace model was proposed, termed the constant plate model (Langseth et a l , 1966; McKenzie, 1967; Parsons and Sclater, 1977; Parsons and McKenzie, 1978). In this model lithosphere of constant thickness, h is assumed to be heated uniformly to Tm at the mid-ocean ridge and thereafter have constant temperatures at its Chapter 8, page 791 surface and base. Initially, as the constant-thickness plate cools, the thermal boundary layer is much thinner than the plate thickness, and the temperature, heat flux, and subsidence is indistinguishable from that of the cooling half space model. However, at a particular age, dependent upon both the assumed thickness of the plate and the mantle temperature, the heat flux and subsidence depart from the trend predicted from the cooling half space model and asymptotically approach a steady state heat flux of qm and depth ds. The thermal, heat flux and subsidence history of the constant plate model may be described by the following equations (e.g. Stein and Stein, 1992; Carlson and Johnson, 1994): Tiz,t)=T h •Ic. n ft z sin| = | exp (-n2ct) where c = K TI2 /h2 , Q(z>t) = 9m I1 + 2 ] £ e x p ( - H 2 c t )] where qm is the asymptotic heat flux and given by qm = k{Tm - Tslllf }/h, and dif) = drld8e+dt 1 - - T E - / ' " 2 exp(-v" 2 cf) 71 where the term j in the summation only takes on odd numbers (1, 3, 5,...), and ds is the asymptotic bathymetry of the seafloor and defined by d = f \ P a r h s m m v >(p - p 1, Parsons and Sclater (1977), the first to champion this numerical model, determined that a constant plate thickness ofh= 125 km with a basal mantle temperature of 1350°C best fit their bathymetry and heat flux data (see PS77 in figure 8.1). Subsequent workers have Chapter 8, page 792 undertaken joint fitting of much larger data sets (in the North Pacific and Northwest Atlantic) which have resulted in a substantially thinner and hotter constant plate model, termed GDH1 (for Global Depth and Heat flow model #1 see GDH1 in figure 8.1) with a plate thickness of only h = 95 ± 15 km and Tm = 1450 ± 250°C (Stein and Stein, 1992). Geotherms for the cooling half space (120 Ma old), the Parsons and Sclater (1977) and GDH1 models are illustrated in figure 8.2 where the Parsons and Sclater and GDH1 profiles are taken from Nagiharaetal. (1996b). Subsequent application of simultaneous fitting of depth and heat flow observations within the framework of the constant plate thickness model for other ocean basins revels that there exists significant differences between the worlds ocean basins. For example, in the Indian Ocean, Shoberg et al. (1993) find best fitting values of h = 80 km; Tm = 1450 °C, while Stein and Stein (1994b) obtain values of h = 90 km; Tm = 1325°C for oceanic lithosphere around the African tectonic plate, h = 150 km; Tm = 1450 °C for oceanic lithosphere adjacent to the South American tectonic plate, and lastly, h = 105 km; Tm = 1425°C for oceanic lithosphere solely from the Northwest Atlantic adjacent to the North American tectonic plate. A l l of these results differ from GDH1, implying that the thickness and mantle temperature values derived by joint fitting the global data set are not a measurement of a fundamental physical property, but simply some averaged value reflecting the mean variations for the pooled global sample set. As noted by first by Davies (1980) and reiterated by McNutt (1995), the constant thickness plate model of Parsons and Sclater (1977; hereafter referred to as PS77), or its latest refinement GDH1, merely provides a better fit to the observations from the Western Chapter 8, page 793 Pacific plate without addressing the question of what process appears to limits the apparent growth of the thermal boundary layer at ages beyond 70-80 Myr. As stressed by Davies (1980), and Davies and Pribac (1993), inspite of the better fit to the bathymetry and heat flow observations, there are a number of reasons why the constant plate model is not appropriate to describe cooling oceanic lithosphere. It is widely accepted that the formation of oceanic crust and lithosphere involves passive upwelling of mantle across the dry peridotite solidus at a depth of « 60 km (for a normal mantle with a potential temperature of 1330 °C). The melt production region at depth below a mid-ocean ridge is shaped roughly as a triangular prism oriented parallel with, but below the mid-ocean ridge axis (see figure 8.3). While the exact details of the shape of the melt region are dependent upon the mantle viscosity beneath the ridge (e.g. Cordery and Phipps Morgan 1993; Su et al., 1994; Plank and Langmuir, 1992) which in turn, controls the interplay of melt buoyancy forces (forces resulting from the density difference between solid mantle and interstitial melt) and the negative pressure gradients caused by divergence of the oceanic lithosphere, a first order observation is that the creation of oceanic crust and lithosphere at a mid-ocean ridge is thermally defined. Therefore, with increasing age the initial lithosphere created at the ridge will cool and thicken. Viewed from this perspective, the explicit assumption in the constant-thickness plate model, that a plate of constant thickness of « 125 km is instantly created at the ridge axis, is seen to be mathematically convenient, but geological fiction. Furthermore, the values of the inferred plate thickness for either the GDH1 or PS77 models (80-125 km) exceed the depth where upwelling mantle intersects the dry peridotite solidus (« 60 km), and Chapter 8, page 794 consequently, would preclude any melt formation (and hence, the formation of ocean crust) i f these thickness estimates are accepted at face value. A further point, which will be discussed in detail in a subsequent section, is that the thickness of ocean crust produced at a mid-ocean ridge is highly sensitive to the mantle temperature. Existing theoretical decompression melt models indicate that the observed, near-uniform ocean crust thickness of 7 ± 1 km correlates with a mantle potential temperature of 1330°C and that increasing this to 1450°C, such as that of GDH1, would result in the production of ocean crust with a thickness on the order of 22 km. Such, high values for the thickness of ocean crust are observed, but are restricted to regions along the mid-ocean ridge system where a mantle plume intersects an active mid-ocean spreading ridge (such as Iceland). Thus, the mantle potential temperature inferred for the latest refinement of the constant plate model is inconsistent with observations of the global variation in ocean crust thickness. As an alternative to the constant-thickness plate model, Parsons and McKenzie (1978) appealed to the onset of secondary, small-scale convection beneath a cooling plate at an age of 70-80 Myr to explain the flattening in bathymetry and heat flow. They proposed that a relatively thin, thermal boundary layer located at the base of oceanic lithosphere would progressively thicken with time until it become convectively unstable at a critical age. At this time, this cold thermal boundary layer would be replaced, via secondary, small-scale convection, with hotter, more buoyant mantle that would supply additional heat to the base of the oceanic plate. This additional heat would then produce the apparent flattening in both bathymetry and heat flux for oceanic lithosphere older than the critical age. Within this framework, Parsons and McKenzie (1978) assumed that the critical age equals the age where Chapter 8, page 795 both the observed heat flow and depth trends depart from predictions of the half space model (* 70-80 Myr). The ability of secondary, small-scale convection to explain flattening of bathymetry and heat flow by providing additional heat to a cooling plate has, as a viable mechanism itself been questioned. As first noted by O'Connell and Hager (1980) using analytical relationships, and later numerically demonstrated by Davies (1988), the actual affect of small-scale convection acting at the base of oceanic lithosphere is to cause greater heat loss, and consequently, increased seafloor subsidence over that predicted from the simple cooling half space model. This effect is exactly opposite to its intended purpose which is to cause decreased subsidence and heat loss. In addition, large characteristic signals of small-scale convection should be evident in the gravity, geoid, and bathymetry fields; all of which should be obvious in oceanic lithosphere older than the critical age of 70 Myr, which they are not (Davies, 1988). While claims have been made that specific linear features of the geoid field for the Pacific plate do indicate small scale convection at depth (e.g. Watts et al., 1985), Renkin and Sandwell (1986) note that these features in the filtered geoid field are numerical artifacts from the application of a sharp edged filter to the total geoid field (commonly the filtering is performed to remove spherical harmonic terms of the observed geoid field with degree less than 11). Therefore, there is at present, no unambiguous observational evidence in favor of the onset of small-scale convection for oceanic lithosphere older than 70-80 Myr. Indeed, recent global compilations of seafloor depth as a function of age have found that the purported critical age of 70 Myr is not uniform globally, with many geographic regions exhibiting ocean bathymetry increasing linearly with the square root of age to ages as great as 160-170 Myr (e.g. the North Atlantic Margin located on North American plate; the Chapter 8, page 796 Argentine Basin located on the South American Plate; Marty and Cazenave, 1989; see figure 4). Furthermore, Marty and Cazenave (1989) demonstrated clearly that those regions of ocean floor that exhibited "flattening" were associated with known hotspot swells (Bermuda and Cape Verde in the equatorial North Atlantic, the Darwin rise in the Western Pacific) leading strong support to earlier studies which had focused on the Pacific plate and invoked the thermal and dynamical affects of present or recent hot spot activity to explain the anomalous bathymetry and heat flow (e.g. Heestand and Crough, 1981; Schroeder, 1984). While some studies recognized the anomalous bathymetry and its direct correlation with hot spot tracks (e.g. Renkin and Sclater, 1988), they argued such activity would have had to affect essentially all of the Western Pacific plate, a possibility they discounted. However, subsequent studies have indeed recognized an extensive, present-day "Super swell" within the Pacific plate (e.g. the French Polynesia Superswell (McNutt and Fisher, 1987; McNutt and Judge, 1990) and fossil "Super swells" (e.g. the Darwin rise (McNutt and Fisher, 1987; McNutt et al., 1990; Larson, 1991; Davies and Pribac, 1993). Thus, rather than the onset of secondary, small-scale convection, the discrepancy between the predicted heat flow and bathymetry for the cooling halfspace model and observations in the Western Pacific is best explained by the affects of past and present hot spots (see also Smith and Sandwell, 1997). Recent re-interpretation by Sclater and Nagihara (1991) of existing heat flow (Epp et al., 1970) and bathymetry measurements in the Gulf of Mexico, a region of Jurassic (« 150 Ma) ocean lithosphere which has not been affected by hot spot magmatism, combined with new heat flow measurements (Nagihara et al., 1996a; b), reveals that this area may provide the best evidence to date in discriminating between the various models describing cooling oceanic lithosphere. Significantly, this area shows no sign that it has been affected by Chapter 8, page 797 subsequent hotspot magmatism. The observed values for heat flow and bathymetry for the Gulf of Mexico are also plotted in figures 8.1 A and 8. IB along with the predicted curves for the halfspace cooling model (HS), the constant-thickness plate model (PS77), and its latest revision, GDH1. It is evident from these figures that the Gulf of Mexico is consistent only with the predictions of the half space cooling model. This is emphasized in a plot of predicted ocean depth versus predicted heat flow (Nagihara et al. 1996b) where the predictions for the PS77, GDH1, and half space models are compared to the Gulf of Mexico observations (see figure 8.5). It is clear from this figure that the Gulf of Mexico observations can not be explained via GDH1 or PS77, since these two models asymptotically approach steady state values for both bathymetry and heat flow that differ significantly from the observations. The constant thickness plate model assumes that a fixed temperature is maintained at a fixed depth everywhere beneath oceanic lithosphere. Thus, the subsidence and heat flow of ocean lithosphere should flatten at the same age («70 Ma) everywhere i f observations in the Western Pacific apply to all oceanic plates. The. observations from the Gulf of Mexico clearly demonstrate that this is not the case with both heat flow and bathymetry continuing to decrease in a fashion consistent with the half space cooling model (note that while bathymetry in the Argentine Basin is also consistent with the half space model beyond the critical age of 70 Myr, the oldest oceanic lithosphere in that region extends only to 120 Myr in contrast to 150 Myr in the Gulf of Mexico. In addition, no heat flow measurements have been made in the Argentine Basin, in contrast to the two heat flow data sets of Epp et al. (1970) and Nagihara et al. (1996a) in the Gulf of Mexico). Additional independent evidence that supports the application of the cooling halfspace model to describe the evolution of oceanic lithosphere comes from recent Chapter 8, page 798 seismological studies. Zhang and Tanimoto (1990; 1991) have studied the dispersion of surface-waves phase velocities, specifically Love waves, as a function of plate age and seismic period. For the Pacific plate they find that their observations may be explained by a gradually thickening plate (see figure 8.6) that very closely matches that predicted for the cooling halfspace. Indeed, the inferred plate thickness from Love waves is virtually indistinguishable from the thickness of the halfspace defined by the 1020°C isotherm (see figure 8.7). In this figure I show the inferred plate thickness evolution from the Pacific, Indian, and North Atlantic plates based on Love waves (Zhang and Tanimoto, 1990) together with the predicted thickness for the cooling halfspace model for the isotherms T = 1020°C and 1145°C. While there are differences between the precise evolution of the North Atlantic and Pacific plates, these differences decrease as a function of age and by 70 Myr and beyond, all three ocean basins are well approximated by the cooling plate model. The results of Zhang and Tanimoto (1990; 1991) also agree with a much earlier surface-wave phase velocity study which used Rayleigh waves to determine the evolution of the Pacific plate (Leeds et al., 1974), Nazca plate (Forsyth, 1975), and Atlantic (Weidner, 1974). While there is nothing unique about the 1020°C isotherm in the above figure (the precise value is dependent upon the adopted value for the thermal diffusivity and mantle potential temperature), the major conclusion from these surface-wave seismic studies is that the a cooling half-space model where the plate thickness continues to grow well beyond the "critical age" of 70 Myr is consistent with these seismic observations. If secondary, small-scale convection were indeed to completely disrupt the base of the oceanic lithosphere for ages greater than 70 Myr, then surface-wave seismic studies, which have their greatest sensitivity to shallow lithosphere and mantle structure, should reflect this, which they do not. Chapter 8, page 799 Another seismic study, albeit using body wave rather than surface waves, corroborates the findings of Tanimoto and Zhang. Woodward and Masters (1991) used a global set of over ten thousand measurements of PP-P and SS-S differential body wave travel times to study upper mantle velocity structure. These differential travel times are primarily sensitive to the upper-mantle velocity structure at the SS bounce points rather than the velocity structure seen by the deeper S-wave raypath (see figure 8.8). This is illustrated in the scatter plots of SS residuals plotted against SS-S residuals and S versus SS-S residuals (the absolute S-wave residuals were determined by cross-correlation of the S-waveform with synthetic waveforms). These plots are reproduced in figure 8.9 and 8.10) and clearly shows a strong correlation of SS to SS-S travel time residual that is not seen in the S to SS-S plot, which Woodward and Masters (1991) note supports a first-order interpretation of their residuals in terms of the velocity structure at the SS bounce point (see figure 8.11). When they evaluated their data in terms of the surface tectonic region of the bounce point, they found that for oceanic regions, both the PP-P and SS-S differential travel times exhibit a strong correlation as a function of seafloor age. Specifically, when they plotted the mean travel time residuals against the square root of seafloor age, a linear correlation emerged (see figure 8.12a and 8.12b), which could be described by; StPP_P =-0.18 ± 0.01 sec/(M>r)1/2 ss-s - -0.51 ±0.01 sec/(Myr)ul The SS-S and PP-P travel time residuals indicate that the correlation with age is consistent with thickening of oceanic lithosphere to ages beyond the inferred critical age of 70 Myr, the age where secondary, small-scale convection is supposed to initiate. Chapter 8, page 800 The major point to draw from consideration of the seismic, heat flow, and bathymetric studies is that the bathymetry and heat flow of oceanic lithosphere of any age, which has not been disturbed by hot spots, is entirely consistent with a cooling half-space model with a mantle potential temperature of roughly 1300-1350 °C. This is the temperature range inferred from fitting the half-space model to oceanic lithosphere younger than 70 Ma (Carlson and Johnson (1994), which based on seismic observations, should apply equally well for any undisturbed oceanic lithosphere. 8.6 The genesis of MORB magmas; decompression melting of mid-ocean ridge basalts. The genesis of mid-ocean ridge basalts (MORBs) is a fundamental question in Earth science and has therefore been studied by a great number of workers. However, only recently has a integrated theoretical model of melt production that relates melt composition, mantle temperature, and degree of extension been formulated (e.g. McKenzie, 1984; White et al., 1987; McKenzie and Bickle, 1988, 1990; White and McKenzie, 1989; Klein and Langmuir, 1987; McKenzie and O'Nions, 1991; Watson and McKenzie, 1991; White, 1988, 1992; White et al., 1992; Watson, 1993; Pedersen and Ro, 1992; Plank and Langmuir, 1992; Langmuir et al., 1992; Latin et al., 1989; 1993; Kostopoulos and James, 1992; Kinzler and Grove, 1992a, b, 1993; Wilson, 1993; Tate et al., 1993; Brown and White, 1994; 1995; Brody et al., 1994; Williamson et al., 1994a, b; Su et al., 1994; Tainton and McKenzie, 1994; Shen and Forsyth, 1995; Iwamori et al., 1995; Plank et al., 1995; Asimow et al., 1995; 1997; Kinzler, 1997). In these models the amount and composition of the melt formed during Chapter 8, page 801 extension is a function of initial lithospheric thickness, mantle temperature, the composition of the convecting mantle (dry or volatile rich) and its related solidus, the nature and efficiency of melt extraction, and the amount and rate of extension. Of these parameters, the most significant is the affect of mantle temperature on melt volume and composition, as commonly described by the mantle potential temperature, the theoretical surface temperature of the mantle when the mantle adiabatic geotherm is extrapolated from depth to the surface (see figure 8.13). In its simplest form, a decompression melt model quantitatively links the melt composition and volume produced by partial melting when upwelling mantle crosses the dry peridotite solidus. Other possible causes of melting, such as the introduction of volatiles, which would lower the dry solidus temperature by perhaps as up to 500°C (e.g. Thompson, 1992; Bell and Rossman, 1992) are not considered here, although I note that while the original theoretical model was parameterized only for dry melting, it has been extended to account for volatile-rich (or "wet") melting for continental settings (e.g. Gallagher and Hawkesworth, 1992; Latin et al., 1993; Iwamori et al., 1995). Also note that the resulting path that the upwelling melt takes after crossing the dry solidus deviates to lower temperature from the mantle adiabat due to the latent heat absorbed by the melting process (see figure 8.14). Consequently, adiabatically extrapolating a surface lava eruption temperature to depth to infer the mantle temperature at melt source region, as undertaken by Solomon (1976), is likely to underestimate the appropriate mantle temperature. With respect to constraining the magnitude of the lateral temperature variations, a key observation in the ocean basins is that away from mantle plumes and fracture zones, the thickness of oceanic crust is nearly uniform a t « 7 ± 1 km (Chen, 1992; White, McKenzie and Chapter 8, page 802 O'Nions, 1992; Brown and White, 1994; see figure 8.15) and largely insensitive to the spreading rate (Chen, 1992; Brown and White, 1994; Su et a l , 1994; West et al., 1994; Niu and Hekinian, 1997). The global uniformity of oceanic crustal thickness indicates that the rate of melt production beneath mid-ocean ridges must be nearly constant because within the framework of the decompression melt model, the predicted melt production rate, and consequently, the predicted melt thickness is very sensitive to the mantle potential temperature (see figure 8.16). Since at mid-ocean ridges, the amount of extension is infinite and mantle upwells to very near the base of the crust (Brown and White, 1994; Iwamori et al., 1995; Shen and Forsyth, 1995), possible additional complications such as variable amounts of extension (e.g. Latin et al., 1990; Williamson et al., 1994a, b) and/or finite duration of extension (e.g. Pederson and Ro, 1992; Brown and White, 1995), and at-depth freezing of melt (e.g. McKenzie, 1989) are not significant in this particular tectonic setting, and hence, will not mask the dominant signature of mantle temperature on melt volume. The parameterization of the original decompression melt model (McKenzie and Bickle, 1988) indicated that normal oceanic crust thickness is consistent with a mantle potential temperature of Tp - 1280 °C. Subsequent refinements, such as adopting a better estimate for the heat of fusion, allowing the mantle to upwell only to the base of the ocean crust rather than to the surface, accounting for the change in volume of the residual mantle subsequent to melt extraction, and consideration of fractional, rather than batch melting, has increased this estimate slightly to Tp = 1330-1350 °C (e.g. McKenzie and Bickle, 1990; White et al., 1992; Brown and White, 1994; Iwamori et al., 1995). In spite of these modifications, the observed scatter in global oceanic crust thickness and M O R B major element geochemistry is well matched by predictions with only slight perturbations to the Chapter 8, page 803 "normal" mantle potential temperature of ± 4 0 °C to ± 6 5 °C (see figure 8.17; Brown and White, 1994; Su et al., 1994, Shen and Forsyth, 1995). The McKenzie and Bickle (1988) decompression melt model considered only major elements, but subsequent studies have extended it to account for trace and rare earth elements (McKenzie and O'Nions, 1991; Whit et al., 1992). Consideration of the pattern of rare earth elements in the normal MORB basalts results in a slightly higher inferred mantle potential temperature of Tp = 1330-1360 °C (e.g. White et al., 1992; Brown and White, 1994) but this is within error of the estimate based on consideration of crustal thickness alone (see figure 8.18). As proposed by White et al., (1992) this discrepancy between the two approaches likely reflects retention of a small amount of melt in the mantle that did not separate completely to form the ocean crust, or to systematic errors in the adopted primitive rare earth element concentration of the source mantle, or to errors in the adopted REE partition coefficients between melt and solid. White et al. (1992) note that the maximum uncertainty in the REE concentrations is « 10%, and if the mantle source concentrations are reduced by this amount, the mean crustal thickness predicted from inversions of the rare earth element patterns is reduced from 8.3 ±1 .5 Km to 7 km, a value which is indistinguishable from the mean seismic thickness of ocean crust (7.0 ± 1 . 0 km). In spite of this minor uncertainty, the spread in thickness predicted by consideration of crustal thickness alone and the spread estimated from REE geochemical inferences is similar (compare figures 8.17 and 8.18) indicating that the relative perturbations in temperature required to explain the observations is also similar. Chapter 8, page 804 While nearly all melt models predict relatively modest lateral temperature variations beneath the global mid-oceanic ridge systems, the model of Klein and Langmuir (1987; see also Langmuir, Klein and Plank, 1992) stands in marked disagreement with the above studies, and instead, explains the full range in normal M O R B chemistry with temperature anomalies of « ± 250 °C. This model is primarily based on global correlations in FeO and Na 2 0, normalized to 8 wt % MgO to correct for shallow level fractionation. N a 2 0 8 0 M g 0 is generally regarded as a good indicator of the extent of melting because it is strongly partitioned in the melt during melting, the partition coefficient is relatively insensitive to variations in mantle composition and the initial concentration within the mantle is not expected to be highly variable (Langmuir et al., 1992; Shen and Forsyth, 1995). In contrast FeO s o M g o i s believed to be a good indicator of the depth of melting, although complications exist because the partition coefficient depends on mantle composition to a greater degree than N a 2 O 8 0 M g O (Shen and Forsyth, 1995). Since the mantle composition of a particular packet of upwelling mantle within the partial melt zone is likely to undergo progressive change during ascent, the predicted Fe0 8 0 M g 0 will also change. Nevertheless, in spite of this complication, all the decompression melt models predict that melts generated at greater pressure have higher Fe0 8 0 M g Q (for a given melting fraction and source composition). Thus, melting at mid-ocean ridges is often interpreted in terms of the observed trends in FeO g 0 M g 0 and N a 2 0 8 0 M g 0 , which Klein and Langmuir (1987) find are negatively correlated (see figure 8.19). This trend is consistent with decompression melt models since hotter mantle will intersect the dry solidus at greater pressure and result in a greater melt fraction and pressure of melting. The greater melt fraction will, in turn, result in lower N a 2 O 8 0 M g Q (by diluting the initial concentration of Na in a larger melt volume) while the greater pressure of melting will result Chapter 8, page 805 in a higher Fe0 8 0 M g 0 , which when considered together result in a correlation consistent with the observed negative correlation. Figure 8.20 illustrates the positive correlation for the global normal M O R B NajOg^ M g 0 compositions and depth of the ridge axis. Note here the wide range in observed N a 2 O 8 0 M go wt0/0 exhibited by normal MORB. In their recent refinement of their melt model, Langmuir et al. (1992) argued that such a large range in N a 2 O 8 0 M g 0 wt% is consistent with large lateral temperature variations (« ±250°C), but not changes in mantle composition (for constant temperature), which predicts a N a 2 0 8 0 M g 0 wt% versus crustal thickness trend that is nearly flat and thus, at odds with the observed global trend (see figure 8.21). However, this conclusion has been challenged by Shen and Forsyth (1995) who find that the range in observed in Fe0 8 0 M g Q wt % is decreased by half when careful corrections for compositional heterogeneity are considered. This in turn, decreases the implied lateral temperature range beneath the mid-ocean ridges to ± 120 °C, with Shen and Forsyth (1995) arguing that at least half of the remaining temperature estimate reflects difficulties in the fractionation correction. In consideration of N a 2 O 8 0 M g 0 wt%, Brown and White (1994) note that a weak correlation exists between N a ^ 0 M g 0 wt% and spreading rate, especially at slow spreading rates (see figure 8.22). They note that as the spreading rate increases beyond a full rate of 15 mm/year , the observed Na 2 0 8 0 M g 0 wt% approaches a constant value of « 2.5 with very little variation (the Australian-Antarctic Discordance, a zone of anomalously deep bathymetry and cold mantle (Wessel and Hayes, 1974; Forsyth et al., 1987; Kuo, 1993; Kuo et al., 1995; West et al., 1994) is the single exception). Because over 90% of the present day global ridge system is spreading at a rate greater than 15 mm/year, the cause of the large variation of Chapter 8, page 806 Na 2 O g o M g 0 wt% that Langmuir et al. (1992) observe, with near constant crustal thickness (see figure 8.21), is not consistent with large temperature variations (since oceanic crustal thickness is very sensitive to mantle potential temperature). Thus, much of the spread in the observed N a 2 O g 0 M g 0 wt% exhibited for the global compilation of normal M O R B ' s likely reflects other processes rather than large temperature anomalies (for example Nielson et al. (1995) suggest that systematic errors in published N a 2 O g 0 M g G wt% values may exist due to loss of Na from susceptible portions of MORB pillow-rim glasses during microprobe analysis). In agreement with the interpretation of MORB geochemistry in terms of only modest variations in mantle potential temperature is the study of Schilling et al. (1995) who report and interpret major element composition of basaltic glasses from a 600 km long traverse along the equatorial Mid-Atlantic Ridge. They find large scale trends in the inferred mantle potential temperature over the full length of the transect. However, the total variation in basalt Na 2 O g 0 M g 0 wt% is well matched by only modest temperature anomalies of only « ± 50 °C using the Klein and Langmuir (1987) decompression melt model (see figure 8.23). While the absolute value of the inferred mantle potential temperatures are model dependent, as demonstrated when the decompression melting model of Niu and Batiza (1991) or Albarede (1992) are substituted for the Klein and Langmuir (1987) parameterization (the inferred absolute temperatures along the transect are systematically shifted by +25 °C and -125 °C, respectively, for these particular parameterizations), the relative trends in temperature, and of particular interest here, the relative magnitude of the inferred lateral temperature variations remains unchanged at A7^ « ± 50 °C. Chapter 8, page 807 While subsequent refinements of the melt model have slightly increased the reference mantle potential temperature from 1280°C (McKenzie and Bickle, 1988) to approximately 1330-1350 °C (e.g. Iwamori et al., 1995), the conclusion, based on the global uniformity of normal M O R B crustal thickness, that global lateral temperature variations are indeed minor, appears to be robust and is not very sensitive to assumptions of the flow field. For example, some studies have noted that the crustal thickness may be sensitive to the relative importance of plate induced upwelling (e.g. the passive flow model of Brown and White, 1994) and thermal and/or compositional buoyancy driven flow (e.g. Su and Buck, 1993; Su et a l , 1994; West et al., 1994; Shen and Forsyth, 1995). In decompression melt models that include compositional buoyancy, (reflecting the density difference between fertile and depleted, melt-free residual mantle) greater variations in predicted crustal thickness are found for low spreading rates and higher mantle potential temperatures (see figure 8.24). This figure shows that while this effect is likely to be important at slow spreading rates, at high spreading rates, characteristic of most of the global mid-ocean ridge system, passive plate-driven flow dominates. Indeed, in a recent review, Parmentier (1995) notes that predictions of large variations in crustal thickness at slow spreading ridges have not been observed (Su et al., 1994) suggesting that compositional buoyancy may be only a second order effect. A value of « ± 40-65 °C for shallow upper mantle temperature anomalies (e.g. Brown and White, 1994; Shen and Forsyth, 1995) contrasts sharply to the « ± 250°C estimate based on global trends i n N a 2 O 8 0 M g O and F e O 8 0 M g O wt % (e.g. Klein and Langmuir, 1987; Langmuir et al., 1992) that is discussed above. This is clearly seen in figure 8.25 where I plot the predicted lateral temperature anomalies at the intersection of the pyrolite mineral physics Chapter 8, page 808 adiabatic geotherm and the composite dry peridotite solidus (based on combining the results of melting experiments on a fertile peridotite composition KLB-1 (Takahashi et al., 1993; Zhang and Herzberg, 1994; Iwamori et al., 1995; Herzberg and Zhang, 1996)). Also shown at the surface are the global mean mantle potential temperatures for "normal" mid-ocean ridges and hot spots, respectively (White et al., 1992; Watson and McKenzie, 1991; Watson, 1993; Iwamori et al., 1995). Visual inspection of this figure clearly shows the difficulty with accepting a value of « ± 250°C for global lateral temperature variations beneath "normal" mid-ocean ridges - at the coldest temperature, upwelling mantle would only just graze the dry solidus, implying virtually no melt production, while at the hottest temperature, upwelling mantle would intersect the dry solidus at temperatures in excess of that estimated for hot spots. In order to distinguish further between these two interpretations (ATp = ± 50°C or ± 250°C), recent studies have combined seismic and geodynamic data, either as a pair, or in combination with M O R B compositional data, to provide added constraints on thermal and compositional variation in the upper mantle. Sheehan and Solomon (1991) inverted for both temperature and compositional affects that simultaneously fit the long wavelength geoid, bathymetry, and differential SS-S travel time residuals along the Mid-Atlantic ridge. The thermal anomalies at depth (AT(k, z)) are related to the predicted bathymetry (Ah(k)) for wavenumber k within the framework of viscous flow theory via (Sheehan and Solomon, 1991): Chapter 8, page 809 where a is the volumetric coefficient of thermal expansion, pmg and p are the mantle and water densities at room temperature and pressure, and z m a x and z m i n are the upper and lower depths over which the thermal anomalies are allowed to vary. In the integral, a transfer function, termed the bathymetry kernel, H(k, z), which is a function of depth and wavenumber, relates the perturbations in temperature to mantle flow from equations of continuity and motion given a set of boundary conditions, a viscosity model, and a constitutive relation between stress and strain (Parsons and Daly, 1983). Likewise, the long wavelength geoid field may be related to the temperature anomalies at depth via: where G is the gravitational constant, g is the surface gravitational acceleration, K is the thermal conductivity, and G(k, z) is the geoid kernel. Lastly, to estimate the two way travel time perturbation from mantle temperature perturbations, Sheehan and Solomon (1991) assumed a value for the temperature derivative for shear velocity ((dVs/dT)p= -0.6 m/sec/K), based on the value inferred by McNutt and Judge (1990) from fitting predicted to observed Love wave surface phase velocities for mid-Pacific lithosphere. This value then allows seismic velocity perturbations to be linked to temperature perturbations via: 2TI G p, 0 a gK Zmax AN(k) = iG{k,z)AT(k,z)dz Z min At(k) = 2 Vg (z)Jl - p2 Vl (z) AT(k,z) dz where At(k) is the travel time anomaly, VSi is the reference shear velocity profile from P R E M (Dziewonski and Anderson, 1981) and p is the ray parameter (sin i/Vs). Chapter 8, page 810 Sheehan and Solomon (1991) found that the best fit was provided by models with a shallow low viscosity layer (40-200 km in depth; with a viscosity 1/100 of the underlying mantle viscosity) and the thermal perturbations constrained to lie within the upper 300 km of the upper mantle (three models were considered where the lateral temperature variations were constrained to lie within a zone from 0 to 150 km, 0 to 300 km, and 0 to 660 km depth, respectively). Their preferred model for the northern Mid-Atlantic ridge has lateral temperature variations of only ± 50 °C and compositional variations parameterized in terms of the molar ratio of Mg to (Mg + Fe) in olivine of ± 2.0 % (Mg/(Mg+Fe). They note that the predicted range in (Mg/(Mg+Fe) for their preferred model is in good agreement with chemical analysis of dredged basalt samples from the north Atlantic which have a range of ±2.5% (Mg/(Mg+Fe) (Michael and Bonatti, 1985). Likewise, comparison of their inferred temperature variation for the North Atlantic is in excellent agreement with that estimated directly to the south in the equatorial Mid-Atlantic by Schilling et al. (1995; see figure 8.26). Zhang et al. (1994) has also noted the excellent spatial correlation along the entire Mid-Atlantic ridge system between bathymetry, MORB chemistry (as parameterized by N a 2 0 8 0 M g 0 wf% data taken from the Klein and Langmuir (1987) compilation), and surface wave velocity anomalies (in the depth interval 48-150 km using their global upper mantle S-wave velocity model RG5.5 (Zhang and Tanimoto, 1991)). To obtain an estimate of the temperature anomalies at depth and assuming that temperature alone is responsible for the observed velocity anomalies, Zhang et al. (1994) adopt a shear wave velocity temperature derivative, {dVsldf)l> = -0.34 m/sec/K, based on averaging the room pressure, but high Chapter 8, page 811 temperature, experimental values for olivine (Isaak et al., 1989; Anderson et a l , 1992). Recall that the affect of temperature on seismic shear velocity may be described by: For the amplitude of their inferred shear wave anomalies, the corresponding temperature variations are ± 304 K at 100 km depth, a value far in excess of that estimated by either Sheehan and Solomon (1991) or Schilling et al. (1995). Zhang et al., (1994) note that at a depth of 40 km RG5.5 possesses velocity anomalies with a variation of dVs « 6% between a mid-ocean ridge and old oceanic lithosphere, which translates into a temperature perturbation of 790 K for their adopted scaling factor. Between a mid-ocean ridge and old, stable continental lithosphere the contrast in velocity anomalies is even greater ( 8 Kg « 8%) giving predicted temperature differences of « 1050 K at 40 km depth. Zhang et al. (1994) believed that both temperature estimates were too high to be physically plausible, implying that the value of (dVs/8T)p was inappropriate. However, Su et al. (1992) has pointed out that both the amplitude and depth extent of the velocity anomalies in the tomographic model RG5.5 are underestimated with respect to that recovered by other seismic tomographic models, demonstrating that, irrespective of concerns over the choice for(dVs /dT)p , this particular tomographic model is flawed. Specifically, Su et al. (1992) demonstrate that the RG5.5 model is incapable of correctly predicting a global set of observed differential SS-S travel time residuals and underestimates the slope of the observed trend in SS and SS-S travel time residuals as a function of age for oceanic lithosphere (e.g. 8tss = a + b^jtage and &ss-s ~c + dJtage )• et al. (1992) conclude that upper mantle amplitudes in RG5.5 are Chapter 8, page 812 underestimated by a factor of « 2-3 across the whole depth extent of the upper mantle, with the shallowest upper 150 km of RG5.5 being the least affected interval. These criticisms of RG5.5 have been acknowledged as largely correct (see Tanimoto and Stevenson, 1994; and Zhang and Lay, 199_) and reflect a limitation of the vertical resolving power of surface waves, the only type of seismic wave used in constructing RG5.5. Therefore, the predicted temperature anomalies estimated by Zhang et al. (1994) are actually too low because the amplitudes of the velocity anomalies are underestimated. Although the issue of the correct magnitude and depth extent of seismic anomalies within the upper mantle was discussed briefly by Zhang et al. (1994), they chose to reduce the magnitude of the predicted temperature anomalies by discarding their original choice of (dVs/dT)p and instead, adopt temperature derivatives from the experimental attenuation and compression velocity study of Sato et al. (1989). This study used ultrasonic measurements of compression velocity and associated attenuation to estimate the change in compression velocity for a typical olivine peridotite composition heated to temperatures near the shallow upper mantle solidus. Using these empirical results, and converting them to shear wave derivatives assuming a constant links Vs to Vp temperature derivatives, Zhang et al. (1994) infer lateral temperature variations below the Mid-Atlantic ridge of 200 ± 100 K. Inspite of this decrease, I believe this temperature estimate is still an overestimate. First, I note that at 40 km depth, the temperature difference between a mid-ocean ridge with an assumed mantle adiabatic geotherm and a conductive geotherm for 120 Ma old oceanic lithosphere is indeed « 790 K (see figure 8.27), a value indistinguishable from the value that Zhang et al. (1994) originally estimated, but discounted. While this similarity is Chapter 8, page 813 likely to be fortuitous, given that the amplitude of the velocity anomalies are underestimated in the tomographic model RG5.5, the simple thermal evolution and temperature structure of shallow oceanic lithosphere does indicate a way to extract an estimate for effective (dVs/dT)/, independent of experimental results. Note that Sheehan and Solomon (1991) used a value of -0.60 m/sec/K, which they acknowledged was greater than anharmonic experimental estimates, such as that of Anderson et al. (1992) (which were originally adopted by Zhang et al., 1994). Sheehan and Solomon justified their selection because it was similar to the value of-0.62 m/sec/K determined by McNutt and Judge (1990) by least squares fitting of predicted and observed surface Love wave phase velocities in the central Pacific for an assumed temperature profile of old to young oceanic lithosphere. Note that at a depth of 40 km, conductive geotherms for old oceanic lithosphere constructed using either the cooling half space model, as advocated here, or the constant thickness plate model, which McNutt and Judge (1990) adopt, differ very little (see figure 8.27) and are also not sensitive to anisotropy in thermal conductivity (e.g. Hearn et al., 1997). Assuming that at 40 km depth, the lateral temperature anomaly between mid-ocean ridges and old oceanic lithosphere is indeed «790 K, what is the magnitude of the expected velocity anomaly? For (dVs/8T)p = -0.62 m/sec/K, the predicted velocity anomaly is 8 Vs « 11%, approximately 1.83 times greater than the magnitude estimated from tomographic model RG5.5 (6%), consistent with the claims of Su et al. (1992) that RG5.5 underestimates the amplitude of the upper mantle 8 Vs by a factor of 2-3. Lastly, I note that the preferred estimate of Zhang et al. (1994) for the magnitude of the upper mantle temperature anomalies of 200 ± 100 K is inconsistent with the magnitude of the Chapter 8, page 814 temperature anomalies (±50°C) inferred by Schilling et al. (1995; see figure 8.23) in the equatorial Mid-Atlantic using the Klein and Langmuir (1987) relationship for N a 2 O g 0 M g 0 wt%. The spread in the N a 2 O 8 0 M g 0 wt% data reported by Schilling et al. (1995) is virtually indistinguishable to that plotted by Zhang et al. (1994), who used the Klein and Langmuir (1987) data set for the complete length of the Mid-Atlantic ridge in outlining the spatial correlation between basalt chemistry and their tomographic velocity anomalies. Thus, had Zhang et al. (1994) utilized geochemical, rather than solely seismic techniques, to estimate the temperature anomalies at depth, they likely would have obtained a significantly lower value than their initial (± 304 K), or preferred values (200 ±100 K). The above studies have focused on the Mid-Atlantic ridge and it is useful to question if the temperature anomalies deduced there are indeed representative of the remaining segments of the global ridge system. A number of similar studies to those of Sheehan and Solomon (1991) have also been undertaken on the South East Indian Ridge separating the Australian and Antarctic continents (Kuo, 1993; Kuo et al., 1995; West et al., 1994). This ridge has attracted attention because of the unusually abrupt along ridge axis variations in bathymetry (see figure 8.28), long wavelength geoid, and basalt chemistry that reach their apex at the Australian-Antarctic Discordance (AAD), a n * 350 km wide, tightly offset median valley (e.g. Weissel and Hayes, 1974; Marks et al., 1990; Forsyth et al., 1987; Klein et al., 1991; Sempere et al., 1991). Kuo (1993) determined differential travel time SS-S residuals for the A A D and invoking only temperature anomalies to explain the observations, calculated predicted SS-S' residuals using temperature anomalies inferred independently from fitting long wavelength geoid and bathymetry data using the viscous flow approach of Sheehan and Solomon (1991). Chapter 8, page 815 Kuo (1993) evaluated the fit to the geoid and bathymetry by restricting the temperature anomalies to a depth interval of 10-150 km or 10-300 km. While either model is capable of fitting the observed geoid, bathymetry, and travel time residual observations, the magnitude of the inferred temperature anomalies for the two depth models are quite different; along-ridge mantle temperatures are predicted to be ± 250 K for temperature perturbations constrained to 150 km, but only ± 85 K for perturbations constrained to the upper 300 km (see figure 8.29). While Kuo (1993) favoured the model with temperature anomalies of ± 250 K , from the above discussion on the relationship between oceanic crustal thickness and mantle potential temperature, such large anomalies are implausible. For example, i f these were real, such large temperature anomalies along the A A D ridge axis would predict oceanic crustal thickness variations from « 40 km on the east to 2 km in the A A D itself. In a subsequent study, Kuo et al. (1995) extended the modeling from 2D to 3D viscous flow modeling in evaluating the fit to the observed fields. The results do not differ appreciably, albeit the magnitude of the inferred temperature anomalies is reduced from ± 250 to ±150 K for anomalies restricted to 10-150 km depth, while for anomalies restricted to the upper 300 km, the temperature variations decrease slightly from ± 8 5 K t o ± 5 0 K . In a similar study, West et al. (1994) modeled long wavelength Bouguer gravity and bathymetry along the A A D and calculated that the observed fields, i f due solely to variations in crustal thickness, were compatible with maximum variations of ± 3 km along the ridge axis. Alternatively, i f the observed fields were solely due to shallow temperature anomalies restricted to the upper 50 km, then the observations could be explained by along axis temperature anomalies of ± 150 K. However, West et al. (1994) noted that these two endmember possibilities are incompatible, in that their inferred temperature anomalies were Chapter 8, page 816 estimated assuming no crustal thickness variations while the estimated of maximum crustal thickness variations ignored variations in mantle temperature. As discussed earlier, there is a strong link in decompression melt models between the predicted oceanic crustal thickness and mantle potential temperature that demonstrates relatively modest temperature variations will produce large variations in crustal thickness (all other factors being equal). Consequently, when considering both factors West et al. (1994) calculated that temperature variations of only ± 50 C, together with minor variations in along-ridge crustal thickness could satisfy the observations. Thus, inspite of the apparent equal success of the two models considered by Kuo (1993) and Kuo et al. (1995) where temperature perturbations were restricted to either 150 or 300 km depth, I believe that only the particular viscous flow model which allows temperature variations to extend to 300 km depth is plausible. To obtain an additional, independent estimate of the temperature variations along the Australian-Antarctic discordance I use the normalized major oxide compositions of basalt dredge samples collected along the A A D (Klien, Langmuir and Staudigel (1991). This data, based on analysis of basalt glasses, is taken from table 3 of Klien, Langmuir and Staudigel (1991) and combined with the empirical relationships between the extent of partial melting, F (wt%) and initial pressure of melting, P(kbar) from Niu and Batiza (1991). The initial pressure of melting, equivalent to the pressure of the intersection of the mantle adiabatic geotherm and the dry solidus, is empirically based on two experimental data sets that evaluated the change in melt composition and fraction as functions of temperature and pressure. Consequently, the relationships, and hence, the inferred temperatures are clearly model dependent. Nevertheless, they offer a simple way to convert the normalized oxide compositions to temperature anomalies via: Chapter 8, page 817 ( [SiQ2] [FeO], P0(kbar) = 25.98 + 0.967 F + 45.27 -5.186 8.0 MgO FJ 8.0 MgO J and f [CaO\ [Al203\ F(wt%) = 19.202 - 5.175 { ^ O ] , , )+ 15.537 |8.0 MgO V \g.0MgO J The initial melting pressures may be converted to equivalent depths and melting temperatures assuming the initial melting pressures represent the intersection of upwelling mantle with the dry KLB-1 solidus. The range in normalized N a 2 0 8 0 M g 0 wt% as a function of depth along the south-east Indian ridge is plotted in figure 8.30 illustrating the anomalous nature of the samples dredged from the A A D itself when compared to the samples lying east and west of the discordance. The associated temperature-depth estimates are shown in figure 8.31. where samples east and west of the Australian-Antarctic Discordance are plotted separately from those samples dredged within the A A D zone itself. Inspection of this figure clearly shows that the spread in temperatures inferred from basalt geochemistry is consistent with along-ridge-axis temperature anomalies of « ± 50-85 C and not with anomalies of « ± 250 C. The inferred temperature anomalies along the South-East Indian Ridge (Kuo, 1993) for both models where anomalies were confined to 10-150 km and 10-300 km are shown in figure 8.32 together with the estimated temperatures anomalies determined here for the Klein et al. (1991) dredge samples. This figure also shows the scatter in the calculated temperatures for the Klein et al. (1991) samples, which may indicate local compositional heterogeneities (see, for example the range in estimated temperatures for the samples located at 115°E west of the AAD) , and also indicates that to further test the predictions of the two models evaluated by Kuo (1993), dredge samples on the far eastern end of the South East Chapter 8, page 818 Indian Ridge should be collected, since it is there that the predicted temperatures of Kuo (1993) differ the most. Lastly, I show the inferred initial melting temperature calculated by Niu and Batiza (1991) using the above equations, for basalt samples collected along a portion of the East Pacific Rise (« 8° to 14°N), a spreading ridge which is characterized by the fastest spreading rates observed on the Earth. The initial melting temperature corresponds to the temperature at depth where the mantle adiabatic geotherm first intersects the dry solidus. While I stress again that the absolute temperatures calculated are model dependent, note in figure 8.33, that the associated along-ridge-axis temperature anomalies only fluctuation very modestly (< ±50 C). Consequently, the temperature anomalies associated with upwelling mantle beneath the East Pacific Rise, are quite small. In summary, it appears that after careful scrutiny, the inferences from normal M O R B chemistry and related geophysical studies of the mid-oceanic ridge systems are consistent and together predict temperature anomalies beneath the global mid-ocean ridge system of « ± 50-85 °K. These estimates are summarized in figure 8.34 where the various estimates discussed above are plotted around the pyrolite mineral physics mantle adiabatic geotherm. The major point is that globally, temperature anomalies throughout the convecting upper mantle, as inferred from M O R B geochemistry and additional geophysical probes, are relatively minor and fluctuate only slightly around the reference adiabat to a depth of at least 300 km. Progressing deeper into the mantle, the next section evaluates temperature estimates for the transition zone (410 - 730 km). Chapter 8, page 819 8.7 Estimates on Lateral Temperature Anomalies in the Transition zone from ScS Reverberations. The results from the previous chapters found that the seismic profiles of p and F 0 , and Vs and Vp, throughout the Earth's mantle are best modeled by a uniform pyrolite bulk composition. Furthermore, the mineral physics calculations demonstrate that a pyrolite composition correctly predicts the mean depth and magnitude of the observed seismic discontinuities that occur within the transition zone (410 km, 520 km, 660 km, and 730 km) in agreement with independent recent laboratory and thermodynamic studies (e.g. Bina and Wood, 1987; Akaogi et al., 1989; Ito and Takahashi (1989); Fei et al., 1990; 1991; Wood (1989; 1990), Bina 1991; Bina and Hellfrich, 1992; Hellfrich and Wood, 1996). Some workers had argued that some, or all, of the above seismic discontinuities were chemical boundaries, or mixed phase and chemical boundaries, where, in addition to the seismic signature of a phase change, these discontinuities fortuitously coincided spatially with changes in bulk chemical composition. However, this situation was addressed earlier where it was shown that density and bulk sound velocity profiles in the lower mantle were highly discrepant with the seismic profiles when they were calculated along a hot lower mantle geotherm, as they should be i f the lower mantle is convectively isolated from the transition zone and upper mantle. This result, when considered together with subsequent results from modeling Vs and Vp profiles for a pyrolite mantle, clearly favors the straightforward interpretation that to first order, a uniform pyrolite bulk composition can explain the seismic observations throughout the whole mantle. While it is not possible to prove that some chemical heterogeneity does not Chapter 8, page 820 exist within the Earth (indeed, the observed heterogeneity in bulk, isotopic, and trace elements observed for mid-ocean ridge melts argues that some chemical heterogeneity must exist (e.g. Hart and Zindler, 1989), the mineral physics modeling does demonstrate that there exists no compelling reason to invoke global changes in bulk chemistry as a function of depth. From the point of view of constraining lateral temperature variations within the mantle, the conclusion that the seismic discontinuities in the transition zone correspond solely to phase changes is important since within this framework, the primary contribution to topography on these discontinuities will then reflect only lateral variations in temperature which act to drive the phase transitions to deeper or shallow depth (depending upon the sign of Clapeyron slope of the phase transition). The laboratory and thermodynamic studies mentioned above, together with the mineral physics modeling presented earlier, demonstrate that the 410, 520, and 660 km seismic discontinuities are consistent with the progressive transition of a - into P-olivine at 410 km depth, p~ into y-olivine at 520 km depth, and finally, the breakdown of y-olivine to silicate perovskite [(Mg,Fe)Si03] and magnesiowustite [(Mg,Fe)0] at 660 km depth. While other breakdown reactions are occurring within the transition zone (the progressive conversion of ortho and clinopyroxene to majorite garnet and the formation of Ca-perovskite are two examples), these, and other reactions, do not appear to occur at the correct depth or the mineral phases are, by volume, insignificant relative to the olivine polymorphs. Specifically because the a-to p-olivine and p-to y-olivine phase transitions have positive Clapeyron slopes, while the breakdown of y-olivine ^Mg-perovskite + Chapter 8, page 821 magnesiowustite has a negative Clapeyron slope, the vertical separation of the 410 km and 660 km discontinuities is sensitive to temperature. In hotter regions (where it is implicitly assumed that the thermal perturbation extends across the full width of the transition zone) the width of the transition zone, as measured by the radial separation of the two phase boundaries will decrease, while in colder regions of the mantle, the transition zone width will increase (see figure 8.35). Thus, seismological studies may either attempt to measure the topography of the mantle discontinuities individually (e.g. Shearer, 1993; Flanagan and Shearer, 1988) or measure the variations in width of the transition zone in total. In the following ScS studies, both types of information are extracted, but it appears the lateral variation in the depth of the mantle discontinuities (410, 520 and 660 km) and hence, the lateral variation in mantle temperature, are reviewed. Revenaugh and Jordan (1987, 1989; 1991a, 1991b, 1991c, 199Id,) have developed techniques to study mantle layering from the study of the horizontally polarized shear waves, termed STf-polarized waves, that bounce back and forth through the mantle following a large earthquake. Because the core and free surface are near perfect reflectors, the multiple ScS phases traverse the mantle many times and record information as they are reflected off internal mantle or crustal seismic discontinuities (see figure 8.36). As noted by Revenaugh and Jordan (1989) these reverberations possess the fortuitous property that they are dynamic analogs; although the raypaths taken for reverberations from top side and bottom side reflections off of the 660 km discontinuity may be different from the earthquake source to the receiver, these raypaths have the same travel time, amplitude and phase at the receiver and hence constructively interfere to produce a strong signal. Analysis of SH waveforms reveals Chapter 8, page 822 an interval, between the fundamental mode surface wave and the first arrivals of multibounce surface waves (SSS2), termed the "reverberative interval" by Revenaugh and Jordan (1989), where the ScS signals of subcritical reflections from mantle discontinuities are isolated from other seismic phases and hence best observed and studied (see figure 8.37). Within the reverberative interval exist large amplitude wave groups, which represent multibounce ScS phases (see raypaths ScS and ScS2) that have reflected off one (or more) internal mantle discontinuities (see raypaths Sm+S+ScS2). The object of the studying these ScS* reverberations is to obtain path averaged estimates for the whole mantle travel time, xScS, the attenuation quality factor QScS> a n d m e apparent two way travel times (T 4 ] 0 , X 5 2 0 , T 6 6 0 ), depths, and normal incidence reflection coefficients, Ro(z) for the mantle discontinuities (e.g. z = 410, 520, 660 km discontinuities). As noted by Revenaugh and Jordan (1991), study of the ScSn and sScSn waveforms allow the four whole mantle and crustal properties (xScS, QScS> xMoh<>> Q-Moho) t 0 D e extracted independently of the internal discontinuity parameters ( t z , Qz, Ro(z)) which are, in turn, extracted from the, topside and underside reverberations. The full methodology to extract this information from the observed waveforms is described in Revenaugh and Jordan (1989; 1991a, 1991b). While in a previous chapter I had made use of the inferred reflection coefficients for the mantle discontinuities by comparing them to simplified mineral physics estimates for the pyrolite composition, in this study it is the 2-way travel times which I focus on. These represent the travel time of the SH wave from the free surface, z 0 down to the discontinuity at depth z; Chapter 8, page 823 2 1 x =2 | dz. SVJz) Revenaugh and Jordan (1991) found significant variation in the inferred travel times for the 18 western Pacific paths they studied, which when combined with the Clapeyron slopes for the olivine phase transitions at 410 and 660 km, allowed these variations in travel time to be interpreted in terms of large scale temperature differences within the transition zone. They related variations in the transition zone differential two-way travel times, where the differential travel time is defined as xn =x 6 6 0 - x 4 1 0 , to temperature differences (AT) within the transition zone via: A x ^ = rdx A dT AT The advantage of utilizing the transition zone differential two way travel time is that it is insensitive to lateral heterogeneity above or below the transition zone, since this is common to both the individual 410 and 660 two way travel time estimates. The differential travel time temperature derivative (for a constant composition) includes contributions from both interface and volumetric contributions via: dT 2 y 2 Vs (dP/dz) -|660 410 + V ST J f The first term on the right hand side, which accounts for displacement of the bounding phase boundaries, includes the Clapeyron slope of the phase change at the particular seismic discontinuity, y z at depth z, Vs is the shear wave velocity at the discontinuities, and (d P/dz) = 0.3897 GPa/km (taken from PREM) is the average pressure gradient as a function of depth. The second term on the right hand side, which accounts for the effects on temperature on the Chapter 8, page 824 average velocity within the .transition zone, is comprised of xu. , the average transition zone 2-way differential travel time (94.00 sec), Vs which is the average transition zone shear wave velocity (5.32 km/sec), and (dVs/df)p , the average shear wave temperature derivative for the transition zone. Revenaugh and Jordan (1991) adopted Y 4 1 0 = 3.9 ± 1.5 MPa/K (Katsura and Ito, 1989), y 6 6 0 = - 2.8 ± 1.5 MPa/K (Ito and Takahashi, 1989) and (dVs/dT) = - 0.44 ± 0.10 m/sec K, the later value taken to be consistent with inferred values from subduction zone slab velocity anomalies (Creager and Jordan, 1986). Together these values combine to give an estimate for the temperature derivative of the differential 2-way travel time of (dTJ2/dT) = - 0.052 ± 0.013 sec/K. Revenaugh and Jordan (1991) note that of the two terms in the above expression, the 1st term dominates and overwhelms the affect of changes in ambient velocity within the transition zone. This interpretation of the differential 2-way travel time is illustrated schematically in figure 8.35 where it is clear that the effect of raising the temperature uniformly within the transition zone acts to decrease the distance between the 410 and 660 km bounding phase transitions, and hence decrease the travel time, relative to the average value. Likewise, the effect of decreasing the temperature uniformly within the transition zone is to cause the distance separating the bounding phase transitions to increase, and hence, increase the differential travel time relative to the mean value. Implicit in this interpretation is that the large-scale temperature variations within the transition zone have vertical scale lengths substantially greater than the separation of the bounding discontinuities. If, however, the vertical scale length is less than the width of the transition zone, then the above interpretation Chapter 8, page 825 of the differential travel time results in a "smeared" temperature estimate that has no straightforward interpretation. I have used the Revenaugh and Jordan (1991b) estimate for (Sx^/dr),, to obtain the associated temperature anomaly, AT in the transition zone. In turn, the AT estimate has been added to the pyrolite adiabatic geotherm to indicate the inferred temperature structure in the transition zone for the corridors studied by Revenaugh and Jordan (1989; 1991). Taken at face value the inferred temperature anomalies are rather modest and agree reasonably well in magnitude to that estimated independently from decompression melt studies of M O R B geochemistry and related variations in oceanic crustal thickness (see figure 8.38). The average "cold" temperature perturbation is « -42 K while the average "hot" anomaly is « 45K. Unfortunately, this good agreement is probably misleading. In a subsequent study, Revenaugh and Sipkin (1994) applied the ScS reverberation technique to earthquakes located in China and the Japan Sea and recorded at stations scattered across China. Although they did not provide values of the differential 2-way travel time for the 14 corridors they studied, they did tabulate the apparent depths to the individual transition zone discontinuities (410, 520, and 660 km). I have converted these depth estimates to temperature assuming that the pyrolite adiabat gives the reference temperature at the reference discontinuity depth (e.g. at 410 km depth, the temperature of the pyrolite adiabat is 1834 K) and using the Clapeyron slope at the 410 km (+3.0 MPa/K Bina and Helffrich, 1994), 520 km (+3.9 MPa/K; Akaogi et a l , 1989), and 660 km (-2.1 MPa/K; Bina and Helffrich, 1994)) phase boundaries to determine the associated temperature of each individual apparent depth estimate. Thus, a shallow apparent depth for the 407 km Chapter 8, page 826 discontinuity corresponds to a calculated temperature of 1741 K (note that the depths are determined relative to an adopted reference shear velocity profile via the relationship 1 1 T z =2 f dz, and hence, as described by Revenaugh and Jordan (1991), they represent "apparent depths", rather than absolute depths, since the depths would change slightly i f a different reference velocity profile was adopted. For their reference profile, they adopted the Vs profile from P R E M (Dziewonski and Anderson, 1981)). Inspection of figure 8.39 reveals that there is substantial heterogeneity in the estimated temperatures across the transition zone. Note that in some of the profiles, the change in relative temperature between the 410 and 520 km discontinuities implies that over this depth interval, the mantle in a particular corridor is getting hotter than normal with increasing depth (e.g. corridors E5 and E6), but that immediately underlying this, the change in relative temperature between the 520 and 660 km discontinuities implies a progressively cooler mantle. These changes in temperature show up as "dog leg" shaped temperature profiles and demonstrate that a key assumption invoked earlier in converting the differential 2-way travel times to temperature, that the corridor-to-corridor differences in TJZ result from large scale temperature variations with vertical scale lengths greater than the width of the transition zone, is not fulfilled. The "dog leg" shaped profiles are direct evidence that the vertical scale length of transition zone temperature variations must be less than the widths of either the 410-to-520 km or 520-to-660 km discontinuities (the very high temperatures implied at the 520 km for 2 of the corridors, WI and W2, can not be real, since the temperatures are much greater than the peridotite solidus at this depth. Independent seismic tomographic studies that have constructed profiles across a north-south trending transect through the Tibetan upper mantle Chapter 8, page 827 find no evidence for such extreme velocity anomalies at 520 depth (McNamara, 1996). Thus, the very large variation in inferred depths, and hence, associated variation in temperature at the 520 km discontinuity for these two particular corridors is highly suspect. Returning to the Revenaugh and Jordan (1991) study for the Western Pacific I converted the apparent depths for the 410 and 660 km phase boundaries into temperature using the method discussed above and plotted these in figure 8.40. It is clear from this figure that these corridors also demonstrate that the vertical length scale of the temperature anomalies within the transition zone is less than the width of the transition zone. Although the 520 km discontinuity was not imaged on the individual corridors, and hence it is not possible to determine i f apparent temperatures fluctuate over relatively short vertical scale lengths, it is evident that virtually all of the corridors have different apparent temperatures at the 410 and 660 km discontinuities that are not consistent with the simple interpretation that large-scale, coherent temperature perturbations extend across the full width of the transition zone. While the exercise of converting the apparent depths into temperature clearly shows that the vertical lengths scale for temperature perturbations within the transition zone are substantially less than the width of the transition zone, these results do imply that there exists a discrepancy between the magnitude of the inferred temperature anomalies at the 410 and 660 km phase boundaries (± 150 K and ± 300 K at the 410 km and 660 km discontinuities, respectively), as estimated here, and that estimated at shallower depths via M O R B chemistry and related mid-ocean ridge geophysical studies (± 50 K). While Revenaugh and Jordan (1991) did correct the apparent travel times (x4 1 0) for volumetric mantle velocity heterogeneity using a composite Harvard model (the shear wave M84C upper mantle model Chapter 8, page 828 (Woodhouse and Dziewonski, 1984) spliced to the lower mantle compression wave model L02.56 of Dziewonski (1984; L02.56 was converted to an S-wave model assuming a constant scaling factor of Ws = 1.1 oVp), there exists the likelihood that discontinuity topography on the 410 and 660 km seismic discontinuities has been mapped into the volumetric perturbations in the tomographic models M84C and L02.56. Neither of these tomographic models explicitly accounted for topography on internal mantle discontinuities when they were constructed (it is assumed discontinuity topography is zero), and thus, these models forces any required velocity heterogeneity into perturbations in the volumetric model. Depending on the parameterization of the tomographic model, the effects of un-modeled discontinuity topography may substantially bias a pure volumetric tomographic model, especially in the regions directly adjacent to the discontinuity (e.g. Rogers and Wahr, 1994; Lavely et al., 1994; Ritzwoller and Lavely, 1994). While Revenaugh and Jordan (1991) acknowledged this possibility, they claim that the affect was small enough to ignore in the analysis of reflection 2-way travel times. A further potential problem with the correction for volumetric seismic structure in ScS studies is the use of a composite model itself. Whole mantle S-wave tomographic models exist (e.g. Su and Dziewonski, 1991; Sue et al., 1994) that render the use of a composite model un-necessary, especially considering that the composite model comprises a mixed S-and P-wave model. Dziewonski and Woodward (1992) and Woodward et al. (1993) constructed two S-wave volumetric tomographic models using the same data sets and methodology except one model (SH8/U4L8) was truncated at the 660 km discontinuity into separate upper and lower models, while the other model (SH8WM13) was parameterized in a single, smooth whole mantle model. Detailed comparison of the two models revealed that the Chapter 8, page 829 split model differed from the whole mantle model in a zone « 150 km wide on either side of the 660 km discontinuity (Dziewonski, 1995). This comparison is likely to underestimate the potential bias introduced by using a combined model because the data sets were identical and both models were of the same wave type. Thus, the use of a mixed S- and P-wave composite tomographic model in ScS studies is very likely to introduce spurious features at the 660 km discontinuity and thereby lead to biased depth estimates for the 660 km discontinuity. Unfortunately, it is not possible to determine either the potential bias in the inferred depths by use of a pure volumetric tomographic model, nor the potential bias due to use of a mixed S- and P-wave volumetric tomographic model. However, other seismic studies, such as SS precursors, have been combined with tomographic models to solve explicitly for both discontinuity topography and volumetric signals and these studies are outlined next. The major finding is that the inferred topography on the transition zone discontinuities is reduced by a factor of 2 when whole mantle volumetric models are extended to explicitly account for topography on the mantle phase boundaries. This in turn, reduces the inferred temperature anomalies at the phase boundaries. 8 . 8 Global Mapping of transition zone discontinuity topography by SS precursors. One potential problem faced by the ScS reverberation studies discussed above is that since they are not global in extent, the results may suffer from regional effects, especially given that the areas studied (Western Pacific) have a preponderance of subduction zones. Thus, the presence of subducting old (150 Ma) oceanic lithosphere within the transition zone Chapter 8, page 830 may introduce velocity heterogeneity that is not accounted for in the estimation of apparent depths (recall the ScS studies use the radial symmetric shear velocity profile from P R E M to convert the travel times to apparent depths. The P R E M velocity profiles are expected to differ from that within a cold slab). A further drawback with utilizing ScS waves is that ideally, the earthquakes should be both large (greater than magnitude 5.7) and deep (depth greater than 75 km) to obtain the maximum signal to noise ratio. Revenaugh and Jordan (1991b) note that significantly greater global coverage is potentially possible, i f shallower earthquakes are used, but with the tradeoff that the signal-to-noise ratio decreases. Consequently, to map global topography on the mantle discontinuities, the ideal seismic phase would provide localized sampling of the boundaries, but be measured over a global extent. Shearer (1990; 1991; 1993; Shearer and Masters, 1992; Flanagan and Shearer, 1998) has pioneered the use of long period SS precursors, which are seismic phases that are underside reflections off the 410 and 660 km discontinuities, and thus, precede the arrival at the receiver of the surface reflected SS phase (see figure 8.41). These phases have excellent global coverage and hence provide truly global maps of 410 and 660 km discontinuity topography (see figure 8.42). Note from this figure the significant increase in the number of observations and therefore, the very good global distribution that is possible with SS precursors (Shearer and Masters (1992), n = 3,139; Shearer (1993), n = 5,884; Flanagan and Shearer (1998), n = 11,207). Differential travel times between the precursor and the SS phase (e.g. SS-S4J0S) provide a measure of the two-way traveltime between the surface and the discontinuity at the bounce point and may be converted to discontinuity depths by assuming a reference radial velocity model and by applying corrections for volumetric mantle structure, surface topography, and crustal thickness (complications due to seismic structure at both the Chapter 8, page 831 source and receiver'regions is relatively unimportant since the raypaths for both the SS and precursor phase, S^S (where d represents the depth of the discontinuity, the precursor is reflected off), travel essentially identical paths in these regions, and thus, the use of differential travel time cancels out these components). As noted by Shearer (1993) the use of the newer iasp91 velocity model (Kennett and Engdahl, 1991) as compared to the older P R E M reference model (Dziewonski and Anderson, 1981) has a relatively minor affect on the predicted depths (e.g. the depth to the 410 km discontinuity changes by 1 km by changing the reference velocity model). However, the particular seismic tomographic model used to correct for upper mantle and transition zone volumetric structure may contribute significantly to the inferred absolute depths. This reflects the variation in the amplitude of the velocity perturbations that are recovered in the various tomographic models (i.e. early Harvard models are in some places 50% larger than that of the Scripps models - in contrast, the geographic distribution of the anomalies for the various models agrees quite well (see review by Ritzwoller and Lavely, 1995). In spite of this uncertainty, the latest version of 410 and 660 km discontinuity topography of Flanagan and Shearer (1998), which I focus on here, uses the S-wave tomographic model S16B30 (Masters et al., 1996) which is a significant improvement over the older models (SH8WM13 (Woodward et al., 1993) and SH10C (Masters and Bolton, 1991)) used by Shearer (1993). S16B30 includes a number of different types of seismic data (free oscillation structure coefficients, surface wave dispersion measurements, S-SS, P-PP, and S-ScS and P-PcP differential travel times, and absolute S- and P-wave body wave travel times) that together, have very good sensitivity to whole mantle structure. This reduces the possibility of systematic bias in the tomographic model due to reliance on only one type of seismic phase Chapter 8, page 832 (for example, tomographic models constructed using only ISC S- and P-wave data). Flanagan and Shearer (1998) also note that using the latest Harvard model (Su et al., 1994) results in 410 and 660 global topography that is indistinguishable from that using S16B30, implying that the discrepancy in amplitude of the seismic anomalies in the different tomographic models has been reduced in the latest generation of tomographic models. Crustal and topographic corrections in both the S16B30 (Masters et al., 1996) and in the Flanagan and Shearer (1988) study were made using CRUST5.0 (Mooney et al., 1995) which provides global sets of both topography/bathymetry and crustal thickness and velocity data. Full details of processing and corrections may be found in Flanagan and Shearer (1998). The final maps of long-wavelength discontinuity topography are shown in figure 8.43 which represents a degree 12 spherical harmonic expansion of the cap averages (the original data was binned into 416 circular caps of 10° radius - the final corrected depth estimates in these bins was then smoothed using spherical splines from which the spherical harmonic expansion was made). The mean depths and peak to peak topography of the discontinuities are: the 410 km discontinuity = 418 km and ± 22 km (406-428 km) the 520 km discontinuity = 515 km and ± 27 km (500-527 km) the 660 km discontinuity = 660 km and ± 38 km (643-681 km). The full data sets for the 410 and 660 km discontinuities are plotted as a function of their uncertainties in figure 8.44. Also shown are the mean upwards and downwards deflections when only those depth estimates with uncertainties less than 10 km are considered. To estimate the associated temperatures with their depth estimates I have converted the individual depth estimates in to related temperature by combining the pyrolite mineral Chapter 8, page 833 physics geotherm with the Clapeyron slopes for the discontinuities. For example, at the "410" km discontinuity, I have assumed the geotherm at 418 km depth correctly gives the average mantle temperature for this discontinuity and then simply determined the associated temperature of the particular depth estimates using a Clapeyron slope of +3.0 MPa/K (Bina & Helffrich, 1994). These temperature estimates and the values for the adopted Clapeyron slopes are shown in figure 8.45. Inspection of this figure reveals that the inferred individual temperatures span a relatively wide range that exceeds that determined earlier for shallower depths based on MORB geochemistry. This is not surprising in that detailed thermal models of subduction oceanic lithosphere predict significantly colder temperatures than the upper mantle and transition zone geotherm. In figure 8.45 I plot the temperature path of the cold core of the Pacific plate subducting beneath the Northern Japan trench (Hellfrich et a l , 1987). At 410 km depth the cold core of a slab is as much as 1200 K colder than the mantle adiabatic geotherm. However, note that the top of the slab is much warmer than the core, with its predicted temperature at 410 km nearly coinciding with the minimum predicted temperature anomaly inferred from the topography of Flanagan and Shearer (1998). This difference is not significant and likely reflects the difference between the spatial distribution of the cold thermal anomaly of the slab and the horizontal area over which the S4lQS precursor samples. While the cold slab may have a cross-slab thickness of 150 km (when the entrained sheath of cooler mantle is also considered, this width may increase to 300 km), the horizontal footprint of the SS precursor is likely to be 1000 km square. Thus, the SS-S4]()S differential travel time represents a large scale horizontal average over a much larger spatial area than simply the subducting slab width, even in areas of known subduction where old, and thus, thick oceanic lithosphere is downwelling. Indeed, the large scale averaging inherent in SS-Chapter 8, page 834 SdS differential travel times studies is not a problem herein, since the focus is on the average temperature perturbations around the mantle adiabat. In this vein, when I calculate the mean absolute deflection and its associated temperature, the discrepancy between it and the mean temperature perturbations at shallow depths is decreased with the mean lateral temperature variations at the 410 km being 7.21 km and « ± 86 K , while that at 660 km depth being 9.47 km and « ± 185K (see figure 8.46). While this agreement is encouraging, recall that topography on the mantle discontinuities trades off with the magnitude of the adjacent volumetric velocity variations such that the magnitude of the SS-S^S inferred topography may be somewhat biased since the tomographic model (S16B30) used to correct for volumetric velocity variations assumes no discontinuity topography. While ultimately, a joint inversion for both boundary topography and volumetric velocity variations would be ideal (and is planned, Guy Masters, personal communication), at present, the Scripps tomographic models do not account for this feature. However, Vasco et al. (1995) incorporated the original SS-S4jnS and SS-SfifinS differential travel times of Shearer (1993), together with a large data set of ISC P, PP, S, and SS-phases, to construct joint, whole mantle S- and P-wave tomographic models that simultaneously solved for both volumetric velocity heterogeneity and boundary topography on the 410 and 660 km discontinuities. While this particular study does not use the updated and expanded set of SS-S4]nS, SS-S^20S, and SS-SfifinS differential travel times of Flanagan and Shearer (1998), it demonstrates the affect of a joint inversion on the magnitude of the inferred discontinuity topography. Vasco et al. (1995) found that the mean absolute deviations of the 410 and 660 km boundaries are 4.8 ±0.8 km and 4.2±1.3 km respectively, Chapter 8, page 835 approximately one half the magnitude estimated by Flanagan and Shearer (1998). These mean absolute deflections correspond to lateral temperature anomalies of « ± 58 K and « ± 82 K at the 410- and 660-km discontinuities, respectively, and these are also shown in figure 8.46. It is clear from this figure that the effect of a joint inversion for both boundary and volumetric velocity variation has significantly reduced the inferred mean lateral temperatures at the 660-km discontinuity. Consequently, the relatively minor discrepancy between the magnitude of the average temperature anomalies inferred at the 410 km and 660 km discontinuities using the original SS precursor depths of Flanagan and Shearer (1998) and that at shallow depths using MORB chemistry is largely removed. It is anticipated that the decrease found by Vasco et al. (1995) will not change with the inclusion of the larger Flanagan and Shearer (1998) data set, since by increasing the number of transmitted and reflected seismic phases, the ability to minimize the erroneous mapping of boundary topography into large-scale volumetric velocity heterogeneity is increased. Thus, the larger data set (11,207 versus 5,884) will likely only refine, but not substantially change the conclusions reached by Vasco et al. (1995). A subsequent joint S- and P-wave tomographic study by Vasco and Johnson (1998) that added PcP, ScS, PKPab, PkPdf and SKSac phases to the previous data sets used in Vasco et al. (1995), resulted in joint S- and P-wave tomographic models with modeled 410- and 660-km topography which is similar to that found in their earlier study. Lastly, recall that Revenaugh and Jordan (1991) suggested that the thickness of the transition zone, as measured by the two-way differential travel time, could be interpreted in terms of large-scale temperature anomalies under the assumption that the vertical length scale of the temperature variations exceeded the width of the transition zone. In contrast, I found Chapter 8, page 836 that the individual depths to the 410- and 660-km discontinuities as estimated via the ScS reverberations (and where given, the 520-km) were not correlated and hence, argued that vertically coherent temperature anomalies do not extend across the full width of the transition zone. This question may also be addressed using the SS precursor depths of Flanagan and Shearer (1998). I have plotted the depth variations of the 410-km discontinuity against the variations of the underlying 660 km discontinuity in figure 8.47. This figure demonstrates that the observations are widely scattered and therefore, as also noted by Flanagan and Shearer (1988), it is clear that the data do not correspond to the expected trend i f the discontinuities were indeed sensitive to a common temperature anomaly that extended across the full vertical depth extent of the transition zone. Thus, one conclusion which may be drawn from SS precursor studies, which have true global coverage as opposed to ScS studies which do not, is that the vertical length scale for the temperature anomalies affecting the 410, 520 and 660 km discontinuities is much narrower than the full transition zone thickness. While coherent temperature affects are expected where mantle plumes or subducting slabs penetrate across the transition zone, note that the cross-section width of slabs (250 km) or plumes (<200 km) are smaller than the sampling width of the S^S bounce points for the underside reflections (about 1000 km (Shearer, 1992)). Consequently, while there is a broad correlation with depressions or "troughs" in the 660 km discontinuity and present day subduction zones (Shearer and Masters, 1992; Flanagan and Shearer, 1998), the 410 km discontinuity topography is poorly correlated with known surface position of subduction zones and with the underlying 660 km discontinuity topography. Chapter 8, page 837 As suggested by Flanagan and Shearer (1998) a possible explanation for this observation is that subducting slabs may spread out or "lay down" on the 660 km, and hence, spread the cold slab temperatures over a wide geographic area of the 660 km discontinuity. This would increase the chance that SS precursor reflections could detect them. In contrast, subducting slabs likely pass through the 410 km discontinuity relatively undisturbed. While this scenario receives some support from numerical convection models that suggest the 410 km discontinuity promotes convection across it while the 660 km discontinuity acts to hinder vertical flow (e.g. Tackley et a l , 1993; Solheim and Peltier, 1994a, b), I note that the these numerical models are being run using adopted boundary conditions, which for some parameters, are far removed from Earth-like values. Thus, the "ponding" of downwelling mantle flow that these convection simulations find at the 660 km discontinuity are likely to be numerical artifacts, and hence, of little direct relevance to the Earth's present day mantle. For example, in figure 8.48 I plot the lateral temperature anomalies inferred from the mean deflections predicted for the 410- and 660-km discontinuities from the numerical convection model of Solheim and Peltier (1994a) from their run where the 660 km Clapeyron slope was fixed at -2.1 MPa/K and the 410 km Clapeyron slope was fixed at +3.0 MPa/K, both values consistent with the most recent thermodynamic analysis of the experimental results (Bina and Helffrich, 1994). While this particular run adopts many Earth-like input parameters, the resultant geotherm is approximately 250 °K too hot when compared to the pyrolite mineral physics geotherm. In addition, the convection model predicts mean lateral temperature anomalies of « ± 460 K and « ± 375 K at 410- and 660-km depths, values which are significantly greater than the seismic inferences. Chapter 8, page 838 Recall that the average convection geotherm is « 250 K hotter than the pyrolite mineral physics geotherm, so there exists the problem of widespread melting of upwelling mantle flows if the convective geotherm is accepted at face value. Note that at both the 410 and 660 km discontinuities, the upwelling flows imply widespread melting of the mantle at these depths (recall that the up arrows represent an arithmetic average of the total boundary deflection, and consequently, indicate the existence in the convective model of many zones with greater localized boundary deflections, and hence, even hotter upwelling flows. Furthermore, the numerical convection simulation does not incorporate the 520 km discontinuity, which would act to increase the geotherm below this depth by roughly 35 K. Such a temperature increase would shift the predicted 660 km temperatures to higher values, and consequently, exacerbate the problem between the mantle solidus and the inferred temperature of upwelling flows. Such "super" hot flows would likely cross both the KLB-1 solidus and liquidus profiles (see figure 8.48), and imply widespread partial melting in the transition zone (under the assumption that this convective simulation is relevant to the Earth). However, partial melting at either the 410 or 660 km depths is not consistent with recent 3D seismic attenuation models (Romanowicz, 1994; 1995; Bhattacharyya et al., 1996) which possess relatively modest (30% fluctuations) variations about the reference attenuation profile over the uper mantle and transition zone. Note, too that the particular numerical run illustrated in figure 8.48 adopted values for both the 410 and 660 km Clapeyron slopes which agree with the best estimates for these two parameters (Bina and Hellfrich, 1994), and importantly, predicts virtually no partial layering at the 660 km discontinuity (Solheim and Peltier, 1994b). Numerical runs with increased values for the 660 km Clapeyron slope, result in increased boundary deflections (together with increased partial layering of the mantle) Chapter 8, page 839 which are in even greater disagreement with the seismic boundary topography of Flanagan and Shearer (1998) or Vasco et al. (1995). Thus, the direct application of the existing numerical convection studies to interpreting the Earth's mantle remains doubtful. An alternative idea in explaining the observation of 660 troughs without associated 410 km domes at known subduction zones in the Flanagan and Shearer (1998) data set, is that subducting slabs convectively thicken in cross-section when traversing the 660 km phase transition. The disproportion of y-olivine into Mg-perovskite and magnesiowustite results in a fine grained assemblage (Rubie, 1984; Ito and Sato, 1991) which will be significantly weaker, via transformational plasticity (e.g. Poirier, 1985; p. 213; Panasyuk and Hager, 1998) than the overlying slab and ambient lower mantle. When this weak rheology is combined with the increased stress acting on the slab as it penetrates into the more viscosity lower mantle (Mitrovica and Forte, 1997) the net effect will be to thicken the slab (Rubie, 1984; Fischer et al., 1988; Ito and Sato, 1991; Kirby et al., 1996). Thus, the horizontal "footprint" of a cold subducting slab in the immediate vicinity of the 660 km discontinuity should be greater than that at the shallower 410 km discontinuity, and hence, may explain the absence of subduction related 410 km domes in the SS precursor derived topography. At the Kuril-Kamchatka subduction zone, located in the western Pacific (see Figure 8.49). Fischer et al. (1988) evaluated possible thickening in slab via a simple numerical model which parameterized thickening via the parameter y, which represents the ratio of the thickness of the slab after undergoing thickening to the thickness prior to phase-change modulated modification (see figure 8.50). The depth interval over which the thickening occurred was held fixed between 580 and 750 km. They undertook three modeling studies Chapter 8, page 840 where they varied the imposed thickening in the slab (see figure 8.51) and compared the predicted travel time residuals to observations. They concluded that the travel times could be satisfied by models where the slab thickened by a factor of two (g = 2), but not by values significantly greater than this. In terms of the seismic observations of Flanagan and Shearer (1998) it may be that the broad thickening in the slab as it descends through the transition zone results in a wide enough slab to create a seismically-visable "trough" at the 660 km discontinuity, in contrast to the relatively narrow perturbation at the 410 km discontinuity. While studies using SS precursors have true global coverage, a potential limitation, as alluded to above, is the large horizontal "footprint" at the depth of the discontinuities (1000 km). To obtain higher resolution at subduction zones regional studies of the transition zone discontinuities near subduction zones have utilized near-source converted seismic phases. These studies are reviewed next. 8.9 S-to-P wave conversions and discontinuity topography near subduction zones As noted in previous chapters, the 410-, 520-, and 660-km seismic discontinuities are interpreted to reflect the sequential phase transitions of olivine and its polymorphs in response to increased pressure in the mantle ("410" = a-olivine —>• P-olivine, "520" = P-olivine —> y-olivine, "660" = y-olivine —> Mg-perovskite plus magnesiowustite; Bina and Wood, 1987; Wood, 1989; 1990; Katsura and Ito, 1989; Ito and Takahashi, 1989; Akaogi et al., 1989; Fei et al., 1991). While pressure is the dominant driving force for these reactions, these reactions are also temperature sensitive such that the exact pressure, and hence depth, at Chapter 8, page 841 which the above three phase transition occur, will depend upon the local temperature structure of the mantle. Thus, variations in depth for the 410-, 520-, and 660-km seismic discontinuities may be used to infer insitu mantle temperatures (e.g. Shearer, 1992). One of the most obvious places to search for variations in the depths of discontinuities is at subduction zones where cold, oceanic lithosphere descends into the mantle. Finite difference computer models which calculate the temperature structure of subducting oceanic lithosphere suggest that the interior, or core, of the subducting lithosphere will only warm slightly during its descent from the surface through the 410- and 660-km discontinuities (e.g. Creager and Jordan, 1986; Fisher et al., 1988; Helffrich et al., 1989) such that the slab may be as much 1000 °K colder than the ambient convecting mantle at 660 km depth. Such a large temperature deficit with respect to the ambient mantle should elevate the depth of the 410-km, but depress the depth of the 660-km discontinuities, respectively. As noted above in summarizing studies using ScS reverberations, such changes in depth have been documented using these long-period (25-50 seconds) seismic phases. One potential drawback with these particular phases is that the lateral resolution is « 1000 km (Vidale & Benz, 1992; Shearer, 1992) and hence, these studies are capable of resolving only relatively long-wavelength variations in the depths of the discontinuities. At subduction zones, the temperature structure should have much shorter wavelength features (« 100 km length scale), since thermal diffusion is not predicted to have appreciably broadened the thermal anomaly of the downgoing lithosphere by simple conduction during the 10 million years or so that it takes the slab to traverse the upper mantle and transition zone. This is well illustrated in figure 8.52, taken from Marone and Liu (1998), which shows the predicted temperature Chapter 8, page 842 structure for the Tonga subduction zone. While deformation within the slab is expected to thicken the slab perpendicular to its plane, and hence, broaden the temperature field (e.g. Fischer et al., 1988), this affect is likely to only occur over the lower part of the transition zone where fine-grained mixtures of new mineral phases are likely to predominate and thus, lead to superplastic deformation which will facilitate slab thickening (Ruby, 1984; Ito and Sato, 1991; Kirby et al., 1996; Panasyuk and Hager, 1998). Thus, to accurately determine the seismic discontinuity depths at and adjacent to subduction zones, shorter period seismic waves are necessary to probe for these deflections. Vidale and Benz (1992) utilize the dense regional network of short-period (0.2 to 5.0 Hz) seismometers in the Western United States to combine records of distant subduction earthquakes to image faint near-earthquake reflections and conversions off the seismic discontinuities near the subducting slabs (see figure 8.53). The advantage of combining records from hundreds of permanent short-period stations that span a geographic distribution of « 1000 km is that data "stacking" techniques may be employed to enhance the signal-to-noise ratio and thus detect relatively weak seismic phases (see also Benz et al., 1994). Furthermore, the short period records have a lateral resolution of « 10-100 km, and thus, should be able to better resolve details of any depth variations of the seismic discontinuities. Vidale and Benz (1992) studied 6 subduction earthquakes and focused on seismic phases that are recorded between the arrival of the direct P-waves and surface reflected P-waves (seismic waves, termed /?P-phases, that start as upgoing P-waves and are reflected off the Earth's surface to become downgoing P-waves (see figure 8.54). Within this time window, they recognized S660P phases, waves which start as downgoing 5-waves that are partially Chapter 8, page 843 converted to a downgoing P-waves at the 660 km discontinuity, and P-wave reflections off the underside of the 410 km discontinuity. Although not shown correctly in this schematic figure is that the S660P phase samples the 660 km discontinuity about 100 km from the intersection of the seismicity that defines the downgoing slabs and the discontinuity (on the "sea ward" side of the subduction zone). If the subducting lithosphere has not undergone any internal deformation during its descent, then thermal models predict that the 660 km discontinuity should not be greatly perturbed this distance from the slab. This proposal has received some support from the earliest long-period SS precursor studies of 660 km discontinuity topography where the 660 km discontinuity was observed to lie at the "normal" depth on the seaward side of the Kurils subduction zone (see figure 8.55). The upper panel of this figure shows the seismicity within the subducting Pacific plate beneath northern Japan together with the long-wavelength topography inferred for the 660 km discontinuity. The lower panel is an enlargement of the immediate area adjacent to the 660 km discontinuity and illustrates that the topography to the right of the intersection of the subducting Pacific slab with the 660 km discontinuity shows only minor undulations. In contrast, the 660 km discontinuity at the slab-discontinuity intersection, and for 1,700 km to the west, is depressed below the reference depth. High resolution tomographic models for this area show that the Pacific slab lies horizontally on the 660 km boundary for a few hundred kilometers (van der Hilst et al., 1991), but that ultimately it can be tracked clearly into the lower mantle down to the core-mantle boundary (van der Hilst et al., 1997). Vidale and Benz (1992) find that their high resolution study detects significant depression of the 660 km discontinuity by up to 30 ± 10 km for the Tonga subduction zone and slightly less (25 km) at both the Izu-Bonin and South America subduction zones. They Chapter 8, page 844 infer from their observations that the cold thermal structure of the slab, as envisioned by deformation-free kinematic slab models, is incomplete, and that some slab thickening must occur. To determine the associated temperature for the discontinuity depths they estimate, I have converted their depths to temperature by assuming that the pyrolite mineral physics geotherm gives the correct average temperature across the upper mantle and transition zone. Under this assumption, the pyrolite geotherm gives the reference temperature at the 410- and 660-km discontinuities, and when combined with estimates for the Clapeyron slope of the 410- and 660-km phase transitions, allows the temperature for shallow or deeper depths to be calculated. Figure 8.56 shows the estimated temperatures for the discontinuity depths of Vidale and Benz (1992) together with the adopted values for the Clapeyron slopes for the upper mantle phase transitions as determined by Akaogi et al. (1989) and Bina and Helffrich (1994). Also shown is the calculated temperature path for both the cold core and the top of the slab for the N E Japan subduction zone (Helffrich et al., 1989). Similar calculations for Tonga (see figure 8.59) and for the Kuril (Fischer et al., 1988) subduction zones indicate that the central core of the subducting slabs in these regions is not very different from this inference. Of note in figure 8.56 is that for the two earthquakes in Tonga where Vidale and Benz (1992) were able to record reflections and conversions from the 410- and 660-km discontinuities, the temperature anomaly at 410 km is significantly less than that expected within the cold core of the downgoing slab. They interpret these rather modest 410 km temperatures as measures of the temperature adjacent to, rather than within, the slab. Consequently, the discontinuity deflections, and hence, inferred temperatures are not believed Chapter 8, page 845 to be recording the maximum possible temperature anomaly. Alternatively, the depths of the 410 km discontinuity may not represent the depth along the equilibrium temperature-pressure conditions defined by the Clapeyron slope, as shown in figure 8.56 but instead represent the depths on the kinetically hindered, meta-stable phase boundary (see figure 8.57). In this situation, the abnormally cold temperatures within the subducting slab kinetically retard the conversion of alpha to beta olivine such that the equilibrium boundary is deflected downwards to greater depths (e.g. Sung and Burns, 1970; Kirby et al., 1996), as illustrated schematically in figure 8.58. The upper figure corresponds to the kinetically hindered case, while the bottom figure represents the equilibrium case. Unfortunately, due to the limited number of earthquakes (6) evaluated by Vidal and Benz (1992) it is not possible discriminate between these two possible interpretations with their observations alone. However, recent studies (see below) have enlarged the number of events, and consequently, allow this question to be addressed. Richards and Wicks (1990) used 300 observations of deep earthquakes located with the Tonga subducting slab, recorded in a local dense array in central Australia, to search for S660P conversions from the 660 km discontinuity. They divided the Tonga subduction zone into three, north-south trending sections, following previous studies which had documented distinct differences in slab-dip and stress release patterns along the strike of the Tonga slab (Giardini and Woodhouse, 1984; 1986). This division also allowed Richards and Wicks (1990) to examine the geographical variability of the S660P conversions, and hence depth of the 660 km discontinuity. In the North and South sections clear S660P conversions were documented with depths from 660 to 690 km (no clear conversions were recorded for the central section, which Richards and Wicks (1990) argue reflects unfavorable fault Chapter 8, page 846 propagation for these events). These results have been converted in to temperature, following the simple method used above, and are plotted in figure 8.59. Lastly, of additional interest here is that for events in both the Northern and Southern section, Richards and Wicks (1990) also recognized a second, subtle S-to-P seismic phase which followed the S660P conversions by « 5 seconds. When converted to depth, the apparent depth lies between 700 and 740 km depth, but Richards and Wicks (1990) admitted that the origin of this second phase was unknown, and hence, did not focus attention on it, nor attempt an interpretation of these observations. However, within the framework of a pyrolite composition mantle, this second arrival likely represents conversions off the base of the majorite to perovskite phase transition or the base of the ilmenite breakdown to perovskite transition, either of which is predicted to exist at « 720 to 740 km depth (see figure 8.60). These phase transitions are relatively wide (occurring from 660 to 730 km depth along the ambient reference mantle adiabatic geotherm) and are responsible for the steep S- and P-wave velocity gradients that immediately underlies the 660 km discontinuity. Consequently, S-to-P conversions from the base of it would be expected to be weaker in amplitude than the S660P conversions, which originate from a narrow 4 km thick phase transition. Support for the interpretation that the weak "post S660P conversions" observed by Richards and Wicks (1990) comes from a recent seismic study which stacked seismograms from long-period SS precursors where the bounce point occurred only under oceanic areas on the Earth (Shearer, 1996). To match the stacked observations, the thickness of the steep velocity zone underlying the 660 km discontinuity was thinned, with the base of the steep velocity zone at 760 km Chapter 8, page 847 depth (the depth assigned in the iasp91 reference seismic model) being reduced to 727 km, a depth in excellent agreement with predictions based on mineral phase equilibria. Niu and Kawakatsu (1995) have also looked for S660P conversions beneath the Tonga subduction zone, but used records from Japan and California seismic networks. Raypaths to Japan wil l be nearer to the underside of the slab-660 intersection than raypaths to California. Because the predicted temperature of the slab is expected to decrease rapidly with proximity to the slab core, the raypaths to Japan are expected to give deeper depths to the S660P conversions than raypaths to California (see figure 8.61). This is indeed what Niu and Kawakatsu (1995) find, with the Japan S660P conversions depths being roughly 10-30 km deeper than those depths estimated from California records (see figure 8.62). These depths have been converted into apparent temperature assuming the mineral physics adiabat represents the reference geotherm for the mantle and a value for the 660 Clapeyron slope of— 2.1 MPa/K (see figure 8.63). Also shown in this figure is the predicted geotherm in the slab core at the Tonga subduction zone (from Marone and Liu (1998)). This represents the maximum cold temperature perturbation relative to the ambient mantle, since any part of the slab perpendicular to the slab core will be warmer than this geotherm. Of interest is the deepest S660P conversion (730 km) which plots very near the core temperature at this depth. Interestingly, the conversion point does not lie directly down dip of the trend of the slab, as defined by deep earthquakes with the Tonga slab, but off to the side, implying that the Tonga slab has thickened as it traverses across the 660 phase change, supporting the models of Fischer et al. (1988) discussed earlier (see figure 8.51). Wicks and Richards (1993) undertook a second S660P conversion study, but for the Izu-Bonin subduction zone, located southwest of Japan (see figure 8.64). This subduction zone is Chapter 8, page 848 similar to Tonga in that old (>150 Ma) Pacific oceanic lithosphere is subducting into the mantle, but contrasts with Tonga at 660 km depth, in that recent, high resolution P-wave tomographic studies indicate the Izu-Bonin slab is sub-horizontal, appearing to lie on the 660 km discontinuity (van der Hilst et al., 1991; 1993). Wicks and Richards (1993) again analyzed seismic waves which convert from shear to compressional mode at the 660 km discontinuity beneath the Izu-Bonin subduction zone. By comparing the predicted travel time difference between a S660P converted phase and direct P-wave (&ts P - 6tpP""ilc""J ) for a modified iasp91 velocity model, where the 660 km discontinuity depth varied in depth, with the observed travel time difference (&ts P - &p0hsened ), they determined the depth of the S660P conversion point. Their results for the two cross-sections they studied are re-plotted in figure 8.65 and 8.66 Overall, they find a deflection of the 660 km discontinuity of between 46 and 80 ± 10 km, with a rough mean of 60 km, values which are, in general, greater than that found in their previous study of Tonga (mean 30 km). Furthermore, they note that the depressed zone is 200-300 km wide, approximately 2 to 3 times the predicted plate thickness for old oceanic lithosphere. This apparent thickening is consistent with the slab thickening by a factor of two if a relatively weak slab encounters a more viscous lower mantle (Gurnis and Hager, 1988; Fischer et al., 1988). Following the procedure outlined earlier, I converted their conversion depths to temperature along the 660 km phase transition and theses are plotted in figure 8.67. Inspection of this figure reveals that the inferred temperatures span a range from 700 K, consistent with temperatures predicted for the cold core of the Izu-Bonin slab (900 ± 100 K; Meade and Jeanloz, 1991), to 1800 K, consistent with temperatures for the top of the slab. Chapter 8, page 849 Recently, Collier and Helffrich (1997) investigated the topography of both the 410 km and 660 km seismic discontinuities in the Izu-Bonin subduction zone using reflected and converted phases for earthquakes both above and below the 410 km discontinuity recorded on seismic arrays in the Western United States and England. By stacking the data they were able to identify and contour the displaced depths of both discontinuities (see figure 8.68). I have superimposed the trends of the two cross-sections of Wicks and Richards (1993) over their contoured discontinuity maps and the corresponding topography along these lines re-plotted in figures 8.69 and 8.70. Qualitatively, their results agree with that predicted by the intersection of a cold slab with the positive (negative) Clapeyron slope of 410 (660) km phase transitions. Surprisingly, they infer a very wide thermal anomaly at 410 («450 km), roughly double the expected width of the thermal halo associated with a subducting slab (e.g. Helffrich et al., 1989). This may suggest that either the subducting slab is deforming and thickening at much shallow depths than currently envisioned (e.g. Fischer et al., 1988), or that cooling of entrained mantle on either side of the slab is more efficient that expected. At the 660 km discontinuity their inferred depressions are less so than that estimated by Wicks and Richards (1993), but Collier and Helffrich (1997) note that their observations are actually agree within the uncertainty where both studies have good data coverage (note that the depth estimates of Wicks and Richards (1993) involve projecting all of their observations onto two single cross-sections, whereas, the Collier and Helffrich (1997) depth anomalies are taken exactly along the cross-section trend). Converting the depth estimates of Collier and Helffrich (1997) into temperature (see figure 8.71), it is evident that their depth anomalies correspond to a Chapter 8, page 850 somewhat lower range in total inferred temperature relative to that of Wicks and Richards (compare with figure 8.67). A n important finding of their study is that the inferred topography of both the 410 km and 660 km seismic discontinuities is elevated and depressed, respectively. This finding is completely consistent with predictions when a cold subducting slab intersect the a-olivine to (3-olivine phase boundary at 410 km, and the y-olivine dissociation reaction (to Mg-perovskite + magnesiowustite) at 660 km depth. While not emphasized in reviewing the above studies, the observed topography provides, in addition to temperature estimates within the transition zone, further evidence against the interpretation that either the 410 or 660 km seismic discontinuities correspond to chemical boundaries (e.g. Bass and Anderson, 1984; Anderson and Bass, 1984; 1986; 1986; Gasparik, 1997). Computer models (Hager and Raefsky, 1981; Christensen and Yuen, 1984) and tank models (Kincaid and Olson, 1986; Guillou-Frottier et al., 1995; Griffiths and Turner, 1988a, b; Griffiths et al., 1995) have demonstrated that the intersection of a subducting slab with a chemical boundary will result in substantial depressions in the chemical boundary on the order of 100-300 km relief. Therefore, the elevation of the 410 km seismic discontinuity in and adjacent to the Izu-Bonin slab as documented by Collier and Helffrich (1997) is very strong evidence that this seismic discontinuity does not represent a change in bulk chemistry of the mantle (e.g. Anderson and Bass, 1984; 1986). Furthermore, the topography of the 660 km seismic discontinuity is consistent with that predicted for the intersection of a cold subducting slab with the y-olivine to Mg-perovskite + magnesiowustite phase boundary, but not with the predicted 100-300 km depression which should mark the intersection of a cold slab with a chemical boundary. Chapter 8, page 851 8.10 Spreading Ridges and Mantle Plumes The above studies have largely concentrated on depressions and elevations of the 410 and 660 seismic discontinuities in, or around, subduction zones where it is expected that cold oceanic lithosphere will result in cooler mantle temperatures. In terms of explicitly documenting hotter temperatures associated with hot, upwelling mantle, two studies stand out. Lee and Grand (1996) used SS precursors to map the depths of the 410 and 660 km seismic discontinuities below the East Pacific Rise, the active mid-ocean spreading ridge separating the Pacific and Nazca plates. They found that while the absolute depths inferred for the two discontinuities was dependent upon the reference seismic model used to reduce the data, the relative width of the transition zone between the 410 and 660 km discontinuities was not. They compared their transition zone width to that determined from averaging SS data for only oceanic bounce areas (Shearer, 1996) and found that the EPR was within uncertainty of the global mean (EPR 240±3 km; global mean 243 km). Thus, mantle upwelling beneath spreading ridges does not extend any deeper than the 410 km seismic discontinuity, as some previous tomographic studies had advocated (e.g. Su et al., 1992), which suggests upwelling beneath ridges is a passive, rather than active process. The results from the M E L T experiment (MELT Seismic team, 1998; Shen et al., 1998) agree with Lee and Grand (1997), but place even tighter bounds on the depth of upwelling. Webb and Forsyth (1998) find that waveform inversions of seismograms for regional event with paths which follow the spreading ridge require low shear wave velocities down to only 150-170 km depth, at which point the velocity profile beneath the East Pacific Rise is Chapter 8, page 852 indistinguishable from that underlying 150 Myr Pacific lithosphere (Gaherty et al., 1996). A similar result was found by X u and Wiens (1998) for the active spreading ridges in the Fiji and Lau back-arc basins. Together, these results suggests that upwelling mantle flow at spreading ridges is a passive process and largely confined to depths shallower than 150-170 km depth. In contrast, oceanic hotspots are generally accepted as the surface expression of cylindrical shaped plumes of hot, upwelling mantle that arise from convective instabilities in a thermal boundary layer (e.g. Wilson, 1963; Morgan, 1971; Sleep, 1992; Steinberger and O'Connell, 1998). Petrologic, isotopic, and geodynamic studies have led workers to advocate positive temperature anomalies of 150-250 K, relative to normal mid-ocean ridge mantle potential temperatures (McKenzie, 1984; White et al., 1992; 1995). In contrast, global tomographic studies have largely been unable to clearly resolve plume anomalies within the mantle, reflecting the relatively narrow width of the plume stems (« 100 km) with respect to the resolving wavelength («1000 km) of the global seismic models. Recently, regional seismic studies have specifically focused on the seismic structure of plumes in the upper mantle (e.g. VanDecar et a l , 1995; Wolfe et al., 1997). At Iceland, Wolf et al., (1997) find anomalously low S- and P-wave anomalies that extend from the surface expression of the Iceland hotspot to 400 km depth, but the conversion of the anomalies into corresponding temperatures is difficult given that the velocity anomalies likely reflect the combined effects of temperature, anelasticity, anisotropy, and presence of widespread partial melt. In contrast, below the Iceland hotspot in the transition zone, Shen et al. (1996) studied P-to-S wave conversions from the 410 and 660 km Chapter 8, page 853 discontinuities using the same regional array of broadband seismometers. The differential travel time anomalies (8r„ -btp ) for these converted phases indicate that the width of the transition zone (410 to 660 km depth) is 23 ±9 km thinner than the width of iasp91 reference seismic model (250 km) implying temperatures «180 ± 70 K hotter than ambient mantle. This study cannot distinguish if this reflects a deeper 410 km, a shallower 660 km, or both, and hence, the thinner width is simply plotted schematically in figure 8.72 as a box with its 660 km temperature tied to 2150 K. Also plotted is a plume geotherm calculated via the analytical equations of Griffiths and Campbell (1991) for a long-lived plume conduit which incorporates the effects of entrainment of cool, ambient mantle. In calculating the plume geotherm, I have specified both the source region temperature anomaly (1500 K at the core-mantle boundary) and the surface temperature anomaly (200 K) and solved for the required entrainment to satisfy these constraints. Furthermore, I explicitly adopt the core-mantle boundary as the source region for plumes, since mineral physics modeling of a pyrolite mantle demonstrates that there is no thermal boundary layer existing anywhere within the present day mantle, and in addition, it has been demonstrated that the idea that plumes can originate from perturbations within the body of the mantle implausible (Griffiths, 1986). The resulting plume temperature anomaly was then simply added to the pyrolite mineral physics geotherm with no correction made for the shift in depth of the 410, 520, or 660 km phase boundaries that should occur for the plume geotherm, relative to the reference depths. It is clear that the thin width of the Iceland transition zone, as documented by Shen et al. (1996), is consistent with the predicted Chapter 8, page 854 temperatures for a plume conduit with entrainment occurring throughout the depth of the mantle. At present there is an apparent discrepancy between the relatively low maximum excess temperature anomaly («500 K) allowed at the plume source region as estimated by simplified, cylindrical finite element, models of plumes (Abers and Christensen, 1996; Farnetani and Richards, 1995; Farnetani, 1997) and the interpretation of laboratory experiments which allow a much higher source temperature anomaly (e.g. Richards and Griffiths, 1989; Griffiths, 1986; Griffiths and Campbell, 1991; Griffiths, 1991). A major difference between the simplified cylindrical finite element models and the analytical equations derived from tank experiments is that the finite element models have only considered perfectly vertical plume conduits, in contrast to tank models, which explicitly studied entrainment of ambient material in inclined plume conduits in the presence of a background convective flow. Deflected plume conduits have much higher rates of entrainment than purely vertical conduits, and hence the temperature anomaly of the plume decreases much faster with increasing height from the source region. Inclined plume conduits are indeed predicted for mantle plumes originating at the core-mantle boundary and traversing through the present day mantle flow field (Steinberger and O'Connell, 1998). Therefore, I believe the calculated plume geotherm in figure 8.72 is a good approximation to the temperature structure expected for the Iceland hotspot in this depth interval. 8.11 Lower Mantle Thermal Anomalies Chapter 8, page 855 Below the transition zone, where the depth of the olivine phase transitions, as recorded by the depths of the 410, 520 and 660 km seismic discontinuities, acted as insitu thermometers (e.g. Shearer, 1992), there does not exist any further global seismic discontinuities, at least as resolved by the recent reference seismic models (e.g. CREMO (Montagner and Anderson, 1989), iasp91 (Kennett and Engdahl, 1991); SP6 (Morelli and Dziewonski, 1993); akl35 (Kennett et al., 1995); akl35-Q (Montagner and Kennett, 1996)). While some regional studies of near-source S-to-P converted phases at the Tonga subduction zone have argued for a global discontinuity at 920 km depth (defined as a 2.4% positive jump in the S-wave velocity profile, approximately 40% of the 660 km seismic discontinuity, based on the ratio of the S920P/SmP amplitude (Kawakatsu and Niu, 1994). Note that this dV$ estimate depends almost entirely upon the Vs profile and is insensitive of the density profile), subsequent studies at other subduction zones in Indonesia, Japan, and Izu-Bonin find that there is significant depth variation on this proposed discontinuity (from 900 to 1080 km) with a strong correlation at the Indonesian subduction zone with the change in age of subducting lithosphere along the trench (Niu and Kawakatsu, 1997). Although Kawakatsu and Niu (1994) favoured an interpretation where this discontinuity marked a global change in bulk composition of the mantle, the results from the mineral physics calculations in the previous chapters demonstrates that no such change in composition is required to satisfy the density and velocity profiles (V&, Vs, Vp) of the reference seismic models across the full depth extent of the lower mantle. I re-iterate that while their inferred velocity jump is slight, a chemical boundary will be associated with a thermal boundary layer (e.g. Jeanloz and Richter, 1979; Olson, 1981; Schubert and Spohn, Chapter 8, page 856 1981; Spohn and Schubert, 1982; Kenyon and Turcotte, 1983), for which there is no evidence, either from mineral physics, or from statistical analysis of the radial correlation of the seismic heterogeneity in existing tomographic models (e.g. Jordan et al., 1993; Puster and Jordan, 1997). Furthermore, recent high temperature and pressure experiments demonstrate that the pyrolite assemblage is stable throughout the complete pressure extent of the lower mantle (Boehler, et al., 1997; Kesson et al., 1998) and refute recent claims that Mg-perovskite dissociates into stishovite and periclase at 70 GPa (Meade et al., 1995; Saxena, et al., 1996; Saxena, 1997). Indeed, in contrast to the claim that Mg-perovskite breaks down to its constituent oxides at high pressure, Boehler et al.(1997) find that at 74 GPa and 2600 K , S i 0 2 and MgO actually combine to form Mg-perovskite rather than dissociate, and speculate that Saxena's results likely reflect large temperature gradients in their laser-heating diamond anvil apparatus. In agreement, Kesson et al. (1998) find that the full pyrolite assemblage of Mg-perovskite + Ca-perovskite + magnesiowustite is stable in their diamond anvil experiments from the top of the lower mantle to temperatures and pressures equivalent to the core-mantle boundary. Regional seismic studies which have attempted to isolate horizontal discontinuities between 770 and 1000 km from S-to-P near source conversions for earthquakes in Izu-Bonin subduction zone, recorded by hundreds of stations in the Western United States, reveal that no near-horizontal discontinuity with a shear-wave velocity jump above 1% can be detected in the mantle beneath the Pacific plate (Castle and Creager, 1997). While their study documented "660" SfifinP conversions at depths in agreement with previous studies (Vidale and Benz, 1992; Wicks and Richards, 1993), no evidence for a spatially coherent Chapter 8, page 857 discontinuity beneath the 660 km discontinuity was found, as would be expected i f a global chemical discontinuity existed somewhere within this depth interval. Le Stunff et al. (1995) used P'P' precursors to argue for mantle discontinuities at 785 and 1200 km depths beneath Africa, in rough agreement with the depths inferred by Niu and Kawakatsu (1997). However, while the signals they interpreted in favour of "785" reflector have been clearly observed by other studies (Xu et al., 1998), the latter study demonstrates these signals are consistent with arrivals of PePPKP seismic phases, a feature predicted from standard seismic reference models, rather than a seismic discontinuity at 785 km depth (signals corresponding to the inferred 1200 km discontinuity were below the detection capability of the seismographs in the X u et al., (1998) study, and thus, remain unsubstantiated). As an alternative interpretation to a global chemical discontinuity, the 920 km discontinuity may reflect the effects of localized phase reactions occurring in the garnet-dominated oceanic crust of the subducting slab, and consequently, would be expected to occur only at subduction zones (Vidale, 1994). In support of this hypothesis are the experimental observations of Boehler et al. (1997) that garnet exhibits extremely slow transformation kinetics below 2000 K (for experiments on M g 3 A l 2 S i 0 3 pyrope to 50 GPa) such that the transformation to Al-bearing Mg-perovskite is retarded, and thus would not be completed at the "normal" maximum depth of 730 km along the ambient mantle geotherm. While Kesson et al., (1994) experimentally evaluated M O R B mineralogy from 45 to 100 GPa and argued that garnet should completely transform to perovskite by «900 km depth, the samples in their experiments were heated to temperatures between 2000-3000 K , and consequently, reaction kinetics was unlikely to be a factor in their experiments. Interestingly, Chapter 8, page 858 the calculated temperature at the top of the Japanese slab reaches « 2000 K in roughly the 920-1000 km depth interval (see figure 8.73), suggestive that both the large depth variation of the "920" discontinuity and the positive correlation with age of the subducting oceanic lithosphere along the Indonesian trench which Niu and Kawakatsu (1997) document, reflects the interplay between the age-dependent thermal structure of the downgoing slab and its garnet-dominated ocean crust with the 2000 K isotherm. Thus, fast subduction of very old oceanic lithosphere will result in the top of the slab reaching the 2000 K isotherm at depths exceeding the "920" km depth, while slower subduction (or younger, hotter oceanic lithosphere) will facilitate thermal equilibration of the top of the slab such that it reaches 2000 K at, or slightly shallower than, "920" km depth. While speculative, this hypothesis does provide a testable interpretation of the 920 km observations without conflicting with experimental and theoretical mineral physics observations that strongly favour a uniform composition throughout the bulk of the lower mantle with slabs traversing far deeper than either the 660 km or 920 km depths (e.g. regional tomographic models clearly show the Indonesia slab to a depth of at least 1500 km (Widiyantoro and van der Hilst, 1996, 1997), a depth well beyond the 920 km chemical boundary). Thus, unlike the transition zone, in the lower mantle there are no global seismic discontinuities, and hence, no related discontinuity topography which may be used to infer lateral temperature anomalies (I ignore the basal chemical and thermal boundary layer that comprises the D" layer). Thus, one is faced with the task of directly converting the lateral velocity anomalies, as recovered in seismic tomographic models, into equivalent lateral variations in temperature, under the implicit assumption that the velocity anomalies represent only temperature perturbations in a mantle of relatively uniform composition. I note in Chapter 8, page 859 passing that such an assumption is, in fact, a very robust one in that the previous chapters of this study have clearly shown that a uniform pyrolite composition provides an excellent fit to the reference density and bulk sound velocity profiles on one hand, and shear and compression velocity profiles on the other, all of which are calculated along a self-consistent adiabatic geotherm. Furthermore, the relative ratio of S- to P-wave velocity anomalies throughout the mantle, as described by the dimensionless logarithmic ratio (d\nVs/d\nV,,)p , is well matched by the predicted profile for a pyrolite mantle, indicating that the relative amplitude of lateral S- to P-wave velocity anomalies recovered by global seismic tomography is consistent with that produced by thermal perturbations. Therefore, it is with some confidence that I treat the lower mantle velocity anomalies as reflecting simply thermal perturbations. Seismic anomalies may be related to temperature via (e.g. Jordan et al., 1993): 8^(r,e,<|») Vs(r) where the shear wave perturbation is a function of radius, latitude, and longitude. A more complete expression, taking into account the effects of anelasticity and the presence of partial melt is given by Sobolev et al. (1996; 1997). Neither of these additional factors will be consider here. While it has been commonly believed that thermal buoyancy is largely driving convection (e.g. Turcotte and Schubert, 1982), recent experimental mineral physics results (Chopelas, 1992) combined with seismic tomography have been used to infer extremely large dT (r) Chapter 8, page 860 temperature anomalies, bT in the lower mantle on the order of +2500 °K to -2000 °K (Yuen et al., 1993; 1994; Cadek et al., 1994) from the relationship: 87Yr,8,fr) _ ( Ship ^ Tadiabat (O Kd\nVSJ MgO f 1 ^ T v a ( r ) y 8^(r,e,4> Vs(r) where a(r) is the thermal expansivity as a function of radius (r), bVs represents the shear wave seismic anomaly as a function of radius(r), latitude (9) and longitude ((()), Vs(r) is the reference S-wave velocity profile, and (dlnp/SlnJ^.)^ 0 is the dimensionless, isothermal scaling factor for MgO that maps shear wave variations into density anomalies. The density anomalies, when combined with the thermal expansion term, result in temperature anomalies 87(r). Figure 8.74 gives the experimental profiles for MgO, A1 2 0 3 , and Y A G garnet, all determined by the analysis of the pressure-dependent frequency shift of acoustic modes measured from Cr + 3 doped specimens (Chopelas, 1990; Zhang and Chopelas, 1992; Chopelas, 1996). Doping with a transition metal ion is required such that laser-induced fluorescence results in observable acoustic modes within the vibrational sideband spectrum. This fluorescence spectrum is the product of electrostatic interactions between the Cr + 3 ions and the vibrations of the host lattice (Zhang and Chopelas, 1994). The acoustic modes are then converted to shear and compression velocities via the relationship: V _ a co ^(Ref) ^Ref 1 0 Ref where a is the unit cell constant (for cubic minerals given by a — (Vcellwhere Vceu is the unit cell volume), co is the acoustic mode frequencies, V is the sound velocity, and the Chapter 8, page 861 subscript Ref denotes the reference state at room pressure (Chopelas, 1992). The relationship between sound velocity and acoustic modes may be recast by taking the logarithmic derivative with respect to density: d\nV ain P J 7 , 5 In co Ship + JT ( d h W ainpj 7 Chopelas (1992) states that (dlna/51np)7. = -1/3 while (dlnco/31np)7, = y, , the mode Gruneisen parameter. Thus, this relationship simplifies to: dlnpj7. / . 3 Inspite of the relatively simplicity in obtaining ( d l n p / S l n F ^ (the inverse of the above function), there are some shortcomings of the experimental technique. It cannot be applied to all minerals of interest because a suitable cation site must exist to accept the Cr + 3 ion. In addition, this experimental technique allows only isothermal scaling factors to be estimated (note the subscript "T" on the term (<91np/dlnKs)r ), whereas it is the isobaric parameter, (Slnp/SlnJ^.)^ which is of geophysical interest in converting velocity into temperature anomalies. Yuen et al (1994) claim that using the isothermal instead of the required isobaric parameter results in 30% error, but it is not clear how this estimate was obtained. Lastly, the measured "parameter (d\np/d\nVs)T is purely anharmonic and consequently, does not account for anelastic contributions. As mentioned above, Yuen et al. (1993; 1994) and Cadek et al. (1994) utilized Chopelas's (1992) isothermal scaling factor for MgO, (dlnp/SlnF,,.)^ 4 ' 0 and the thermal expansion coefficient, a, as a function of pressure from Chopelas and Boehler (1992) to Chapter 8, page 862 estimate the magnitude of the temperature anomalies in the lower mantle. However, before presenting these results note that the use of periclase as a proxy for a pyrolite mantle is less than ideal because MgO, the magnesium endmember of magnesiowustite, comprises only approximately 10% by volume of the lower mantle mineral assemblage, and thus, it is uncertain as to how representative its material properties are of the complete lower mantle assemblage. Figure 8.75 plots the extrema of the temperature anomalies for the S-wave tomographic models of Su and Dziewonski (1991; SH425.2) and Woodward et al. (1993). In general, the calculated temperature extrema for both tomographic models are broadly similar; the inferred hot anomalies exceed that of the cold anomalies in the deepest mantle indicating in general a difference between hot and cold anomalies. Note, however, this is the reverse from what is documented for the upper mantle and transition zone, where the range and magnitude of the cold temperature anomalies, especially that documented at subduction zones, far exceeds the magnitude associated with plume conduits, such as that beneath Iceland (compare the relative differences between the plume geotherm and the pyrolite adiabat to that between the cold core of the Tonga slab in figure 8.73). Note too, that the temperature anomalies in figure 8.75 correspond to the broad, long wavelength upwelling and downwelling mantle flows as captured by the degree 8 and 12 expansion of the velocity anomalies in these two particular tomographic models, respectively. Thus, these temperature extrema do not represent narrow plume conduits or subducting oceanic lithosphere, since both features are thinner than the resolving scale of either tomographic model. For example, note the difference between the relatively modest temperature anomalies inferred from discontinuity topography as resolved by long Chapter 8, page 863 wavelength SS precursors (see figure 8.45) to the extreme temperature perturbations inferred from short-wavelength, seismic converted phases at subduction zones (see figure 8.67). Thus, the temperature extrema estimated by Yuen et al. (1993) and Cadek et al. (1994), inspite of the extraordinary magnitude, should actually correspond to minimum temperature estimates. To put these temperature extrema in context of the mineral physics pyrolite adiabat, I have re-plotted them around this geotherm (see figure 8.76). It is clear from this figure that for both tomographic models, there exists a conflict between the magnitude of the hot anomalies and the inferred lower mantle solidus and liquidus based on the diamond anvil melting experiments of Zerr et al. (1997) and the shock-wave melting estimate of Holland and Ahrens (1992). If the hot extrema are real, the magnitude of the hot anomalies imply that upwelling material exceeds the melting curve of the lower mantle in the basal one third of the lower mantle, and perhaps, near the 660 km seismic discontinuity. However, radial models of shear attenuation, as embodied in the dimensionless parameter, seismic Qs, all exhibit low attenuation, and hence high Qs values, across the lower mantle, exactly the opposite of what is expected i f a widespread partial melt existed in the lower mantle (see figure 8.77). Again, note that these temperature extrema correspond to the long-wavelength upwelling and downwelling flows, and not the maximum temperature extrema which occur in hotspot conduits, which are likely to exceed these temperatures by a factor of 2 (e.g. the inferred temperature at the 410 km discontinuity from long wavelength observations is ± 58 K (Vasco et al., 1995; see figure 8.45), roughly one half of that inferred from S-to-P conversions within the hotspot conduit below Iceland (Shen et al. 1996; see figure 8.72). Using the Su and Dziewonski (1991) tomographic model, Yuen et al. (1993) constructed the temperature anomalies along a great circle cross-section through the central Chapter 8, page 864 Pacific with the intent of constructing the temperature structure of the Pacific superplume. Their figure is re-plotted here (see figure 8.78) and illustrates clearly the plume-like upwelling coming off the core-mantle boundary located south of Hawaii. Even though these temperatures are very high, note that had Yuen et al. (1993) used the Woodward et al. (1993) model, the magnitude would be even greater. Indeed, the large magnitude of these temperatures did concern Yuen et al. (1993) and they speculated that, in addition to temperature, perhaps the hot velocity anomalies also reflect contributions from chemical anomalies such as iron enrichment (e.g. Anderson, 1975). By appealing to both iron enrichment and temperature, the required magnitude of the temperature anomaly is reduced, since some component of the velocity anomaly reflects chemical, as opposed to thermal, perturbations from the reference composition. Stacey (1993) has also argued that lower mantle velocity anomalies cannot reflect purely temperature effects. Yuen et al. (1994) next focussed on the cold anomalies which they noted could be up to 2000 K below the ambient mantle at D" layer depths (see figure 8.76). They argued, on the basis of results from three-dimensional numerical convection models, which included the effects of the 410 and 660 km phase transitions (e.g. Honda et al., 1993; Steinbach et al., 1993; Tackley et al., 1993; Solheim and Peltier, 1993; 1994a, b), that these cold temperature anomalies represented cold subducted lithosphere that had only recently, "avalanched" into the lower mantle. These numerical models demonstrate that i f the 660 km phase transition has a large enough Clapeyron slope (< -3.0-4.0 MPa/K), then it may act to temporarily retard subducting lithosphere (200-500 Ma), until sufficient gravitational forces have built up to overcome the resistive force of the phase change. At this time, the ponded slabs, suddenly "avalanche" (also termed "flush events" or "catastrophic overturns" in the numerical Chapter 8, page 865 convection literature) into the lower mantle such that relatively large amounts of cold lithosphere rapidly reach the base of the mantle. Honda et al. (1993) found that in their 3D cartesian numerical model, the cold, avalanched material would reach the D" layer at the base of the mantle with temperatures roughly 1000 K below the ambient lower mantle. Yuen et al. (1994) noted that even colder anomalies may be obtained when the numerical model is modified to incorporate depth dependent thermal expansivity, viscosity, and spherical shell geometry (e.g. Steinbach et al., 1993; Steinback and Yuen, 1994). While the numerical convection models provide an appealing explanation for the extraordinarily cold thermal anomalies it should be noted that the avalanche-mode of partial layering exhibited by these models is heavily dependent upon the adopted input boundary conditions of the numerical model. For example, none of the published numerical convection models demonstrate avalanche-mode partial layering when the Clapeyron slope of the 660 km phase transition is set at y 6 6 0 = -2.1 MPa/K, the thermodynamically optimized value when all the experimental data for the y-olivine to Mg-perovskite + magnesiowustite breakdown reaction is considered (Bina and Helffrich, 1994). It is only when abnormally large values for y 6 6 0 are adopted (e.g. Tackely et al. (1994) found partial layering in their 3D spherical convection models for y 6 6 0 = -4.0 MPa/K, but not for values of -3.0 MPa/K), together with inappropriate boundary conditions, that partial layering occurs in the convection models. For example, compare the numerical convection geotherm and its calculated mean 410 and 660 km phase boundary deflections to the pyrolite mineral physics adiabat and the seismically observed deflections plotted in figure 8.48. This particular numerical convection model is a two-dimensional axi-symmetric model with adopted values of y 4 ] 0 = +3.5 MPa/K Chapter 8, page 866 ^ ^ 7660 ~ -2.1 MPa/K, which are consistent with the recommended values of Bina and Helffrich (1994). Inspite of the abnormally hot geotherm and the excessively large magnitude of the predicted 410 and 660 km phase boundary deflections, this convection model predicts virtually no partial layering due to the transition zone phase boundaries (Solheim and Peltier, 1994a; p. 15,873. They calculate a layering parameter, P 1 0 , a dimensionless measure of the degree of partial layering, which for the run illustrated in figure 8.48 is P 1 0 = 0.13. A value of P I 0 = 0 indicates no layering due to the 660 km phase boundary, while a value of 1 indicates perfect layering. Avalanche partial layering occurs for numerical runs with P 1 0= 0.56). Since Solheim and Peltier (1994a, b) admit that decreasing the overall temperature of their numerical models, either by decreasing the amount of internal radiogenic heating assigned to the model, or by decreasing the adopted core-mantle boundary temperature, results in a decreased propensity towards partial layering, it is evident that i f their numerical model was re-run at appropriate Earth-like values (such that their convection geotherm agrees with the mineral physics adiabat), then the possibility of partial layering would be non-existent. Further note that Tackely et al. (1993) point out that going from two dimensional axi-symmetric to full three-dimensional spherical geometry also decreases the propensity for partial layering. The validity of the "avalanche" partial layering exhibited by some of the numerical convection models is important in the context of rationalizing the extremely cold temperature anomalies calculated by Yuen et al. (1994). They note that avalanche events are required to rapidly move ponded oceanic lithosphere at the 660 km phase transition to the base of the lower mantle; such extremely cold anomalies are not generated in their numerical convection models when steady state subduction dominate. Thus, the question of how cold are the Chapter 8, page 867 anomalously fast seismic anomalies, as recovered by tomographic models, has implications beyond just purely temperature considerations. The question of whether or not the fast seismic anomalies in the Woodward et al. (1993) SH8WM13 tomographic model, which occur at the core-mantle boundary, represents subducted oceanic lithosphere was statistically tested by correlation analysis between the spatial distribution of past subduction sites and the fast seismic anomalies (Yuen et al., 1993; Cadek et al., 1994; Kyvoalova et al. (1995). The distribution of paleo subduction sites was taken from Richards and Engebretson (1992) and expanded in spherical harmonics to degree and order eight. The correlation coefficients were calculated as line integration of the subduction zones and the fast seismic anomalies and expressed as a function of radius via (Cadek etal., 1994): where L is the line following the subduction trench, 8Fis the seismic anomaly, and subscript Max indicates the maximum seismic anomaly at that particular radius. The results for different age windows (Cadek et al., 1994) is re-plotted in figure 8.79 for the Woodward et al. (1993) tomographic model, together with 98% confidence interval which was estimated by numerical experiments using random seismic anomalies with a flat spectrum. Similar results were presented by Yuen et al. (1994) and the technique is outlined in greater detail in Kyvalovaetal. (1995). In general, there is a strong correlation for virtually all ages in the upper one third to two thirds of the lower mantle, with the depth of correlation generally increasing with C(r) - L Chapter 8, page 868 increasing age. Nevertheless, a decrease in correlation occurs just above the D " layer and appears to be "sandwiched" between strong correlations both above and below. Cadek et al. (1994) found similar results for other tomographic models. They interpreted their results as evidence that subduction into the lower mantle was episodic and not steady state, consistent with their appeal to "avalanche" partial layering as the explanation for the cold temperature anomalies. Thus, the gap in correlation between the subduction sites and the tomographic model is taken as evidence of a period of restricted subduction across the 660 km phase boundary, reflecting partial layering in the mantle, while the strong correlation below represents the remnants of an earlier "avalanche". Before accepting such an interpretation, it is worth while to note that the rms amplitude of the S-wave velocity anomalies in the Woodward et al. (1993) model is weakest in the lower most mantle. Therefore, an alternative interpretation of the gap in the spatial correlation at » 2000-2500 km depth is that this may reflect deficiencies in the tomographic model, essentially due to poor ray coverage. A n earlier correlation study between subduction sites and seismic anomalies by Scrivener and Anderson (1992) found similar patterns, albeit they argued that the good correlation at the top of the lower mantle was either an artifact of the tomographic models, where a shallow, upper mantle slab signal had been smeared radially into the lower mantle, or that the slabs were entirely restricted to the upper mantle, but thermally (and/or viscous) coupled to convective downwelling in a chemically distinct lower mantle. In this scenario, cold slabs lying on the top of the lower mantle would cool it and trigger cold downwellings (see figure 7.80). However, in a follow up study Ray and Anderson (1994), using only a single, first-generation S-wave tomographic model (Tanimoto, 1990) found good spatial correlations at both the top of the lower mantle and at the core-mantle boundary, which they Chapter 8, page 869 interpreted, like Yuen et al. (1994), to reflect the results form episodic "avalanche" events in a isochemical mantle. Lastly, Wen and Anderson (1995) updated the volume and location of oceanic lithosphere subducted over the last 130 Myr using the latest magnetic anomaly data and plate rotation parameters describing the relative motion between the Earth's plates. The resulting subduction volume was expanded in spherical harmonics and compared against the seismic anomalies from four independent tomographic models. Although they documented, via correlation analysis, the same general spatial and radial patterns as had been found earlier, they interpreted the decrease in correlation at approximately 1000 km depth to indicate that subducted slabs are trapped near the top of the lower mantle. They acknowledged that the 660 km seismic discontinuity was unlikely, in light of their correlation analysis, to be a chemical boundary, but instead retreated deeper into the mantle and appealed to the "920" km seismic discontinuity (Kawakatsu and Niu, 1994) as a potential chemical boundary, and hence, mechanical barrier to subducting slabs. However, it should be noted that not all of the tomographic models they utilized posses a drop in correlation at «1000 km depth. Of note is that the early version of the Scripps S16B30 S-wave tomographic model (Masters et al., 1992; termed UCSD2 in Wen and Anderson, 1995) exhibited an excellent correlation (>90%) between 0-30 Myr subduction volumes and fast seismic anomalies from 400 to 1555 km depth, while for older time windows of 30-60, 60-90, and 90-130 Myr, this level of correlation was evident from 1022 km to the base of the mantle at 2891 km depth. Thus, this tomographic model refutes the claims of Wen and Anderson (1995) that the spatial correlation between subduction and tomographic models drops at « 1000 km, and instead, strongly suggests that such decreases Chapter 8, page 870 may, as proposed above, reflect shortcomings in resolution of the particular tomographic model. This inference is supported by the most recent high resolution tomographic models (Grand, 1994; Grand et al., 1997; van der Hilst, et al. 1997) which clearly show continuous sheets of fast seismic anomalies extending across the full extent of the transition zone and lower mantle beneath the Japan and Central American subduction zones. As calculated by Yuen et al. (1994), the spatial distribution, together with the magnitude of the temperature anomalies at the core-mantle boundary is re-plotted in figure 8.81. It is immediately clear from this figure that the spatial distribution of the cold anomalies at the base of the mantle bears a striking similarity to the present day subduction zones. Indeed, this is emphasized in figure 8.82 where the hatched area represents the paleo subduction sites over the last 180 Myr (Richards and Engebretson, 1992; the similarity between the modern subduction zones and the integrated paleo-sites for the last 180 Myr reflects the long life time of circum-Pacific and paleo-Tythes subduction zones). To summarize the interpretations of Yuen et al. (1993; 1994) and Cadek et al. (1994), they argue that on the basis of extreme magnitude of the hot temperature anomalies that the slow seismic anomalies in the lower mantle do not reflect purely temperature effects, and instead, likely represent combined chemical and thermal effects. In contrast, they accept the extremely cold temperature anomalies at face value, and argue that these correspond to subducted oceanic lithosphere that has abruptly been flushed into the lower mantle during an avalanche event in an isochemical mantle. Within this framework, Yuen et al. (1994) state that such extremely cold temperature anomalies at the core-mantle boundary, would not be consistent with steady-state subduction. Chapter 8, page 871 The inference of chemical anomalies in the lower mantle is in conflict with the conclusions drawn from the previous chapters where I demonstrated that a uniform pyrolite bulk composition, when applied across the whole mantle, provides an excellent match to the reference seismic density and bulk sound velocity profiles along a self-consistent adiabatic geotherm. In addition, when the pyrolite model was extended to model Vs and Vp profiles, the resulting predicted profiles again gave an excellent fit to the reference shear and compression velocity profiles. Lastly, the pyrolite model was used to calculate a radial profile of the dimensionless parameter {d\nVs ld\nVp)p , which relates the relative magnitude of the shear wave velocity anomalies to the associated compression wave anomalies. This predicted profile gave an excellent match to the latest seismic inferences, as estimated from joint, whole mantle S- and P-wave tomographic models, across the full extent of the mantle, indicating that temperature perturbations alone, could indeed reconcile seismic and mineral physics inferences of the relative magnitude of 8 ^ and bVp throughout the whole mantle. To resolve the discrepancy between a chemical or thermal interpretation for the lower mantle velocity anomalies, and to further investigate the magnitude of the temperature perturbations in the lower mantle, I use the pyrolite mineral physics model to calculate the adiabatic scaling factor (d]np/d\nVs)p throughout the mantle, and use this to re-calculate the extrema SPvalues of Cadek et al. (1994). 8.12 Methodology To correct the estimated lower mantle temperature perturbations of Cadek et al. (1994), a profile of the isobaric, dimensionless, logarithmic density to shear wave scaling Chapter 8, page 872 factor, (d In p/d In Vs )p is required. I use the pyrolite mineral physics model, described in the previous chapters, to calculate the shear wave temperature derivative, (dVs/dT)p , by re-calculating the mineral physics model «100 °K above and below the reference geotherm. Thus, by re-running the pyrolite model slightly above and below the reference geotherm, the temperature derivative of velocity may be approximated by taking the average of the finite difference between the hot (cold) and the reference Vs profile: AF, ~2 rphol rp ref K1 1 J + ( y*f _ yscold ^ rp ref rp cold Note that the pressure coordinate does not change when the velocity (and density) profiles are re-calculated either 100 °K above or below the reference geotherm. Thus, I am calculating at a particular depth (or pressure) a "colder" and "hotter" velocity, and then by difference from the average velocity at that depth (or pressure), what the average temperature derivative of velocity ((dVs/dT)p ) is. In a similar fashion, the temperature derivative of the pyrolite density profile may be approximated via: fdp} ydTj rAp} v A7T y _ hot „ ref PP -Pi rphol rpref \ P ~ P J + . ref „ cold rpref _ rp \ p p cold Next, (d In p/d In Vs )p is calculated from its components via the relationship: ' <31np • p ( d\np\ I dT ) 1 P dp] KdT) Vs (dp/dT) {d\nVsJ 'd\nVs^ K dT t 1 Vs 'dVs [dT * p (dVjdT) ) Chapter 8, page 873 Lastly, to correct the temperature perturbations of Cadek et al. (1994), I multiply their extrema temperature profiles by the ratio of the pyrolite (31np/<31nFs)y, profile and the MgO profile: { ) P ~ (8\np/d\nVs)r { ) T where 5T(r)Pg0 represents the radial temperature profiles estimated by Cadek et al. (1994; see figure 8.75), (d lnp /S lnFy)^ 0 is the profile of the isothermal scaling factor (Chopelas, 1992) utilized by Yuen et al. (1993; 1994) and Cadek et al. (1994), and dT(r)™r"'"e represents the calculated isobaric, pyrolite temperature perturbations. This "correction" to their temperature estimates is clearly less than ideal because it would be preferable to apply both the pyrolite thermal expansion profile, tx(r) together with (Slnp/Sln^.)^ to obtain an internally consistent temperature estimate, but nevertheless, this correction does allow the effect of using the required isobaric, rather than isothermal, scaling factor to be clearly determined. I repeat that the radial temperature perturbations estimated by Cadek et al. (1994) represent the mean extremal temperature perturbations estimated from the two particular tomography models they adopted for study. Thus, the "cold" and "hot" temperature perturbations are not necessarily going to be symmetric about the mantle geotherm since the major hot and cold thermal perturbations in the mantle, rising plumes and subducting slabs, have unequal maximum temperature perturbations from the mantle geotherm. An alternative way of estimating temperature perturbations from the tomographic models is to utilize the radial profiles of the rms velocity amplitude. To obtain a rough Chapter 8, page 874 approximation of the magnitude of the positive and negative velocity perturbations, the magnitude of these rms profiles may be simply doubled (Bolton, personal communication): 2 [ 8 ^ L - « 5 r s ( r ) The velocity anomaly may be calculated relative to its reference velocity via: bVJr)= s s re/ x l O O Vs(Tref,P). To determine the required temperature anomaly, &T, which results in a particular velocity anomaly, 5V, the pyrolite mineral physics temperature derivatives may be combined with the reference velocity profile via: Vs(oT,P) = Vs(TaJiahal,P) + Thus, given an rms velocity profile from a tomographic model, it is possible to solve for the necessary rms temperature perturbation, 8T associated with the velocity anomaly. Cadek et al. (1994) used two first generation, S-wave tomographic models, SH425.1 (Su and Dziewonski, 1991) and SH8WM13 (Woodward et al., 1993), to estimate the lower mantle temperature anomalies. Instead I use SH8WM13 and S16B30 (Masters et al., 1996), a second generation whole mantle S-wave model (see figure 8.83). While the rms velocity amplitudes are comparable in the upper mantle and transition zone, they differ across most of the lower mantle. Note that this method will give the average temperature anomaly at depth rather than the most extreme and further, I am assuming that this temperature perturbation applies equally well to describe both the mean positive and negative temperature perturbations. This latter assumption is unlikely to be correct given that subducting slabs may be considerably (8 T Tadiahal) . Chapter 8, page 875 colder than the mantle geotherm compared against how much hotter uprising plumes are than the mantle geotherm. This asymmetry should skew the mean temperature perturbations such that the average "cold" thermal anomalies are not simply mirror images of the average "hot" anomalies, as I am assuming here. To correctly estimate the temperature anomalies the individual velocity anomalies at a particular depth and latitude and longitude should be converted to temperature and then these temperature estimates used to calculate the average "cold" and "hot" anomalies. This is future work. 8.13 Results and Discussion Figure 8.84 plots the corrected temperature anomalies of Cadek et al. (1994) and it is clearly evident that the temperature anomalies have decreased substantially compared to their calculated extrema. The lateral temperature variations now range from « ± 115 °K at 660 km depth to « ± 550 °K at the base of the lower mantle. Figure 8.85 plots the absolute temperature anomalies relative to the pyrolite adiabatic geotherm and inspection of this figure reveals that there is no longer a significant discrepancy between the magnitude of the corrected lower mantle temperature anomalies and the transition zone temperature estimates discussed in the previous sections (see small arrows at the 660 km seismic discontinuity). A simple comparison of figure 8.76, which shows the original temperature extrema of Yuen et al. (1994) to figure 8.85 emphasizes the drastic reduction which has occurred with the application of the isobaric pyrolite (Slnp/SlnF^)^ scaling factor. Neither extremely hot nor extremely cold temperature anomalies remain in the corrected temperature extrema, and Chapter 8, page 876 therefore, the evidence for invoking either chemical anomalies in the lower mantle and or avalanche events has evaporated. A n additional point to be made is that the new temperature anomalies estimated in figure 8.85, lie well below the inferred lower mantle solidus. Thus, the homologous ratio, Tm/T is relatively low, which is qualitatively consistent with radial profiles of seismic shear attenuation (see figure 8.77). Qs profiles exhibit a general trend of progressively increasing QS from relatively low values at shallow depths («100 km), where the mantle adiabat closely approaches the KLB-1 solidus, to high values across the lower mantle. The progressive increase is consistent with the general trend of increasing separation between the adiabat (and associated lateral temperature anomalies) and the solidus. The trend in homologous ratio is also consistent with recent inferences of the radial viscosity profile of the mantle. Recently, Mitrovica (1996) emphasized that the Laurentide glacial rebound observations were actually placing constraints on the average depth-weighted viscosity within a depth interval extending down to 1200-1400 km depth (termed the Haskell average). This interval is much deeper than previous interpretations had considered, and consequently, new profiles of mantle viscosity, which satisfy the Haskell average, exhibit a substantial increase in viscosity with increasing depth (Forte and Mitrovica, 1996; Mitrovica and Forte, 1997). Such profiles are consistent with the general trend between the lower mantle solidus and the temperature anomalies in figure 8.85. Figure 8.86 shows the estimated temperature anomalies from approximating the velocity anomalies as simply 2 X the rms velocity perturbations. For SH8WM13 (Woodward et al., 1993), the predicted temperature anomaly at 660 km depth is ± 114 K and increases smoothly to ±385 K at 2600 km, the top of the D " layer. In spite of being a second generation Chapter 8, page 877 tomographic model, and hence incorporating a larger amount and greater variety of seismic phases, the calculated temperature anomalies of S16B30 are comparable (±130 K at 660 km, ± 485K at 2600 km depth), albeit the temperatures at the top of the D " are higher, given the greater rms velocity heterogeneity in this region. Wysession et al. (1993; 1994) undertook mineral physics modeling of a simplified pyrolite composition (Mg-perovskite and magnesiowustite only) to better understand the likely causes of their velocity anomalies within the D" region. A necessary evil of the seismic technique they utilized in converting the apparent velocities, estimated for diffracted rays, into average velocities, is that they must assume a specific thickness for the D " layer (Wysession et al., 1992; p. 8755). They adopted a thickness of 190 km for the D " layer, but noted that the average velocities (8Vsm = -3.1% to +1.0 %; 5 K > 1 9 0 = -3.2% to +0.8 %) would decrease i f D" is thicker than their choice (subsequent studies (e.g. Kendall and Shearer, 1994) have indeed documented that D" is thicker than that adopted by Wysession et al. (1992) with the mean thickness being «290 km). Wysession et al. (1992) noted that the global average for D" velocity anomalies (« 1.5%) could be explained by lateral temperature anomalies on the order of « ± 200-300 K, with the anomalously slow region under Indonesia (-3.0%) requiring higher values of « + 500 K. Their maximum temperature estimate is plotted as a dark horizontal line in figure 8.83 and 8.84 at 190 km depth and it is clear from this figure that their maximum temperature estimate is comparable to that estimated herein. In spite of the adopting a relatively thin value for the D" thickness, the maximum velocity perturbations (« 2.5 - 3.0 %) estimated by Wysession and co-workers, have been verified in subsequent seismic studies, even for those regional studies which adopted a thicker D " layer Chapter 8, page 878 (e.g. Wysession et al., 1994; 1995a; Wysession, 1996; Masters et al., 1996; Kuo and Wu, 1997; Liu and Dziewonski, 1994; L i and Romanowicz, 1996). Therefore, the good agreement between the independent temperature inference of Wysession et al. (1992) and that calculated here is relatively robust and suggests that temperature perturbations may indeed provide the necessary driving force to explain most of observed D" velocity anomalies. This contradicts earlier claims that the D" velocity anomalies require large scale chemical heterogeneity due to infiltrated liquid iron into the solid mantle (e.g. Jeanloz, 1990; Jeanloz and Lay, 1993; Jeanloz and Romanowicz, 1997). 8.14 Conclusions The purpose of this research is to estimate the magnitude of lateral temperature variations in the mantle. Much of this chapter reviewed and refined estimates for the lateral temperature anomalies in the shallow upper mantle (<410 km) and transition zone (410-660 km). The heat flow, subsidence, flexure at subduction zones, and seismic signature of cooling oceanic lithosphere is consistent with the half-space cooling model where the basal mantle temperature is consistent with independent estimates, derived from theoretical models of decompression melting at mid-ocean ridges. A recent global thermal model, GDH1 (Stein and Stein, 1992) is found to be in strong disagreement with heat flow and bathymetry in old oceans areas which are unaffected by subsequent thermal disturbance from hotspots (e.g. Gulf of Mexico). Furthermore, this model is in conflict with predictions from decompression Chapter 8, page 879 melt models and global observations of trench flexure and related gravity profiles (Levitt and Sandwell, 1995). Major element geochemical trends at mid-ocean ridges, and their associated temperature inferences, are reviewed next. Inspite of considerable initial scatter in the estimated temperature perturbations in the shallow mantle (see figure 8.25), it is found that most studies give consistent results on the order of 87" « ± 50 - 85 K, when additional independent information (e.g. melt chemistry) is considered together with the purely geophysical studies (e.g. Kuo, 1993) (see figure 8.34). Progressing deeper into the mantle, the topography on the major seismic discontinuities in the transition zone is used to infer the lateral temperature variations. Recent global studies using SS precursors (Flanagan and Shearer, 1998) provide excellent spatial coverage and the mean deflections give &Tm « ± 85 K and 5T66Q « + 185 K at the 410 and 660 km seismic discontinuities. However, the depth estimates were calculated using a tomographic model which assumed no topography on the transition zone discontinuities (Masters et al., 1996). Because it is accepted that the magnitude of the velocity heterogeneity adjacent to the mantle discontinuities will trade off with inferred topography, the depth estimates of Flanagan and Shearer (1998) are likely to be biased estimates. This effect is illustrated when the mean deflections calculated from the Vasco et al. (1995) joint 5*- and P-wave tomographic model are utilized. When these models were constructed, velocity heterogeneity and 410 and 660 km boundary topography were simultaneously solved for, the latter being constrained by the Shearer (1993) SS precursor data set. The associated temperature anomalies of the mean deflections are 87 , 4 1 0 « ± 58 K and Chapter 8, page 880 8r6 6 0 « ± 82 K , values which are reduced relative to those of Flanagan and Shearer (1998; see figure 8.46). In contrast, a much wider range of temperature variations is inferred from higher resolution, regional seismic studies near active subduction zones (see figure 8.67 and 8.71). In spite of the significantly greater range than that found from SS precursor studies, the estimated "slab" temperature estimates are consistent with that predicted for the intersection of cold subducting lithosphere with the a-, (3- and y-olivine phase boundaries. Significantly, the positive elevation at 410 km depth at the Izu-Bonin subduction zone is strong evidence this seismic discontinuity cannot be a chemical boundary, since in this case, the seismic discontinuity would be depressed by 100-300 km depth. Furthermore, the downward deflection at the 660 km seismic discontinuity at all of the subduction zones studied thus far is consistent with the magnitude of topography predicted for the intersection of a cold subducting plate with the y-olivine to Mg-perovskite + magnesiowustite phase boundary. In terms of hot mantle upwelling, the recent seismic study beneath the Iceland plume indicates the transition zone is thinner relative to the global width. While this type of study cannot determine i f this reflects a deepening of the 410 km, a shallowing of the 660 km, or both, I find that the thinner width (23 ± 9 km thinner than normal) is consistent with the predicted temperature structure of a plume conduit originating at the core-mantle boundary. In the lower mantle, I use the pyrolite mineral physics model to "correct" the lower mantle temperature estimates of Yuen et al. (1993; 1994) and Cadek et al. (1994) by dividing the isotherm (d\np/d\nVs)Pg0 scaling factor of Chopelas (1992) with the pyrolite (dlnp/dlnVs)p . This significantly reduces the magnitude of their temperature anomalies Chapter 8, page 881 from « ± 600 K and «± 2500 °K at 660 and 2600 km depth respectively to «± 100 K and «+ 480 K . The extreme magnitude of their hot temperature anomalies lead these workers to reject a purely thermal origin for the slow seismic anomalies, and instead, to invoke combined chemical and thermal anomalies in the lower mantle. In contrast, the extremely cold temperature anomalies were accepted as valid, and explained within the context of avalanche-mode partial layering where the convective state of the Earth's mantle episodically undergoes catastrophic overturn, with the result that large volumes of oceanic lithosphere are rapidly deposited on the core-mantle boundary. However, the magnitude of the corrected temperature anomalies requires no special explanations - neither lower mantle chemical anomalies, nor unusual styles of mantle convection. Indeed, the corrected temperature anomalies, or the approximate temperature anomalies estimated via the rms velocity amplitudes, indicate a smooth transition across the whole mantle, with no explicit change in thermal structure. This is important because i f there existed an chemical boundary somewhere within the lower mantle, as proposed by Kawakatsu and Niu (1994, 1997) or Wen and Anderson (1995), it would be accompanied by a strong thermal boundary layer. The tomographic models evaluated here show no abrupt, localized, increase in rms velocity variation, and consequently, no indications of a thermal boundary layer anywhere within the body of the mantle. This is consistent with a simple model of whole mantle convection driven by temperature perturbations, and refutes claims that the relatively low rms variation in velocity in the lower mantle, relative to the upper mantle, is evidence of a different convective style in the lower and upper mantles (e.g. Tanimoto, 1990b). Furthermore, the smooth increase in the temperature anomalies with increasing depth in the lower mantle, which "flares" out to reach a maximum at the top of the D " layer is Chapter 8, page 882 consistent with convection being driven by basal heating, but not by internal heating, since for this case, there would exist no basal thermal boundary layer at the core-mantle boundary (e.g. Jeanloz and Morris, 1986). I conclude that away from chemical and thermal boundary layers that characterize the surface and base of the Earth's mantle: 1) the lateral velocity anomalies as resolved in tomographic studies are consistent with a thermal origin and hence, do not require any systematic chemical component. The magnitude of the inferred temperature anomalies increases smoothly with increasing depth across the mantle from «± 50-85 K below mid-ocean spreading ridges to «± 85 K at the 660 km seismic discontinuity, and finally to «± 485 K at 2600 km, at the top of the D" layer. The smooth increase and the symmetry of the hot to cold temperature anomalies are consistent with a simple picture of whole mantle convection driven by basal heating, and not with models that incorporate either significant amounts of internal radioactive heating, or with models possessing a strongly episodic, avalanche-style mode of convection. 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Chapter 8, page 905 ^ 1 0 0 i 8 0 5 50 2 40 20 1 1 y ' 1 ' 1 | 1 1 1 1 1 1 1 — PS 7 7^ 5 5 ^ - — ^ _ _ _ G D H 1 — -HS^===:====z -— t i l l _ Gulf of Mexico Nagihara et ai, 199 Enn\etaLk97U . 1 1 1 -t ro £ ro x: 0 50 100 Age (Myr) 150 purported onset time of secondary, small-scale convection (Parsons & McKenzie, 1978) 100 Age (Myr) Figure 8.1 Top; Predicted heat flow as a function of age for the cooling half-space model (HS), the original constant thickness plate model of Parsons and Sclater (1977; PS77), and the recent version of it GDH1 (Stein and Stein, 1992). Bottom; predicted subsidence as a function of age for the three thermal models for oceanic lithosphere. Also plotted is the observed bathymetry for the Argetine basin and the Gulf of Mexico. Chapter 8, page 906 4 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 Temperature (K) Figure 8.2 A comparison of conductive oceanic geotherms for the cooling halfspace model (HS), the original constant plate model of Parsons and Sclater (1977; PS77), and the recent constant plate model of Stein and Stein (1992; GDH1). Also plotted is the Pyrolite mineral physics adiabatic geotherm and a representative geotherm for an Archean stable continent. Chapter 8, page 907 Mid-Ocean Ridge —> partial melt zone pure passive flow model path lines of upwelling mantle Figure 8.3 Partial melt zone beneath a mi-ocean ridge predicted from passive upwelling of mantle in responce to the negative pressure head associated with rifting. Chapter 8, page 908 purported onset time of secondary, small-scale A g e ( M y r ) Figure 8.4 Subsidence as a function of age for North Atlantic margin of the North American Plate. Using the parameters of Marty and Cazenave (1989), who noted the bathymetry fit the half-space model to ages of 160-170 Ma. The observed bathymetry is displaced above the predicted HS model due the shallow ridge crest depth - when this reduced (see orange curve), the bathymetry as a function of age now fits the HS model very well. Chapter 8, page 909 4.0 4.5 5.0 J i 5 - 5 £ 6 . 0 Q 6.5 7.0 J l I l [ l I l | III I | l l I I | l I II l | l l l l | l l l M | l l IL 7.5 GDH1 PS77 H 11 i i 11 L i Gulf of Mexico 150 Ma ocean crust Eppetai, 1970 >t aL 1996 . I I I I l l l l l l l l l l l l 100 95 90 85 80 75 70 65 60 55 50 45 40 35 30 Heat Flux (mW/m2) Figure 8.5 Depth versus heat flux predictions for the cooling half-space model, the constant thickness plate model of Parsons and Sclater (1977; PS77) and Stein and Stein (1992; GDH1). Also shown is the Gulf of Mexico (after Nagihara et al. 1996). Chapter 8, page 910 0 50 100 150 200 A g e ( M y r ) Figure 8.6 Top; Seismic structure used to forward model average phase velocities in the Pacific plate as a function of age. Bottom; Age versus average Love wave phase velocities for the Pacific plate. The smooth curves represent predicted phase velocities while the triangles represent observations (after Zhang and Tanimoto, 1991). Chapter 8, page 911 0 20 40 60 80 100 120 140 160 i i i i | i i i i | i i i i | i i i i | i i i i | i i i i | i i i i | i i i i | i i i i | i i i i | i cooling halfspace model (T= 1020 C) Pacific Plate! —North Atlantic Plate cooling halfspace model (T=U45C) Davies, 1980 1 • I CM 0 20 40 60 80 100 120 140 160 P l a t e A g e , t ( m . y . ) Figure 8.7 Predicted plate thickness from Love wave phase velocity modeling of Tanimoto and Zhang (1990). Also shown is the predicted plate thickness for the cooling half-space model using equation 4-124 of Turcotte and Schubert (1982; p. 164) for the 1020 C and I 145 C isotherms. Chapter 8, page 912 surface reflected SS phase Figure 8.8. Schematic diagram illustrating the SS and S raypaths through the Earth's mantle. Chapter 8, page 913 Figure 8.9 Observed S-wave travel time residual versus SS-S residual. The lack of a correlation implies that the observed signal is not due to lower mantle shear structure "seen" by the S-leg (after Woodward & Masters, 1991). Figure 8.10 Observed SS travel time residual versus SS-S residual. The good correlation supports the interpretation that the signal is reflecting seismic structure at the SS bounce point (after Woodward & Masters, 1991). Chapter 8, page 915 S S B o u n c e P o i n t s 0 i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — r 0 50 100 150 200 A g e ( M y r ) Figure 8.11 Schematic diagram illustrating the effect of cooling and thickening oceanic lithosphere with respect to the reflected bounce point of SS raypaths. CO -4 CO O Co J I I L 1 Chapter 8, page 916 ' I 1 1 1 ' I 1 1 •0.51 ± 0.07 sec/(Myr)m J p o / « / = o/~ 7(90 observation, I I l l _ _ l I I I I 6 1 •o o o 0 50 100 150 Age of Seafloor (Myr) 1 0 £- 3 1 1 1 1 1 1 - A _ • l | l l l l | l I " ^ • *• A 1/2-A -0.18±0.01 sec/(Myr]_ A»^_A^ u -A A — I 1 l I 1 l i l l l l l l l l t cn "O 5 "O o I 0 50 100 150 Age of Seafloor (Myr) Figure 8.12 Plot of SS-S (top) and PP-P (bottom) travel time residuals as a function of seafloor age at the SS or PP bounce point (after Woodward and Masters, 1991a). Chapter 8, page 917 Mid-Ocean Ridge mantle potential temperature 1330-1350 C (=1603-1623 K) 0 500 1000 1500 2000 250Q Temperature (K) m e l t i n g by ad iaba t i c upwe l l i ng Figure 8.13 Relationship between mantle potential temperature (left) and the three ways in which melting may be triggered within the mantle (right). Chapter 8, page 918 Lava mantle potential temperature 1200 1400 1600 1800 2000 2200 2400 Temperature (K) Figure 8.14 Melt paths in the partial melt zone for different mantle potential temperatures. The decrease in temperature with melting reflects the latent heat of fusion. Thus, lava eruption temperatures can not be directly extrapolated to depth to infer the mantle temperature. Chapter 8, page 919 40 p 35 \ 30 \ 25 \ 20 I 15 i 10 5 Fratwe zone MORB (2.8 ± /.5 km) normal MORB _| (7.0 ±1.0 km) = i—i 1 0 0 2 4 6 8 10 Ocean Crustal thickness (km) Figure 8.15 Global compilation of the thickness distribution of normal and fracture zone ocean crust thickness (after Brown and White, 1994) Chapter 8, page 920 0 10 2 0 3 0 4 0 Figure 8.16 Predicted melt thickness (ocean crust thickness) as a function of mantle potential temperature (after McKenzie and Bickle, 1988). Chapter 8, page 921 10 8 6 4 2 0 T T T T T T T T T T global mean = 7 ± 1 km ^ ^ ^ ^ ^ ^ ^ ^ ^ mm Tn = 1280 cn Crustal Thickness J 1 1 cn § CO 0 20 40 60 80 100 120 140 Full Spreading rate (mm/year) 160 20 40 60 80 100 120 140 Full Spreading Rate (mm/year) Figure 8.17 (top) Comparison of observed ocean crustal thickness (dots) as a function of full spreading rate at the mid-ocean ridge versus predicte oceanic crustal thickness as a function of mantle potential temperature (after Brown and White, 1994). Figure 8.18 (bottom) Comparison of observed ocean crustal thickness (dots) as a function of REE inversions against predicted ocean crustal thickness as a function of both mantle potential temperature and full spreading rate (after Brown and White, 1994). Chapter 8, page 922 n o 4 . 0 ^ 3 . 5 O W > 3 . 0 q 2 . 5 o o O 2 0 £ 1 . 5 7 . 0 1 -i 1 1 1 1 Global normal MORB Langmuir, Klein, & Plank, 1992-4 • increasing mantle potential j temperture 8 . 0 9 . 0 1 0 . 0 1 1 . 0 FeO(8.0 MgO) wt % t CD OJ CM CH Q. °6 1 2 . 0 Figure 8.19 Global correlation of NajO (wt%) versus FeO (wt%). The correlation may be interpreted to reflect the effects of increasing mantle potential temperature after Langmuir et al., 1992. Chapter 8, page 923 t*vs 4.0 ^ 3 . 5 O OD3.0 o o 2.5 2.0 ° 1 5 £ 1.0 - 1 1 global normal MORB (regional averages) T 0 i i i i t CD n> CM O) 0. 1000 2000 3000 4000 5000 6000 Axial Ridge Depth (meters) Figure 8.20 Global correlation of Na 20 (wt%) versus axial ridge depth (after Langmuir et al., 1992) Chapter 8, page 924 N a p (8.0 MgO) (wt %) Figure 8.21 Global correlation of crustal thickness versus Nap (wt%) from Langmuir et al., 1992. Note the large difference between the predicted effects of perturbations in mantle potential temperature and mantle chemistry on crustal thickness. Chapter 8, page 925 o N 5 .0 i — i — | — i — | — i — | — i — | — i — | — i — | — i — j — r OX) S 3 . 0 q o o ^ 2 . 0 O 4 i . o normal MORB * Australia-Antarctic Discordance Klein, Langmuir, & Staudigel, M91 i i • i i i i i i i i i i i CO CD 0 20 40 60 80 100 120 140 160 Full Spreading rate (mm/year) Figure 8.22 Correlation of Nap (wt%) as a function of full spreading rate (after Brown and White, 1994). Note the large variation for the Australian-Antarctic discordance (Klein et al., 1991). Chapter 8, page 926 Equatorial Mid-Atlantic Ridge using Na^O(8.0 MgO) wt% relationship of Klein & Langmuir (1987) T 500 1000 Cumulative distance along equatorial Mid-Atlantic Ridge (km) Figure 8.23 Inferred mantle potential temperature along the equatorial Mid-Atlantic ridge (after Schilling et al., 1995). Note that the geochemistry is consistant with perturbations of 50 C around a mean mantle potential tempertature of 1330 C. Chapter 8, page 927 Figure 8.24. The effects of compositional buoyancy on predicted oceanic crustal thickness as a function of spreading rate (after West et al., 1994). Predictions which do not include compositional buoyancy are blue lines, while models wich include this are red lines. Note that the largest effect ocurrs only for slow spreading rates. Chapter 8, page 928 0 Mid-Ocean Ridge 120 M a oceanic mantle potential temperature conductive geotherm 1330-1350 C (=1603-1623 K ) ^ Hot-Spot . ^ 1 4 5 0 - 1 5 5 0 C j i f i ' H i \ t Brown & White, tai thickness, REE inver1, ±40K E Klein & Langmuir, 1987; 100 p- Langmuir et al, 1992 Q 150 200 250 300 350 h 400 i—r [global trends of FeO & Na20 ± 250 K Schilling etal, 1995 C Na20 and K&L87 correlation £ equatorial Mid-Atlantic Ridge ±50K (- Zhang, Tanimoto, & Stolper, 1994 Vs anomalies, bathymetry, & MORB chemistry Mid-Atlantic Ridge 200 ± 100 K (60-200 km) Sheehan & Solomon, 1991 SS-S anomalies, Geoid, hathymeti'}\ AlORB chemistry> north Mid-Atlantic Ridge ± 50 K (60-300 km) i ' I ' ' ' 1 i ' ' 0 400 800 1200 1600 2000 2400 Temperature (K) Figure 8.25 Compilaiton of lateral temperature anomalies inferred through melt chemistry and/or ocean crustal thickness plotted around the pyrolite mineral physics adiabat. Note that the estimates of Klein and Langmuir (1987) and Langmuir et al. (1992), if true would imply that temperature perturbations beneath mid-ocean ridges exceed the observed temperature of hotspots. Chapter 8, page 929 10 20 30 40 50 60 70 80 Latitude (°N) North Atlantic Figure 8.26 Inferred temperature anomalies along the North-Atlantic spreading ridge from joint inversion of shear wave travel time residuals and geoid and depth anomalies (after Sheehan and Solomon, 1991). If the temperature perturbations are restricted to shallow depths, the magnitude of the inferred anomalies increases. Chapter 8, page 930 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 Temperature (K) Figure 8.27. Expected maximum temperature contrast between a mid-ocean ridge and old (>100 Ma) oceanic and Archean continental lithosphere at roughly 40-50 km depth. For oceanic lithosphere, the temperature estimate is insensitive to the adopted thermal model (e.g. G D H 1 or coolling halfspace). Chapter 8, page 931 latitude east along the SE Indian Ridge Figure 8.28 Bathymetry along the south-east Indian ridge (after Kuo, 1993). AAD is the Australian-Antarctic Discordance. Chapter 8, page 932 120 Ma oceanic conductive geotherm Mid-Ocean Ridge mantle potential temperature 1330-1350 C (=1603-1623 K) Hot-Spot mantle potential temperature 1450-1550 C (=1723-1823 K) ¥•_.%-_!_ | V I 1 I 1 -I 400 0 250 500 750 1000 1250 1500 1750 2000 2250 2500 T e m p e r a t u r e ( K ) Figure 8.29 Compilation of estimated lateral temperature anomalies beneath the Australian-Antarctic Discordance. Note the large difference between the magnitude of the temperature anomalies when the depth extent of the anomalies is increased from 100 km to 300 km. Chapter 8, page 933 5 s 4.0 KL&saad.grf 3 . 5 O 3 .0 ^ 2 5 o oo o 2 0 z 1 5 1.0 1 i 1 global normal MORB (regional averages) west of AAD AAD # ^ • -• • — east of AAD • $ • - • • • # • — w ! I 1 ! 1 1 0 1000 2000 3000 4000 5000 A x i a l R i d g e D e p t h (meters) 6000 Figure 8.30 Plot of Na-O (wt%) for ocean crust basalts dredged along the SE Indian Ridge (data from Klienetal., 1991. Chapter 8, page 934 120 Ma oceanic conductive geotherm Mid-Ocean Ridge mantle potential temperature 1330-1350 C (=1603-1623 K) Hot-Spot mantle potential temperature 1450-1550 C(=1723-1823 K) 400 -I <u 0 250 500 750 1000 1250 1500 1750 2000 2250 2500 Temperature (K) Figure 8.31 Comparison of calculated mantle potential temperatures from the Nap (wt%) data of Klien et al (1992) using the Niu and Batiza (1991) parameterization. Chapter 8, page 935 80 90 100 110 120 130 140 150 160 170 Longitude East (°) along SE Indian Ridge Figure 8.32 Calculated mantle potential temperatures along the SE Indian Ridge superimposed over the inferred temperature anomalies of Kuo (1993). Chapter 8, page 936 Figure 8.33 Plot of along axis mantle potential temperature for the East Pacif ic Rise (after N iu and Batiza, 1991). Chapter 8, page 937 0 5 0 100 1 5 0 120 M a oceanic conductive geotherm Mid-Ocean Ridge mantle potential temperature 1330-1350 C (=1603-1623 K ) Hot-Spot 1450-1550 C 4 ^ 2 0 0 £ -O h m Q 2 5 0 3 0 0 3 5 0 4 0 0 Niu & Batiza (19911 MORB \hem istry_^ East Pacific Rise -±5QK Westethl., 199*_ Fr\e Air gravity, & athyn^etry Z AA 50 r t Brown & White, \crustal thickness, REE invers ±40K Shen & Forsyth, 1995 re-evaluation of FeO & Na20 ±60K Schilling et ai, 1995 MORB chem is ty equatorial Mid-Atlantic Ridge ±50K Sheehan & Solomon, 1991 SS-S anomalies. Geoid. bathymetry, MORB chemistry northern Mid-Atlantic Ridge ±50 K (10-300 km) Kuo (1993) and Kuo et al (1995) SS-S anomalies, geoid. bathymetry Australian-Antarctic Discordance ± 50 K (10-300 Km) I • I • I • I • I 0 250 500 750 1000 1250 1500 1750 2000 2250 2500 Temperature (K) Figure 8.34 Summary of prefered lateral temperature anomalies beneath the mid-ocean ridge system as estimated by geochemistry and geophysical techniques. These are plotted around the Pyrolite mineral physics geotherm. Chapter 8, page 938 MORB mantle potential temperature Hot-Spot 300 600 900 1200 1500 1800 2100 2400 2700 Temperature (K) Figure 8.35 The effect of varying temperature within the transition zone (410 to 660 km depth). Because of the opposing Clapeyron slopes of the 410 and 660 km olivine phase boundaries, the transition zone will thin or thicken in responce to hotter or colder temperatures. Chapter 8, page 939 Figure 8.36 Schematic raypaths for ScS shear wave (after Revenaugh and Jordan (1991a). Chapter 8, page 940 CZ3 c/3 o in m o o 0 GO O n /-^ -. O n (/> O O C/3 c/o O n Os -JO + Figure 8.37 Representative S H polarized seismogram (time is minutes after earthquake rupture. Right traces are portions o f the seismogram between the ScSn and sScSn wave groups (after Revenaugh and Jordan, 1989). Chapter 8, page 941 Mid-Ocean Ridge 300 600 900 1200 1500 1800 2100 2400 2700 Temperature (K) Figure 8.38 Calculated lateral temperature anomalies in the transition zone based on converting the mean transition zone travel time anomaly. The lateral temperature anomalies were then added to the Pyrolite mineral physics geotherm to obtain absolute temperatures. Chapter 8, page 942 Mid-Ocean Ridge Hot-Spot 300 600 900 1200 1500 1800 2100 2400 2700 Temperature (K) Figured 8.39 Calculated transition zone temperatures derived from the apparent depth of the 410, 520, and 660 km seismic discontinuities tabulated by Revenaugh and Sipkin (1994). Chapter 8, page 943 Mid-Ocean Ridge Hot-Spot 300 600 900 1200 1500 1800 2100 2400 2700 Temperature (K) Figure 8.40 Calculated lateral temperature anomalies at the 410 and 660 km seismic discontinuities by converting the apparent depths of Revenaugh and Jordan (1991) into temperature. Chapter 8, page 944 underside reflections S 4 1 0 S phase Figure 8.41 Schematic raypaths for SS and 410 and 660 km SS precursor seismic phases. Chapter 8, page 945 Figure 8.42 Global plots of the SS bounce points (after Flanagan & Shearer, 1998) Chapter 8, page 946 CO •*! CO Figure 8.43 Smooth maps of topography of the 410, 520, 660 km and the transition zone thickness obtained by applying spherical splines to the cap average data (from Flanagan and Shearer, 1998). Contour intervals are 6 km. Chapter 8, page 947 60 HTTT o u u m 50 | 40 | 30 | 20 | 10 I mean upwards deflection 4" 409.4 km* p m 4 1 8 k m m e a n d e p t h TT TTH .mean downwards deflection 423.8 km • • i s i . 11 f r i t i 0 390 400 410 420 430 440 450 " 4 1 0 " k m d e p t h • 11 ip o 460 60 O GO 20 i 50 §-| mean upwards 40 §- deflection j | 1 64910 km 30 =- . TT 660 km mean depth 1111 n i mean downwards deflection 667.8 km 10 | - . > # I v - m i n o 630 u n a t CT> O CD co 640 650 660 670 680 " 6 6 0 " k m d e p t h 690 700 Figure 8.44 Individual cap average depths of the 410 and 660 km seismic discontinuities as a function of the standard error (data from Flanagan, personal communication). Also shown are the mean depths and the mean upwards and downwards deflections. Chapter 8, page 948 Mid-Ocean Ridge Hot-Spot 300 600 900 1200 1500 1800 2100 2400 2700 Temperature (K) Figure 8.45 Calculated temperature anomalies corresponding to the individual cap average depths of the 410, 520, and 660 km seismic discontinuities. 900 MOR mantle potential temperature 1330-1350 C (= 1603-1625 K) T Chapter 8, page 949 Hot-Spot mantle potential temperature 1450-1550 C (=1723-1823 K) J I I I I 300 600 900 1200 1500 1800 2100 2400 2700 Temperature (K) Figure 8.46 Calculated temperature anomalies corresponding to the mean upwards and downwards deflections from the Flanagan and Shearer (1998) data set. Also shown are temperatures calculated from the mean deflections calculated by Vasco et al. (1995). Chapter 8, page 950 the approximate trend if both the 410- and 660-km discontinuities are affected by the samet temperature anomalies. 630 640 650 660 670 680 690 660 km discontinuity depth (km) Figure 8.47 Correlation of the 410 versus 660 km seismic discontinuity depths. The lack of a trend implies that the vertical extent of the temperature anomalies does not extend across the full width of the transition zone. MORB mantle potential temperature 1330-1350 C(= 1603-1625 K) Chapter 8, page 951 400 600 800 1000 1200 1400 1600 1800 2000 2201) 2400 2600 Temperature (K) Figured 8.48 A comparison between the calculated temperature anomalies inferred from the mean deflections of the 410 and 660 km seismic discontinuities (Flanagan and Shearer, 1998; Vasco et al. (1995)) versus the calculated temperatures from a 2D axisymmetric convection simulation (Solheim and Peltier, 1994b). Chapter 8, page 952 1 2 0 E 1 7 0 E Figure 8.49 Location of the Kuril-Kamchatka subduction zone (after Fischer et al. 1988). Figure 8.50 Plot showing the flow lines of the subducted slab over the fixed interval of 580-730 km depth. The slab thickening is parameterized the the width after thickening divided by the initial width (after Fischer et al., 1988). Figure 8.51 Predicted isotherms for the Kuril slab calculated by a finite difference thermal model which incorporates variable divergent flow and cross strike thickening (after Fischer et al., 1988) Contour interval is 200 C Chapter 8, page 955 Tonga thermal structure D i s t a n c e ( k m ) Figure 8.52 Predicted temperature structure for the Tonga slab (after Marone and Liu, 1998) calculated by a finite difference model. The contour interval is 200 C. Chapter 8, page 956 Western US Array 8_53.grf Figure 8.53 Schematic raypaths for S-to-P converted phases and pP surface underside reflections (after Shearer, 1992). Chapter 8, page 957 Tonga thermal structure D i s t a n c e ( k m ) Figure 8.54 Schematic raypaths for the S-to-P converted phases at the deflected 660 km seismic discontinuity. Raypaths superimposed on the predicted temperature structure for the Tonga slab. Chaper 8, page 958 100 200 300 400 & g 500 600 1 1 1 lllllllllllllllllllll 1 1 Illllllllllllllllllllll - A » -1 z ~— * • • - I I Illlllllllll = * • r , i , i • • • 1 1 1 1 1 1 , 1 , 1 t CD Oi to 0 10 20 30 40 50 60 Dis t ance a long X - s e c t i o n A B (degrees) 70 620 E — r g 6 3 0 640 & 6 5 0 +-* a CD Q 660 CD +-» S 670 r j 680 690 L • I • ~1 11 T T T T "1.700 km • 1 i L X X 1 J. 1 = t a cn «a csi — <o — 0) ^ x: to 10 20 30 40 50 60 Dis tance a l o n g X - s e c t i o n (degrees) 70 Figure 8.55 Top; Slab earthquakes (red triangles) outlining the Japan slab above the estimated depth of the 660 km discontinuity (blue circles. Bottom; enlargement of corrected depths for upper mantle heterogeneity (after Shearer and Masters, 1992). Chapter 8, page 959 half-space oceanic geotherm MORB mantle potential temperature 1330-1350 C(= 1603-1625 K) 900 300 600 900 1200 1500 1800 2100 2400 2700 Temperature (K) Figure 8.56 Inferred temperatures at the 410 and 660 km seismic discontinuities based on converting the seismic depths of the 410 and 660 discontinuities to equivalent temperatures on the olivine phase boundaries. Chapter 8, page 960 conductive old oceanic MORB mantle potential temperature 300 600 900 1200 1500 1800 2100 2400 2700 T e m p e r a t u r e ( K ) Figure 8.57 Alternative interpretation of the temperatures at the 410 km discontinuity assuming that the depths of Vidale and Benz (1992) correspond to the depth of the kinetically hindered alpha to beta olivine phase boundary (roughly 1000 K isotherm). Distance (km) Figure 8.58 Alternative interpretations of the 410 km seismic discontinuity assuming that it is deflected due to kinetic hindering of the conversion (top) or its equilibrium position. cooling half-space M O R B m a n t l e Potential temperature Chapter 8, page 962 1330-1350 C(= 1603-1625 K) 900 300 600 900 1200 1500 1800 2100 2400 2700 Temperature (K) Figure 8.59. Estimated temperatures reflecting S-to-P conversions from a depressed 660 km seismic discontinuity adjacent to the Tonga subduction zone (Richards and Wicks, 1990). 800 fr 900 Chapter 8, page 963 T 250 500 750 1000 1250 1500 1750 2000 2250 2500 Temperature (K) Figure 8.60 Residuum phase diagram (modified after Ita & Stixrude, 1992) which shows the sub-660 km phase boundaries which may explain the second set of S-toP conversions observed by Richards and Wicks (1990). Chapter 8, page 964 Distance (km) Figure 8.61 Schematic plot o f ray paths of S-to-P converted phases directed towards Japan and Cali fornia (after N i u and Kawakatsu, 1995). Chapter 8, page 965 I | l/l I I | I I I I | I I I I | I I I I | I I I ' * trend of deep earthquakes within Tonga slab 740 i i i • i i i ' ' ' i ' ' i ' i Japan recordings USA (California) i l l l l l l 0 50 100 150 200 D i s t a n c e f r o m s l a b c o r e ( k m ) Figure 8.62 Depths of the 660 seismic discontinuity as inferred by the depths of S-to-P converted depths. Red circles represent data to Japan array, blue circles represent US array data. After Niu and Kawakatsu (1995). Chapter 8, page 966 conductive old oceanic M O R B m a n t l e potential temperature 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 T e m p e r a t u r e ( K ) Figure 8.63 Estimated temperature reflecting S-to-P conversion depths from the 660 km seismic discontinuity for the Niu and Kawakatsu (1995) depths. Chapter 8, page 967 130 E 140 E 150 E Figure 8.64 Location of Izu-Bonin Subduction earthquakes recorded at the Warramunga array used by Wicks and Richards (1993). Chapter 8, page 968 100 200 300 400 ^ 5 0 0 Q 600 700 E-800 T ISC earthquake locations Engdahl hypcenters 660 km d Vidale & Bern (199fn S660P conversion depths (Wicks & Richards, 199M (hypoc centers of^ Engdahl and co-workers) ^ 0 .0 2 .0 4 . 0 6 .0 Distance (degrees) along cross section A-A ' Izu-Bonin Subduction zone Figure 8.65 Cross section A-A' across the Izu-Bonin subduction zone showing the ISC earthquakes which define the subducting slab and the S-to-P conversion depths from the 660 km discontinuity (after Wicks and Richards, 1993). Chapter 8, page 969 0.0 2.0 4.0 6.0 Distance (degrees) cross section B-B' Figure 8.66 Cross section B-B' across the Izu-Bonin subduction zone showing the S-to-P conversion depths for the 660 km discontinuity (after Wicks and Richards, 1993). cooling half-space M O R B m a n t l e Potential temperature 1330-1350 C ( = 1603-1625 K) Chapter 8, page 970 900 300 600 900 1200 1500 1800 2100 2400 2700 T e m p e r a t u r e ( K ) Figure 8.67. Estimated temperatures reflecting S-to-P conversions from a depressed 660 km seismic discontinuity adjacent to the Izu-Bonin subduction zone (Richards and Wicks, 1993). Chapter 8, page 971 135 E 140 E 145 E Figure 8.68 Smoothed contour maps of the 410 (top) and 660 (bottom) km discontinuity at the Izu-Bonin subduction zone (after Collier and Helffrich, 1997) Chapter 8, page 972 WicksD.grf -2.0 0.0 2.0 4.0 6.0 8.0 10.0 Distance (degrees) cross section B-B ' Figure 8.69 Depth of the 410 and 660 km discontinuities from the maps of Collier and Helffrich (1997) along the lines of Wicks and Richards (1993) cross section B-B'. Chapter 8, page 973 100 c 200 Er 300 400 L & 5 0 0 Q 600 E-700 800 J ISC earthquake locations^* 410 brrd Collier & Helffrich, 1997\ 660 ford Vidale & Bern (1992) SfifigP conversion depths (Wicks & Richards, 199\ (hypocenter^ of Engdahl and co^-workers^ ~ u i -2.0 0.0 2.0 4.0 6.0 8.0 10.0 Distance (degrees) along cross section A - A ' Izu-Bonin Subduction zone Chapter 8.70 Depths of the 410 and 660 km discontinuities from the maps of Collier and Helffrich (1997) plotted along the cross section A-A' of Wicks and Richards (1993). Chapter 8, page JJtf-conductive old oceanic MORB mantle potential temperature 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 Temperature (K) Figure 8.71 Estimated temperatures for the 410 and 660 km discontinuity depths of Collier and Helffrich (1997). Note that the map of 410 km topography indicates that here the boundary is in equilibrium. Chapter 8, page 975 MORB mantle potential temperature 250 500 750 1000 1250 1500 1750 2000 2250 2500 T e m p e r a t u r e ( K ) Figure 8.72 Plume geotherm calculated with the equations of Griffiths adn Campbell (1991) with a CMB temperature anomaly of 1500 K. Also shown as a box is the calculated width of the transition zone beneath the Iceland plume from differential travel times for S-to-P conversions from both the 410 and 660 km discontinuities. 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 Chapter 8, page 976 MORB mantle potential temperature 1330-1350 C(= 1603-1625 K) J ' ' I ' ' I ' ' I ' ' 500 1000 1500 2000 2500 3000 3500 4000 T e m p e r a t u r e ( K ) Figure 8.73 Possible interpretation of the "920" km seismic discontinuity as the conversion of garnet dominated ocean crust on the top of subducting oceanic lithosphere. Chapter 8, page 977 0.8 1.0 1.2 1.4 1.6 1.8 (dlnp ldlnVs){ Figure 8.74 Comparison of the isothermal dimensionless density to velocity scaling factor for MgO. A l 2 0 3 (Chopelas. 1992) and Y A G garnet (Reichmann. 1993). After Zhang and Chopelas" (1994). 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 Chapter 8, page 978 T 1 1 u & Dziewonski (1991 Woodward et al. (1993) CO a -4000-3000-2000-1000 0 1000 2000 3000 4000 extremal thermal perturbations (K) Figure 8.75 Calculated extremal temperature perturbations across the lower mantle estimated from seismic tomographic models of shear wave perturbations. After Cadek et al., 1994. Chapter 8, page 979 1000 2000 3000 4000 5000 6000 T e m p e r a t u r e ( K ) Figure 8.76 Absolute temperature perturbations across the lower mantle where the relative estimates of Cadek et al. (1994) have been added to the Pyrolite mineral physics adiabatic geotherm. Also shown at 660 km depth are the temperatures corresponding to the mean up and downwards deflections of the 660 discontinuity (Flanagan and Shearer, 1998; Vasco et al., 1995). 0 100 200 300 400 500 600 700 s h e a r a t t e n u a t i o n , Qs Figure 8.77. Radial profdes of the shear wave quality factor Qs taken from seismic studies. Note the high values in the lower mantle relative to the shallow most 100-200 km. The low values at shallow depths are interpreted to reflect the presence of partial melt. If correct, then the high values in the lower mantle suggest that the mantle temperatures are well below the solidus. Q & 1 6 0 0 1700 1800 1900 2000 2100 2200 2300 2400 2500 2600 2700 2800 1 1 T Chapter 8, page 981 ~~l 1 T Pacific lower mantle Superplume longitude = 205° F l 7 0 0 K • I K _d 500 K — 900 K H O O K 1300K 1500 K i 1 3 E 80 60 40 20 0 -20 -40 Latitude (degrees) -60 -80 Figure 8.78 Estimated plume temperatures throught the Pacific Superplume below the central Pacific (after Yuen et al. 1993). The large magnitude of the anomalies led Yuen et al. (1993) to reject a purely thermal origin for the seimic anomalies, and instead, appeal to both thermal and chemical anomalies. Chapter 8, page 982 Correlation Figure 8.79 Correlation of cold thermal anomalies in seismic tomographic SH8WM 13 (Woodward et al., 1993) with the surface distribution of subducting regions for the past 180 m.y (Richards and Engcrbretson (1992). Figure after Cadek et al. (1994). Chapter 8, page 983 T h e r m a l l y c o u p l e d -b u t l a y e r e d c o n v e c t i o n Figure 8.80 Schematic illustration of the convective flow in a chemically stratified mantle (adapted after Anderson, 1983). Schematic isotherms of convection are illustrated where subducting slabs trigger thermally linked cold convective downwelling in the the lower mantle. Chapter 8, page 984 0 30 60 90 120 150 180 210 240 270 300 330 360 Longitude (degrees) isotherms in 200 K intervals Figure 8.81 Cold thermal anomalies at the core-mantle boundary (CMB) for the SH8 WM13 (Woodward et al., 1993) tomographic model. The contour intervals of temperature are in intervals of 200 K as calculated by Yuen et al. (1994). Figure after Yuen et al. (1994). Chapter 8, page 935 0 30 60 90 120 150 180 210 240 270 300 330 360 Longitude (degrees) isotherms in 200 K intervals Figure 8.82 Cold thermal anomalies at the core-mantle boundary (CMB) for the SH8WM13 (Woodward et al., 1993) tomographic model. The heavy shaded area encloses the area of paleo-subduction zones in the last 180 m.y. based on the plate reconstructions of Richards and Engerbretson (1992) expanded to spherical harmonic order 8. Figure after Yuen et al. (1994). 0 100 200 300 400 500 600 700 800 900 1000 1100 /gS 1200 J2 1300 1400 'S 1500 g<1600 Q 1700 1800 1900 2000 2100 2200 2300 2400 2500 2600 2700 2800 r j T T j TTT Chapter 8, page 986 r • Sh8WM13 (Woodward et al. 199m S16B30 (Masters etal., 1996) J_I_L 1111111111111111111 r 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 rms amplitude of the relative velocity perturbations Figure 8.83. The rms amplitude of SH8WM13 and S16B30 shear wave tomographic models discussed in the text. Chapter 8, page 987 O H Q o 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 1 T T T Su & Dziewonski (1991) -J Woodward et al. (1993) -4000 -3000 -2000 -1000 0 1000 2000 3000 4000 Thermal perturbations (K) derived from seismic tomographic data Figure 8.84 Corrected relative extremal temperature perturbations across the lower mantle. Chapter 8, page 988 1000 2000 3000 4000 5000 6000 Temperature (K) Figure 8.85 Corrected absolute extremal temperature perturbations across the lower mantle. Also shown are the calculated temperature anomalies from the mean upwards and downwards deflections of the 410 and 660 km discontinuities of Vasco et al., 1995. Chapter 8, page 989 1000 2000 3000 4000 5000 6000 T e m p e r a t u r e ( K ) Figure 8.86 Calculated temperature perturbations across the whole mantle for the rms velocity anomalies from the S-wave tomographic model S16B30 (Masters et al., 1996). Chapter 9 Summary and Future Work Chapter 9, page 991 9.1 Abstract This thesis has largely concentrated on modeling and interpreting the density and velocity structure of the Earth's mantle. The thermoelastic data used to achieve this has been compiled from the published literature, or in limited circumstances, estimated using a variety of indirect techniques. Together, this data has been used to forward model the density, bulk sound, shear, and compression velocity structure of the Earth for two different compositional models. The simplest one, termed pyrolite, views the Earth's mantle as homogeneous to first order with the seismic discontinuities representing the effects of phase transitions within an uniform bulk composition. The second model, termed piclogite, interprets the mantle in terms of chemically and convectively isolated layers with all or some of the seismic discontinuities representing chemical and thermal boundaries. In this final chapter I summarize the results of the individual chapters and discuss preliminary results of future research where the conclusions of the pyrolite mineral physics model are used to leverage new insights into related fields. Chapter 9, page 992 9.2 Introduction and Summary of chapters "The chemical composition of the Earth's mantle has evaded five decades of probing by earth scientists. Questions remain as to whether the mantle is chemically layered and, i f it is chemically layered, as to the scale and nature of the layering. The debate between pyrolite and eclogite, although often appearing to be settled, still surfaces with a renewed vigor... The apparent disarray in defining the "bottom line" stands in contrast to the steady progress that has been made in many separate fields, placing us at the door of understanding mantle chemistry." Weidner, 1986, p. 251. In this thesis I have used mineral physics modeling to address the question of mantle chemistry and whether or not the mantle is chemically layered. Unlike the situation faced by Weidner (1986) and many subsequent workers, there exists today a large body of experimental thermoelastic data which allow the question of mantle chemistry to be probed with greater confidence. Many of the previous studies had to resort in large part to ingenious techniques to infer many unmeasured mineral properties, often described under the term "mineral systematics". While this study has also been forced to estimate some mineral properties, the scope of such "educated guessing" is at a minimum. In addition, by dividing the modeling study into two parts, the first focussing on density and bulk sound velocity, the second on shear and compression velocities, it is possible to concentrate first on testing compositional models utilizing measured properties. Then when the focus shifts to V$ and Vp profiles where a very limited amount of educated guessing is required, it is done within a framework where the temperature profile, bulk compositional, and the thermoelastic properties are held fixed at values used in the previous part of the modeling study. This minimizes the number of free parameters which may be adjustable to improve the fit and in addition, focuses only on the values for the few minerals with unmeasured temperature or pressure derivatives of the shear modulus. Chapter 9, page 993 Hence, in chapter 2, using updated, published experimental data, I evaluated two competing mineralogical models for the composition of the mantle, the uniform pyrolite and chemically-layered piclogite models (see figure 9.1), using calculated one dimensional profiles of density (p) and bulk sound velocity (V®) to measure the success of these two models in satisfying the seismologically inferred profiles. Although the results presented here, using newer thermoelastic data for pyroxenes, which supercedes that which was used in an earlier study (Calderwood, 1996a), the final results differ little. Unlike Ita and Stixrude (1992; 1993), I find that the mineralogy of a uniform bulk composition provides an excellent fit to the seismic properties of the whole mantle along a self-consistent adiabatic geotherm which lacks any thermal boundary layers internal to the mantle. Notably, the use of the latest thermoelastic properties for Ca- and Mg-perovskite (Wang et al., 1994; 1996; Funamori et al., 1996) allowed the pyrolite model to successfully satisfy the observations. In contrast, the mineralogy of a chemically layered bulk composition results in predicted profiles which cannot satisfy the observations, either in the shallow region of the transition zone, or in the lower mantle i f it is assumed that the 660 km seismic discontinuity represents a chemical boundary. It is often stated that a chemical boundary at 660 km may be invisible seismically (e.g. Jeanloz, 1991; Lay, 1994; Agee, 1998). For example Agee (1998, p. 199), in a recent review of transition zone mineralogy and seismic structure, states "The experiments of Ito and Takahashi (1989) showed that the abrupt discontinuity may be explained by an isochemical phase transition of y-spinel to (Mg,Fe)Si0 3- perovskite + magnesiowustite. However, because the same transformation can occur in peridotite, chondrite, komatitite, and Chapter 9, page 994 number of other hypothetical mantle compositions, a chemical boundary or abrupt change in rock type at 660 km may be difficult to distinguish from an isochemical 660." Such a claims that a chemical boundary at the 660 km discontinuity may be invisible are simply false and result from not considering the effects of the large temperature jump of the thermal boundary layer. For example, Jeanloz (1991) argued that a chemical boundary would be invisible based on comparing calculated jumps in density (Ap), Vs (AV$) and Vp (AVp) for an isochemical phase change against those calculated for a chemical change at the 660 km discontinuity associated with an increase in silica and/or iron content in the lower mantle. However, the calculated jumps in density and velocity were all calculated at room pressure and temperature conditions, rather than the high temperature and pressure conditions characteristic of the 660 km discontinuity. Furthermore, even had this been done, it is irrelevant and misleading to compare the density and velocity properties of two chemically distinct layers along the same temperature structure; the deeper chemical layer will lie along a significantly hotter geotherm than the immediately overlying layer (e.g. Jeanloz and Richter, 1979). Chapter two demonstrates that when the properties of piclogite lower mantle are calculated along a hotter geotherm, inferred from the 3D spherical convection simulations of Glatzmaier and Schubert (1993; see figure 9.2), a chemically distinct lower mantle results in large jumps at the 660 km discontinuity and distinctive density and bulk sound velocity profiles across the lower mantle (see figure 9.3). Indeed in contrast to every seismic model published to date, which shows positive jumps across the 660 km discontinuity, the predicted piclogite properties show a negative jump in V® across the 660. In short, a chemical boundary within the mantle is not invisible, but instead, results in distinctive and measurable material properties both at the Chapter 9, page 995 boundary and within the lower layer which should be detectable through seismological studies. In chapter 3, I extend the mineral physics modeling to predict one dimensional profiles of shear (Vs) and compression (Vp) velocity across the upper mantle and transition zone for the pyrolite compositional model. I elected to model only this assemblage since a piclogite assemblage fails to satisfy the more stringent test of density and bulk sound velocity profiles performed in the previous chapter. Previous studies that modeled upper mantle Vs and Vp profiles suffered from having to estimate many of the necessary temperature and pressure derivatives required in the calculations, and hence, the results were ambiguous and controversial. Depending upon the values adopted for key minerals, different workers claimed that the seismic Vs and Vp profiles in the upper mantle and transition zone were consistent with either a uniform chemical composition or a chemical layered one. Fortuitously, many of these critical material properties (p, (d\x/dT)p ,(d^i/dP)T ) are now experimentally measured and this study incorporates the latest results. I find that the predicted pyrolite profiles of Vs and Vp are in excellent agreement in terms of both velocity gradient and absolute velocity with the latest, high-resolution regional seismic profiles. The predicted mineral physics profiles also give a mutually consistent estimate of the olivine content of the mantle from the velocity jumps at the 410 km seismic discontinuity. Lastly, the predicted Vs and Vp normal-incidence reflectivity of the 410 km, 520 km and 660 km discontinuities match independent seismic estimates from SsS reverberation studies (e.g. Revenaugh and Jordan, 1991), and PP precursor studies (e.g. Estabrook and Kind, 1996). Chapter 9, page 996 In the lower mantle, the difficulty of estimating values for both the temperature and pressure derivatives of the shear modulus of Mg-perovskite was addressed in a two stage fashion. In chapter four I initially placed bounds on (d[i/dT)p, by focussing on decompressed properties of the lower mantle and then in chapter five forward modeled Vs and Vp profiles by adjusting the value of the pressure derivative, (d\x/8P)T of Mg-perovskite to minimize the misfit between predicted and observed profiles. I justified this approach on the basis of the results of chapter two where it was shown that a pyrolite composition provides an excellent fit to both lower mantle density and bulk sound velocity profiles. Assuming that the pressure dependence of the shear modulus of Mg-perovskite does not exhibit pathologic behaviour, the predicted pyrolite Vs and Vp profiles should also provide an equally good fit to the seismic profiles. The results of this chapter give a very good fit to the seismic velocity profiles under the assumption that a 3rd order Birch-Murnaghan equation of state was appropriate to model the shear properties of perovskite. I also evaluated predicted piclogite Vs and Vp profiles along a hot lower mantle geotherm and found that i f the 660 km discontinuity is a chemical boundary separating a lower mantle piclogite composition from an overlying pyrolite one, the predicted jumps and velocity profiles in the chemically distinct lower mantle are both extreme and unrealistic (see figure 9.4). However, direct experimental values for both (d[i/dT)p and (d\x/dP)T have recently been determined and when combined with information from molecular dynamics studies indicate that a 4th order equation of state is required to satisfy these two data sets. When these modifications are incorporated, as outlined in chapter six, the resulting Vs and Vp profiles give a better fit to the seismic profiles, and significantly, do not alter the Chapter 9, page 997 conclusion that a pyrolite compositional model fits the seismic Vs and Vp profiles whereas a piclogite model, calculated along a hot lower mantle geotherm, does not. In chapter seven, of which a preliminary report was given by Armstrong and Calderwood (1996), I utilize the pyrolite mineral physics model of Vs and Vp to evaluate the ratio of relative Vs and Vp velocity heterogeneity in the mantle as determined by the parameter (dlnVs/dlnVp)p. Prior estimates of (d\nVs/d\nVP)p deduced from seismic tomography were interpreted as requiring either large scale chemical heterogeneities or widespread partial melt within the lower mantle. Neither scenario agrees with our mineral physics results where a melt-free and uniform pyrolite mantle matches the seismic profiles. I find that the predicted pyrolite profile of ( S l n F ^ / d l n F ^ is in good agreement with the various seismic estimates (see figure 9.5), and hence, there is no discrepancy between the tomographic models and a melt-free, uniform bulk composition mantle. In chapter eight, I first summarize geochemical and seismic estimates on the magnitude of lateral temperature anomalies across the upper mantle and transition zone. Then, using the pyrolite mineral physics model of Vs and Vp, I estimate new extremal bounds on lateral temperature anomalies in the lower mantle. Previous studies had concluded that extremely large temperature anomalies, dT exist in the lower mantle on the order of +2500°K to -2000°K. The extreme magnitude of these 87" lead these researchers to reject a thermal origin for the seismic anomalies (5 Kg) and instead, to invoke chemical anomalies in the lower mantle, implying that chemical, rather than thermal, buoyancy is largely driving lower mantle convection. In contrast, I find that the inferred magnitude of the lateral temperature anomalies are significantly reduced with 87" now ranging from « ± 100 °K at 660 Chapter 9, page 998 km to « ± 4 8 0 °Kat the top of the D" layer (see figure 9.6). I conclude that away from chemical and thermal boundary layers, the lateral seismic anomalies resolved in tomographic studies are largely thermal in origin and consequently, the dominant force driving mantle convection is indeed thermal buoyancy (Calderwood, 1997c). 9.3 Caveats and non-uniqueness Inspite of the conclusions reached in the previous chapters that a uniform pyrolite composition provides an excellent fit to the seismic properties of the whole mantle, it is important to recognize that it is not possible to claim this particular composition is unique in fitting the observed seismic velocity models. This reflects a number of uncertainties, both in the thermoelastic data base and the inferred mineralogy of the pyrolite bulk composition, but also in the seismic models themselves. Indeed, although in this study, as is convention in previous mineral physics studies, the global reference seismic models are treated as the observational reference frame against which the mineral physics models are compared to, these seismic models are themselves subject to refinement. For example, in comparing the predicted Vs and Vp transition zone velocity gradients to the seismic models I found that an excellent match existed for recent, high resolution regional oceanic seismic models which included both a 520 km seismic discontinuity, and which allowed velocity gradients above and below this discontinuity to differ. Older seismic models which do not have this discontinuity have transition zone velocity gradients which represent an average of unknown weight for the two different velocity gradient (from 410 to Chapter 9, page 999 520 km and from 520 to 660 km depth). I state "unknown" in the sense it is not clear i f a particular seismic model was constrained predominantly by travel times for rays with turning depths in the upper, or lower, or middle regions, of the transition zone, and furthermore, i f the constraints included both P- and S-wave constraints in these regions. Consequently, the transition zone velocity gradients in these older seismic model are unlikely to accurately reflect the true velocity gradient in either depth interval. Because isochemical compositional models predict velocity gradients very different from these old seismic models, it was concluded by some that such compositional models may be rejected as viable candidates of mantle mineralogy (e.g. Duffy and Anderson, 1989; Ridgen et al., 1991; 1992). This conclusion is an erroneous deduction reflecting deficiencies in the reference seismic models used to evaluate the mineral physics models. Furthermore, because the seismic velocity at a particular depth may reflect several processes in addition to just the bulk composition (thermal anomalies, volatile content, degree of mineral alignment) it is impossible to claim from a purely mineral physics perspective, that a unique composition satisfies the seismic models. Nevertheless, inspite of such admissions of non-uniqueness, it should be stressed that useful conclusions can be reached concerning the chemical composition of the Earth's mantle. Instead of evaluating a plethora of compositional models, I have focussed on evaluating only two end-member models: the well known isochemical pyrolite and chemically layered piclogite compositional models. Inspite of not being able to claim that the pyrolite composition is a unique solution to the Earth's seismic properties mantle, I am able to demonstrate that of the two, it is the successful model, perhaps representing one of a family of "pyrolite-like" bulk compositions (olivine contents ranging from 58 to 62 vol%) Chapter 9, page 1000 that can satisfy the seismic properties. On the other hand, although it has often been claimed that the non-uniqueness of comparing predicted properties, calculated via mineral physics, to seismic ones allows a wide range of compositional models which include chemically layered ones (e.g. Duffy and Anderson, 1989; Vacher et al., 1998), such assertions must be examined critically. For example Duffy and Anderson (1989) claimed that the upper mantle (<400 km) seismic properties could be fit by a mixture of "seismically fast" minerals such as jadeite and garnet, combined with a "seismically slow" minerals such as pyroxene, with or without any olivine. They concluded (p. 1905) that "the upper mantle did not provide any means to distinguish between petrological models". While such mixtures may indeed satisfy a particular velocity profile, these claims are misleading and irrelevant to the question of whether or not a chemically distinct mineralogy, such as piclogite, can satisfy the seismic properties of a particular region of the mantle. Simply mixing a selected subset of minerals together and essentially ignoring the full suit of minerals which are thermodynamically stable for a particular chemical bulk composition is not a meaningful exercise. In a similar vein, Zhao and Anderson (1994) modeled the density and velocity properties of a simplified pyrolite, piclogite, and chondrite mineralogy along a single adiabatic geotherm in the lower mantle. A l l three models resulted in very similar fits to the seismic properties, with the result that Zhao and Anderson (1994) claimed that within the uncertainty of the thermoelastic data, most compositional models are permitted and that a chemically distinct lower mantle composed of piclogite could not be ruled out. As acknowledged above, mineral physics can not uniquely define the lower mantle (or upper mantle) bulk composition. However, as I have shown in chapters two (see figure 9.3) and five and six (see figure 9.4), a chemically distinct lower mantle can be ruled out Chapter 9, page 1001 when the predicted properties are calculated along an appropriate lower mantle geotherm which reflects the thermal boundary layer associated with a chemical boundary. It is simply not valid to invoke a chemically distinct layer within the mantle, but then calculate its material properties along a geotherm concordant with that of the overlying mantle as Zhao and Anderson (1994) do. Thus, in chapter two where I compared the predicted pyrolite and piclogite and p profiles to the seismic observations I was not testing the original chemically layered model proposed by Anderson (1979) where chemical boundaries were placed at 210 km, 410 km and 660 km depth. Subsequent seismological studies have concluded that the 210 km seismic discontinuity inferred by Anderson (1979) and included into the P R E M global reference seismic model is not a global feature, which it should be i f there exists a chemical boundary at this depth. Neither do I test the chemically layered model of Bass and Anderson (1984) which has a shallow pyrolite mantle underlain by a piclogite composition with the boundary at the 400 km seismic discontinuity. The later model was evaluated by Ita and Stixrude (1992) where they modeled the upper mantle with an adiabatic geotherm with a 1700 K mantle potential temperature overlying a piclogite transition zone modeled along a hotter geotherm with a 2200 K adiabat. This temperature offset simulated the thermal boundary layer which should occur at the 410 km seismic discontinuity. They found the misfit between the predicted piclogite density and bulk sound velocity profiles, already significant enough to warrant rejection of this model, increased significantly. In addition, the 2200 K transition zone adiabat lies uncomfortably near the solidus profile which implies widespread partial Chapter 9, page 1002 melting within the transition zone, since thermal perturbation associated with convective flow may be approximately « + 100 K around the average mantle geotherm. Alternatively, they fixed the transition zone temperature profile along a geotherm with a 1700 K mantle potential temperature and decreased the adopted upper mantle adiabat to one with a 1200 K mantle potential temperature. In this case it is now the predicted upper mantle density and bulk sound velocity profiles which significantly misfit the observations. In addition, I note that an upper mantle adiabat anchored to a 1200 K mantle potential temperature is in complete conflict with independent constraints on the upper mantle potential temperature provided by theoretical decompression models of the melt volume, major element, and REE chemical composition of mid-ocean ridge basalts (e.g. McKenzie and Bickle, 1988; McKenzie and O'Nions, 1991; White et al., 1992; Iwamori et a l , 1995). These petrologic models are consistent with a global, average upper mantle potential temperature of 1330-1350 °C (1603-1625 K) with lateral temperature anomalies at the near surface of approximately ± 40-65 °C (see chapter 8). Thus, as shown by Ita and Stixrude (1992), the effects of a 410 km chemical and thermal boundary layer lead to a severe misfit between predicted and observed density and bulk sound velocity profiles on one hand, and implausible temperature structures on the other. Recently Vacher et al. (1998) repeated this exercise but assumed that the 660 km seismic discontinuity represents a chemical boundary, but adopted only a 250 K thermal boundary layer at this depth. Although they acknowledged that the predicted density and velocity jumps at the 660 km were in poor agreement with the observations and that the lower mantle would possess extreme and unrealistic Vs and Vp velocity profiles, they Chapter 9, page 1003 surprisingly claimed that the agreement was essentially as good as that found for the isochemical case when uncertainties in the unmeasured temperature derivative of the shear modulus, (dp /dr )p for Mg-perovskite were considered. They further asserted that the interpretation of seismic data using mineral physics fails to discriminate between whole mantle and layered convection, a conclusion they noted was consistent with that previously reached by Zhao and Anderson (1994) and Stixrude et al. (1992). In contrast, when I assume that the 660 km seismic discontinuity represents a chemical boundary between a piclogite lower mantle and pyrolite upper mantle and transition zone, I conclude that a chemically layered mantle may unambiguously be rejected. How can I reach a conclusion so diametrically opposed to others? First, I adopt a much higher value for the temperature jump of across a 660 km chemical boundary (1200 K), after the numerical results of Glatzmaier and Schubert (1993) who find a temperature jump of this magnitude between the convectively layered and whole mantle spherically averaged geotherms predicted from 3D spherical numerical convection simulations of mantle convection. While this temperature jump exceeds the range of values initially proposed to characterize a mid-mantle thermal boundary layer (500-1000 K; Jeanloz and Richter, 1979) the 1200 K value is actually a conservative estimate when considered in light of the temperature jump (4700 K) required to satisfy global heat flux constraints across a 660 km chemical boundary when a temperature dependent viscosity is considered (see section 9.23). In contrast, Vacher et al (1998) do not justify their use of only a 250 K temperature jump across an assumed 660 km chemical boundary layer, but admit that even with this jump their predicted lower mantle velocity profiles are in their words, "extreme and unrealistic". Secondly, I utilize density and V0 as the Chapter 9, page 1004 discriminants, rather than density and Kg and Vp profiles. As I have noted, the thermoelastic properties required to model p and V® profiles are measured; specifically the temperature derivative for the bulk modulus, (dKT/dT)p for Mg-perovskite has been derived from measured experimental observations by a number of different labs, and there is reasonable agreement upon its value. In contrast, Vacher et al. (1998) inferred a value for (d[i/dT)r , perhaps because they did not have access to the single experimental value of (d\x/dT)r for Mg-perovskite (Sinelnikov et al., 1998). In summary, inspite of the acknowledged non-uniqueness of comparing particular compositional models to seismic observations, I find that it is possible to rule out the piclogite chemically layered model when the effects of the associated thermal boundary layer are considered. Chapter 9, page 1005 9.4 References Agee, C.B., 1998. Phase Transformations and seismic structure in the upper mantle and transition zone. IN: Ultrahigh Pressure Mineralogy: Physics and Chemistry of the Earth's Deep Interior. Hemley, R.J., ed. Mineralogical Society of America, Reviews of Mineralogy, vol., 37, pp. 165-200. Anderson, D.L., 1979. Chemical stratification of the mantle. Journal of Geophysical Research, vol. 84, 6297-6298. Armstrong, R.L., and Calderwood, A.R., 1996. Mineral physics estimates of the ratio of relative Vs and Vp velocity heterogeneity in the lower mantle. EOS Transactions of the American Geophysical Union, Fall meeting, F754 Calderwood, A.R., 1996a. Mineral Physics constraints on the Chemical composition and Temperature of the Earth's mantle from Density and Bulk sound velocity profiles. EOS Transactions of the American Geophysical Union, Spring meeting, S261. Calderwood, A.R., 1997c. A Thermal origin for Seismic Anomalies from Mineral Physics modeling of a Pyrolite mantle and seismic Tomography. EOS Transactions of the American Geophysical Union, Fall meeting, F19. Duffy, T.S., and Anderson, D.L., 1989. Seismic velocities in mantle minerals and the mineralogy of the upper mantle. Journal of Geophysical Research, vol., 94, 1895-1912. Estabrook, C.H., and Kind, R., 1996. The Nature of the 660 kilometer Upper Mantle Seismic Discontinuity from precursors to the PP Phase. Science, vol., 274, 1179-1182. Funamori, N . , Yagi, T., Utsumi, W., Kondo, T., Uchida, T., and Seki, M . , 1996. Thermoelastic properties of MgSi0 3 perovskite determined by in situ X-ray observations up to 30 GPa and 2000 K. Journal of Geophysical Research, vol., 101, 8257-8269. Glatzmaier, G.A., and Schubert, G., 1993. Three-dimensional Spherical models of layered and whole mantle convection. Journal of Geophysical Research, vol., 98, 21,969-21,976. Ita, J., and Stixrude, L. , 1992. Petrology, Elasticity, and Composition of the Mantle Transition Zone. Journal of Geophysical Research, vol., 97, 6849-6866. Chapter 9, page 1006 Ita, J., and Stixrude, L. , 1993. Density and Elasticity of Model Upper Mantle Compositions and Their Implications for Whole Mantle Structure. IN: Evolution of the Earth and Atmospheric Sciences, IUGG volume 14, 111-130. Ito, E., and Takahashi, E., 1989. Postspinel Transformations in the System Mg 2 Si0 4 -Fe 2 Si0 4 and some Geophysical Implications. Journal of Geophysical Research, vol., 94, 10,637-10,646. Iwamori, H. , McKenzie, D., and Takahashi, E., 1995. Melt generation by isentropic mantle upwelling. Earth and Planetary Science Letters, vol., 134, 253-266. Jeanloz, R., 1991. Effects of phase transitions and possible compositional changes on the seismological structure near 650 km depth. Geophysical Research Letters, vol., 18, 1743-1746. Jeanloz, R., and Richter, F .M. , 1979. Convection, Composition, and the Thermal State of the Lower Mantle. Journal of Geophysical Research, vol., 84, 5497-5504. Lay, T., 1994. The Fate of Descending slabs. IN; Annual Reviews of Earth and Planetary Science, vol., 22, 33-61. McKenzie, D., and Bickle, M.J. , 1988. The volume and composition of melt generated by extension of the lithosphere. Journal of Petrology, vol., 29, 625-679. McKenzie, D., and O'Nions, R.K., 1991. Partial Melt Distributions from inversion of Rare Earth Element Concentrations. Journal of Petrology, vol., 32, 1021-1091. Rigden, S.M., Gwanmesia, G.D., Fitz Gerald, J.D., Jackson, I., and Liebermann, R . C , 1991. Spinel elasticity and seismic structure of the transition zone of the Mantle. Nature, vol., 354, 143-145. Rigden, S.M., Gwanmesia, G.D., Jackson, I., and Liebermann, R . C , 1992. Progress in High-pressure ultrasonic interferometry, the Pressure dependence of Elasticity of Mg2Si04 polymorphs and constraints on the composition of the transition zone of the Earth's Mantle. IN: Hish Pressure Research: Application to Earth and Planetary Sciences. edited by Y . Syono and M.H . Manghnani, pp. 167-182, American Geophysical Union, Washington, D.C.. Revenaugh, J., and Jordan, T.H., 1991a. Mantle layering for ScS reverberations 3. The Upper Mantle. Journal of Geophysical Research, vol., 96, 19,781-19,810. Chapter 9, page 1007 Sinelnikov, Y.D. , Chen, G., Neuville, D.R., Vaughan, M.T., Liebermann, R.C., 1998. Ultrasonic shear wave velocities of MgSiOyperovskite at high pressure and temperature and the composition of the Lower Mantle. Science (in press). Vacher, P., Mocquet, A. , and Sotin, C , 1998. Computation of seismic profiles from mineral physics: the importance of the non-olivine components for explaining the 660 km depth discontinuity. Physics of the Earth and Planetary Interiors, vol., 106, 275-298. Wang, Y . , Weidner, D.J., Liebermann, R.L., and Zhao, Y. , 1994. P-V-T equation of state of (Mg,Fe)Si03 perovskite: constraints on composition of the lower mantle. Physics of the Earth and Planetary Interiors, vol., 83, 13-40. Wang, Y . , Weidner, D.J., and Guyot, F., 1996. Thermal equation of state of CaSiO"3 perovskite. Journal of Geophysical Research, vol., 101, 661-672. Weidner, D.J., 1986. Mantle model based on measured physical properties of minerals. IN; Chemistry and Physics of Terrestrial Planets, Advances in Physical Geochemistry vol., 6. Saxena, S., (eds.)., 251-274. White, R.S., McKenzie, D., and O'Nions, R.K., 1992. Oceanic crustal thickness from seismic measurements and rare earth element inversions. Journal of Geophysical Research, vol., 97, 19,683-19,715. Zhao, Y . , and Anderson, D.L., 1994. Mineral physics constraints on the chemical composition of the Earth's lower Mantle. Physics of the Earth and Planetary Interiors, vol., 85, 273-292. Chapter 9, page 1008 Continental Crust and Lithosphere 410 km 520 km 60 km 2600 CMB Tiborgrf Continental Crust and Lithosphere isochemical composition = Whole Mantle D" region (thermal and chemical I WMantle.grf Figure 9.1 Schematic representation o f a chemically layered mantle (top), such as the piclogite compositional model, and a chemically uniform mantle (bottom) such as the pyrolite model. 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 Temperature (K) Figure 9.2 The pyrolite geotherm compared to the whole mantle and enforced layered mantle geotherms calculated from 3D numerical simulations of mantle convection (Glatzmaier and Schubert, 1993). The adopted lower mantle piclogite geotherm used in this study is also shown. 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 h Q 1700 O 1600 I— 1800 1900 K 2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 n n | P T i Q T ^ density Pyrolite akl 35 Piclogite lower mantle adiabat anchor temperature = 3 1 0 8 K • h i l l region of reduced seismic velocity gradients D " layer • 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 r 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.510.(10.511.0 density (g/cm3)/ Bulk Sound Velocity (km/sec) Figure 9.3. Predicted density and bulk sound velocity profiles of pyrolite and piclogite as a function of depth across the lower mantle. The piclogite assemblage is calculated along a hotter geotherm than the pyroltie composition. -a 100 2 0 0 300 400 500 600 700 800 900 1000 1100 1200 1300 ^1400 5 1500 &1600 Q 1700 1800 1900 2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 Chapter 9, page 1011 7 4.00 5.00 6.00 7.00 8.00 9.00 10.00 11.00 12.00 13.00 14.00 Velocity (km/sec) S wave, P wave Figure 9.4 Comparison of the predicted bulk VS and VP velocity profiles of piclogite and Pyroltie as a function of depth in the lower mantle to the global reference seismic models akl35 (Kennett et al., 1995), akl35-F (Montagner and Kennett, 1996). (din Vsldln VP)? Figure 9.5. A comparison of the predicted Pyrolite anharmonic scaling factor with the preferred seismic estimates which are discussed in the text. 2900 1000 2000 3000 4000 5000 6000 T e m p e r a t u r e ( K ) Figure 9.6 Corrected absolute extremal temperature perturbations across the lower mantle. Also shown are the calculated temperature anomalies from the mean upwards and downwards deflections of the 410 and 660 km discontinuities of Vasco et al. (1995) and plume and Tonga slab geotherms. Chapter 9, page 1014 9.5 Future work: Introduction There exist a number of ways in which the pyrolite density and velocity profiles calculated in this dissertation may be further used to elucidate the composition and dynamics of the Earth's mantle. First, the predicted profiles may be tested in a variety of rigorous ways against the seismic observations. Two such ways are outlined below and involve additional testing of the density profile from comparisons between predicted and observed free-oscillation frequencies, and direct testing of the density and Vs and Vp profiles over the width of the transition zone. Second, the profiles may be refined and improved by incorporating the effects of both anelasticity and partial melt, two processes which were ignored in constructing the anharmonic profiles presented in the previous chapters. While chapter 7 argued against a partial melt existing within the lower mantle, it has long been argued that the shallow upper mantle (<410 km) may contain a partial melt phase, and hence it is worthwhile to evaluate this mechanism in that region (Calderwood, 1998b, c). Third, this dissertation focussed largely on the density and velocity properties of the bulk of the Earth's mantle and ignored, in large part, the shallow structure of the oceanic and continental upper mantle, and the deep structure of the D " layer at the base of the mantle. Now, it is natural to focus in on these two chemical and thermal boundary layers with the pyrolite model since this dissertation has demonstrated that this particular geochemical model provides an excellent fit to the intervening seismic observations which join these two regions, and thus, it is natural to test its applicability in the boundary layers (Calderwood, 1997b, c). Fourth, the conclusions of this dissertation have implications for a number of related disciplines in Earth Science, such as the next generation of seismic reference models, mantle seismic tomography Chapter 9, page 1015 models, mantle convection simulations, the mantle geotherm, the origin, structure, and thermal profile of plumes, the thermal Rayleigh number of the Earth's mantle, estimates of the mantle convective mixing time, the thermal and electrical conductivity profiles of the mantle and core, the thermal budget of the Earth, the age of the inner core, the viscosity profile of the mantle (Armstrong and Calderwood, 1998) and the constraints a temperature and pressure dependent viscosity profile places on the temperature jump of a hypothesized 660 km boundary layer, Sm-Nd isotopic modeling of crust-mantle differentiation and evolution (Calderwood, 1997c, d, e, 1998a), the distribution of alkali metals (Cs, Rb, K) in the Earth in light of their high pressure metalization, the distribution of Ce, Pb, Nb, and U within the Earth and the constraints this places on the mass of the present day depleted mantle, the distribution of heat producing elements (U, Th, K) within the Earth and the associated heat flux and rare gas evolution of the atmosphere, mantle, and core. While research in these areas is completed, instead of presenting these results in this forum, I will only briefly touch on a few of these topics to demonstrate the utility of the pyrolite mineral physics model in leveraging new advances in these fields. Chapter 9, page 1016 9.6 References Armstrong, R.L., and Calderwood, A.R., 1998. Constraints on the Earth's Viscosity from a Frequency, Temperature, and Pressure dependent Mantle Q: The Viscosity model. EOS Transactions of the American Geophysical Union, Fall meeting, F885. Calderwood, A.R., 1997a. A Mineral Physics model of Upper Mantle Continental Anisotropy (abstract). 9 t h Annual IRIS Workshop. Calderwood, A.R., 1997b. A Mineral Physics model of Upper Mantle Oceanic anisotropy and Volatile content of the Oceanic Low Velocity Zone (abstract). Harvard Workshop on Continental Roots. Calderwood, A.R., 1997c. Sm-Nd Isotopic modeling of the Evolution of the Earth's Depleted Mantle and Crust revisited: 1) the Time of Crust-Mantle Differentiation and the Mass of the Depleted Mantle. In Seventh Annual V.M. Goldschmidt Conference, p. 39, LPI Contribution No 921, Lunar and Planetary Institute, Houston. Calderwood, A.R., 1997d. Sm-Nd Isotopic modeling of the Evolution of the Earth's Depleted Mantle and Crust revisited: 2) The Age of Crust-Mantle differentiation and the mean Samarium-147/ Neodymium-144 and Neodymium-143/Neodymium-144 ratios of the Depleted Mantle. Seventh Annual V.M. Goldschmidt Conference, p. 40, LPI Contribution No 921, Lunar and Planetary Institute, Houston. Calderwood, A.R., 1997e. Sm-Nd Isotopic modeling of the Evolution of the Earth's Depleted Mantle and Crust revisited: 3) Testing Crustal Growth Models with and without Recycling Against a Hadean to Recent s N d(0 database. In Seventh Annual V.M. Goldschmidt Conference, p. 40, LPI Contribution No 921, Lunar and Planetary Institute, Houston. Calderwood, A.R., 1998a. Sm-Nd isotopic modeling of the evolution of the Earth's depleted mantle and crust: Estimates of Continental Recycling and accretion rates. In Geological Society of America Annual National Meeting, Toronto. Canada, vol., 30, no. 7, p. 207. Calderwood, A.R., 1998b. Constraints on the Earth's Viscosity from a frequency, Temperature, and pressure dependent Mantle Q: the Q model. EOS Transactions of the American Geophysical Union, Fall meeting Supplement, vol., 79, no. 45, F885. Calderwood, A.R., 1998c. Anelastic and Mineral Physics constraints on the Chemical Composition and Temperature of the Earth's mantle. EOS Transactions of the American Geophysical Union, Fall meeting, F867. Chapter 9, page 1017 9 . 7 Future work: Direct seismic tests of the predicted profiles. The predicted density and velocity profiles presented in this dissertation have, to large degree, been simply compared to the seismic observations across the mantle. This procedure follows that of previous mineral physics studies, but such a procedure is less than ideal. A potentially more rigorous way to determine if the predicted profiles satisfy the observations is to use the predicted profiles directly in seismic studies when modeling seismic observations. Although there are many potential collaborative studies which may be undertaken, two particular projects which have significant promise are outlined below. The first involves utilizing the pyrolite mineral physics model directly in calculating the amplitude of SS and PP precursor seismic phases for transition zone underside reflections, while the second involves utilizing the density profile in calculating free-oscillation normal modes. Chapter 9, page 1018 9.8 Future work: Stacked SS precursor phases and transition zone density and velocity structure Chapter 3 compared the predicted pyrolite V$ and Vp velocity profiles against many upper mantle seismic profiles, one of which was the shear wave model SSFIT1 of Shearer (1996). SSFIT1 (see figure 9.7) was constructed to satisfy a global stack of oceanic, long-period seismograms in the epicentral distance 110°-180° which revealed SS phase underside reflections off the upper mantle discontinuities. An important feature of this data stack was that it revealed a clear image from a 520 km discontinuity, in addition to the expected reflections from the 410 and 660 km discontinuities. Furthermore, by stacking the data along an expected travel time curve for a 550 km discontinuity phase (Shearer (1996) notes that this particular depth is arbitrary and is used to obtain a travel time curve nearly parallel to both the 410 and 660 km precursors), the data collapse into a single trace. The features of this trace are sensitive to the depth and reflectivity of the transition zone discontinuities and to the velocity gradients between the discontinuities. This data trace is plotted in figure 9.8 and compared against a model trace constructed from synthetic SS precursor waveforms computed from an early version of the pyrolite velocity model. The details of forward modeling SS precursor waveforms from a velocity profile is outlined in Shearer (1996) and was used to construct the model trace save for a modification where the program now is capable of using both the pyrolite density and velocity profiles. In contrast, the SSFIT1 model was generated by modifying the iasp91 velocity model (Kennett and Engdahl, 1991), but under the assumption that the density profile is simply scaled to the shear wave velocity profile by a constant (e.g. p = aVg where a is a constant). The calculations and figure 9.7 Chapter 9, page 1019 were generated by Peter Shearer (personal communication) and illustrate the success (or failure) of an earlier version of the pyrolite mineral physics model to directly fit seismic data. On one hand the amplitudes for both the 410 and 660 km discontinuities are overestimated relative to the data stack, but the 520 km discontinuity is fit quite well. Furthermore, the trough which precedes the 660 peak is well matched by the pyrolite mineral physics model. This feature reflects the steep velocity gradient zone which directly underlies the 660 discontinuity and Shearer (1996) found that to fit this feature, the width of the gradient zone in the iasp91 velocity model needed to be decreased from 760 km to 727 km depth. By comparison, the high gradient zone in the pyrolite mineral physics model ends at 730 km depth, in good agreement with that inferred by Shearer (1996). The goal of this collaborative modeling is to further test the pyrolite model by using it directly in the seismic modeling. By using self-consistent density and velocity profiles in forward modeling the oceanic data stack, it is anticipated that any significant discrepancies between the pyrolite model and the data may be quickly highlighted. To see i f these discrepancies, such as the mis-fit between the synthetic and observed data trace amplitudes of the 410 and 660 discontinuities, are fatal flaws of the mineral physics model it will be necessary to evaluate whether such mis-fits can be reduced by adjusting the experimental thermoelastic mineral physics data within their uncertainties. Recently Shearer and Flanagan (1998) combined results from both PP and SS-precursors as a function of incidence angle to place constraints on the 410 and 660 km density jumps. Near-vertical reflections are sensitive to the impedance contrast across the discontinuity (the product of the density and velocity jumps) and consequently cannot separately resolve the individual density or velocity jumps. However, at shallower incidence Chapter 9, page 1020 angle, the reflection coefficients respond differently to velocity and density jumps which thereby allows the individual velocity and density jumps to be resolved. They utilized the amplitude of both PP (Flanagan and Shearer, 1998) and SS precursors (Flanagan and Shearer, 1997) off the underside of the 410 and 660 discontinuities as a function of incidence angle. Of interest here is that the S-wave and density jumps are nearly equal at about 6%, which for the density jump, is a significant reduction compared to the P R E M model (AV$ = +6.64%; Ap = +9.77%). The results of Shearer and Flanagan (1998) are in good agreement with the pyrolite model which predicts a AVs jump of +6.7% and a Ap jump of +5.2% at the 660 km seismic discontinuity. 9.9 Preliminary Conclusions This thesis has compared the predicted pyrolite velocity and density profiles to the seismic profiles in a largely semi-quantitative manor which is less than ideal. A more productive way in which to refine and apply the mineral physics models is through collaborative work where the calculated profiles are used directly in seismological modeling and I present initial results where the profiles are used in forward modeling the seismic property of the transition zone. This work is in its infancy but hold much promise to rapidly advance the understanding of the deep Earth. Chapter 9, page 1021 9.10 References Flanagan, M.P., and Shearer, P .M. , 1997. Global Mapping of Topography on Transition zone velocity discontinuities by stacking SS precursors. Journal of Geophysical Research, vol., 103, 2673-2692. Flanagan, M.P., and Shearer, P.M., 1998. PP Precursors: Another way to image Upper Mantle discontinuities. EOS Transactions of the American Geophysical Union, Fall meeting, F641. Kennett, B .L .N . , and Engdahl, E.R., 1991. Traveltimes for global earthquake location and phase identification. Geophysical Journal International, vol., 105, 429-465. Shearer, P .M. , 1996. Transition zone velocity gradients and the 520 km discontinuity. Journal of Geophysical Research, vol., 101, 3053-3066. Shearer, P .M. , and Flanagan, M.P., 1998. Resolving the average velocity and density jumps across Upper-Mantle discontinuities by modeling the range dependence of SS and PP Precursor Amplitudes. EOS Transactions of the American Geophysical Union, Fall meeting, F641. 0 100 E-200 300 400 500 Q 600 700 800 900 1000 i i j i i i i Chapter 9. page 1022 I I I I | I I I I | M i l | -j h I I I I I I Pyrolite mineral physics model l i i i i ii — -\ \ *— iasp91 — Illlllllllll — 1 C O .a I CO 4.50 5.00 5.50 6.00 6.50 s h e a r v e l o c i t y ( k m / s e c ) Figure 9.7 A comparison of the shear wave velocity model SSFIT1 (Shearer, 1996), the starting model iasp91 (Kennett and Engdahl, 1991) and the predicted pyrolite mineral physics profile. Chapter 9, page 1023 Figure 9.8 A comparison between a predicted synthetic SS precursor waveform data stack and the observed oceanic data stack of Shearer (1996). The full details of generating SS precursor waveforms from an upper mantle velocity model is described in Shearer (1996) and was used here except that the density profile for the predicted trace uses both the pyrolite S-wave velocity and density profiles, in contrast to SSFIT1, where the density profile was simply a scaled version of the iasp91 velocity model. This plot, generated by Peter Shearer, uses an earlier version of the pyrolite model described in chapter 3. Although the amplitudes of both the 410 and 660 precursors are slightly overestimated, note the good fit to the 520 km discontinuity and the trough that precedes the 660 peak. Shearer (1996) demonstrated that this trough reflects the steep velocity gradient immediately underlying the 660 discontinuity and modified the iasp91 S-wave velocity profile to better fit the data stack by reducing the width of this zone from 760 to 727 km depth. In the pyrolite mineral physics model this steep gradient zone extends to 730 km depth Chapter 9, page 1024 9.11 Future Work: Forward models of Normal mode Free Oscillation frequencies for the pyrolite mineral physics density profile. Kennett (1998) has recently investigated the density profile of the Earth as constrained by the latest inferences for the mass, moment of inertia, and a recent set of observed normal mode frequencies. The normal mode frequencies posses some sensitivity to the density profile through self-gravitational effects induced by the deformation associated with the lowest radial and spheroidal modes. However, as noted by Kennett (1998) the observed frequencies are also partially dependent upon the velocity structure, so this data set is not solely influenced by the density profile alone. Although he investigated possible perturbations to the density structure in both the core and mantle, I will only focus on his results for the upper and lower mantle. In the upper mantle, Kennett (1998) adopted the P R E M velocity, Q, and density profiles with those parts for the core and lower mantle held fixed. In the upper mantle, the velocity and Q structure were also held fixed but the density profile was permitted to vary. I replot the 50 best density models around the original P R E M density profile together with the predicted pyrolite density profile (see figure 9.9). Overall there is good agreement between the range of the 50 best models and the mineral physics pyrolite model. For example, in the transition zone, all of the new density models are denser than the original P R E M profile, as is the predicted pyrolite profile. Similarly, immediately underlying the 660 km discontinuity, all of 50 best models prefer a less dense structure compared to the original P R E M model again just like the pyrolite density model over this depth interval. Lastly, it is interesting to note that the density jump across the 660 km discontinuity decreases in the 50 best models, a feature also exhibited by the pyrolite model. Chapter 9, page 1025 Turning to the lower mantle, Kennett (1998) fixed the P R E M velocity and density structure at their original values in the upper mantle and core, but allowed the density structure across the lower mantle to vary. Unfortunately, Kennett (1998) elected not to utilize the same parameterization of density as a function of depth as is followed in the P R E M model, where cubic polynomials were used to describe the density. Instead, a set of discreet intervals with linear gradients in radius was adopted. Additional smoothing constraints (continuity in density) were also added to allow changes in the density gradient along the lower mantle profile, but still along a continuous density profile. I re-plot the density perturbation to P R E M [ (8p = p m o d e l - p , , R m ) ] as a function of depth (see figure 9.10) showing the two cases discussed by Kennett (1998) together with the difference between the pyrolite model and P R E M . The heavy shaded area outlines the best-fitting models while the light shaded area outline a broad range of successful models. There exists good agreement between the general behaviour of the best fitting density models and the pyrolite model with respect to P R E M . For example, in the depth interval above 1200 km depth both the best fitting and broad span of density perturbations to P R E M are less dense than the original P R E M model as is the pyrolite model. In contrast, below 1200 km depth the preferred density structure is slightly more dense than the P R E M profile, but so is the pyrolite density structure. While the cross over to lower density occurring roughly at the top of the D" region which appears in Kennett's preferred models is not exhibited in the pyrolite profile, this discrepancy is not significant. The pyrolite density profile used to generate the 8p profile shown here was calculated along an adiabatic temperature profile, and hence, does not include any thermal boundary layer effects in the D" layer. Including a super-adiabatic Chapter 9, page 1026 temperature profile would reduce the predicted pyrolite density profile across the D" region and likely achieve better agreement with the density perturbations of Kennett (1998). However, I caution that the density decrease across the D" region in both of the perturbed density models calculated by Kennett (1998) may be an artifact from keeping the P R E M velocity structure in this region fixed. For example Kumagai et al. (1992) used specific D " sensitive spheroidal normal modes to determine the velocity and density structure of the D " region. They concluded that i f both the perturbations to the S- and P-wave velocity structure have the same sign, then the density perturbation is positive (they used one set of normal modes which are very sensitive to bVp to determine that P-wave perturbations were negative relative to P R E M , but for the remaining modes, there existed a trade off between 8Vs and 8p). The inferred spherical density and velocity models of Kumagai et al. (1992) are re-plotted in figure 9.11 together with the P R E M profile. Support of their inference that both S- and P-wave profiles possess negative velocity gradients across the D " region comes from the global seismic reference model SP6 (Morelli and Dziewonski, 1993). They found that it was impossible within the confines of a fixed D " thickness model to fit the empirical travel time-distance curves without a negative velocity gradient at the base of the mantle for both P and S. In addition, Revenaugh and Jordan (199Id) observe a positive reflector at the top of the D" layer from ScS reverberations, which they note requires a density increase at this discontinuity. Thus, neither the free-oscillation study of Kumagai et al. (1992) which allowed the D" velocity structure to vary, nor the ScS observations of Revenaugh and Jordan (1991b) are consistent with the strong density decrease exhibited in density models of Kennett (1998). Chapter 9, page 1027 With respect to the pyrolite model presented in this dissertation it is relatively straight forward (Guy Masters, personal communication) to calculate predicted normal mode frequencies with the same computer program (MINOS) developed by Guy Masters, that was utilized by Kennett (1998). By adopting both the velocity and density profiles from the pyrolite mineral physics model, one may start with self-consistent profiles and directly test the ability of this model to match the observed normal mode frequencies. Furthermore, satisfying the observed normal mode frequencies is a much more rigorous test of the mineral physics model than a simple comparison to either the akl35 (Kennett et al., 1995) or PREM density profiles since this seismic data set can distinguish between the akl 35 and PREM models (Guy Masters, personal communication), and hence resolve subtle features which are not obvious from visual comparisons. 9.12 Preliminary Conclusions The comparison here between the density differences between PREM and the perturbed models of Kennett (1998) and between PREM and the mineral physics pyrolite model are encouraging and strongly suggest that additional modeling be undertaken. Specifically, rather than use the PREM density, velocity, and seismic Q models, it would be instructive to adopt the pyrolite density and velocity profiles together with the temperature, pressure and frequency dependent seismic Q model (outlined in section 9.18) when forward modeling the normal mode frequencies of the Earth. Chapter 9 , page 1 0 2 8 9.13 References Kennett, B .L .N . , 1 9 9 8 . On the density distribution within the Earth. Geophysical Journal International, vol., 1 3 2 , 3 7 4 - 3 8 2 . Kennett, B .L .N. , Engdahl, E.R., and Buland, R., 1 9 9 5 . Constraints on seismic velocities in the Earth from traveltimes. Geophysical Journal International, vol., 1 2 2 , 1 0 8 - 1 2 4 . Kumagai, H . , Fukao, Y . , Suda, N . , and Kobayashi, N . , 1 9 9 2 . Structure of the D" layer inferred from the Earth's free oscillations. Physics of the Earth and Planetary Interiors, vol., 7 3 , 3 8 r 5 2 . Morelli, A. , and Dziewonski, A . M . , 1 9 9 3 . Body wave traveltimes and a spherically symmetric P- and S-wave velocity model. Geophysical Journal International, vol., 1 1 2 , 1 7 8 - 1 9 4 . Revenaugh, J., and Jordan, T.H., 1 9 9 1 . Mantle layering for ScS reverberations 4 . The Lower Mantle and core-mantle boundary. Journal of Geophysical Research, vol., 9 6 , 1 9 , 8 1 1 -1 9 , 8 2 4 . Chapter 9, page 1029 D e n s i t y ( k g / m 3 ) Figure 9.9 Comparison of the PREM density profile against 50 successful density models (Kennett, 1998) which satisfy Earth mass, moment of inertia, and observed normal mode frequencies. Also shown is the predicted pryolite density model. 2000 h-2100 F-2200 2300 2400 I-2500 2600 2700 h-2800 F-2900 -50 -40 -30 -20 -10 0 10 20 30 40 d e n s i t y p e r t u r b a t i o n (kg /m3) 50 Figure 9.10 A comparison between the density perturbation to PREM (Kennett, 1998) when the PREM lower mantle density profile is adjusted to satisfy mass, moment of inertia, and a recent set of observed frequencies for particular normal modes. Also shown is the difference between pyrolite and PREM density profiles. Chapter 9, page 1031 Velocity (km/sec) density (g/cmA3) Figure 9.11 A comparison of the spherical models of Kumagai et al. (1992) with respect to the PREM and SP6 models. Kumagai et al., (1992) held the velocity and density structure above a 200 km thick D" region fixed, while the structure in D" was varied. Chapter 9, page 1032 9.14 Future work: Implications for the 3 r d generation of joint S- and P-wave tomographic models. The joint whole mantle models S16B30 and P16B30 are currently being augmented by a large data base of long period S-wave mantle discontinuity precursor differential travel times (5r s s_ s s , &tss_s^s , &tss_s^s ; Flanagan and Shearer, 1998), a parallel P-wave precursor data set (&tpp_PtmP , &tpp_p p , &tPP_P<MP ; Flanagan and Shearer, in progress), PcP, PKPab, PKPbc absolute travel times (e.g. Rodgers and Wahr, 1993), and PKP(ab-df) differential travel times (Shearer and Toy, 1991), to increase sensitivity in P-wave structure near the core-mantle boundary, and an expanded set of normal mode structure coefficients (e.g. Widmer et al., 1991a, b; He and Tromp, 1996; Resovsky and Ritzwoller, 1988). In addition, incorporating the affects of anisotropy in the upper mantle (e.g. Laske and Masters, 1998) and inner core (e.g. Shearer, 1994) will also be added. It is well known that a strong trade off exists between volumetric velocity heterogeneity and internal mantle boundary deflections (Woodward and Masters, 1991; Lavely et al., 1994; Ritzwoller and Lavely, 1994a; Rogers and Wahr, 1994; Vasco et al., 1995; Vasco and Johnson, 1998), but with the addition of the SS-SdS and PP-PdP data sets of Flanagan and Shearer (1998; in progress) the affects of the transition zone boundary topography on adjacent volumetric heterogeneity will be minimized. Moving deeper into the mantle, the next significant boundary is the core-mantle boundary. Vasco and Johnson (1998) also allowed for core-mantle boundary topography (and inner-outer core boundary topography) in their joint whole Earth S and P-wave tomographic models that extend throughout the mantle and core. The amplitude of the inferred topography is, as C M B Chapter 9, page 1033 topography models go, quite high with peak to peak deflection of 8 km (by comparison, in a controversial study (e.g. Pulliam and Stark, 1993; Stark and Hengartner, 1993; Rodgers and Wahr, 1993) Morelli and Dziewonski (1987) using PcP and PKP(bc) travel time anomalies, inferred peak to peak deflections of 6 km). However, Vasco and Johnson (1998) admit that there exists a strong trade off between C M B topography and the velocity heterogeneity directly above in the D" layer, as had been noted previously by others (e.g. Gudmundsson, 1989; Pulliam and Stark, 1993; Stark and Hengartner, 1993; Rodgers and Wahr, 1993) and suggested that the PcP data set would have to have improved global distribution and size to reduce such trade off. A similar trade off between the inferred core-mantle boundary topography from analysis of dominantly S-sensitive normal modes and the value of (d\nVs/8lnVp)p has been recognized by L i et al. (1991a). They adopt constant lower mantle values of (d\nVs/d]nVP) = 2.0 and (d\np/d\nVP) p = 0.5 and find the predicted C M B topography to be broadly similar to Morelli and Dziewonski (1987a) but with a significantly reduced topography with of peak to peak deflections of ± 3 km. They also find that positive C M B topography is associated with low-velocity zones in the overlying mantle, consistent with dynamic predictions from viscous flow models (Richards and Hager, 1984). Inspite of the recognized tradeoff between D" velocity heterogeneity and C M B topography, I believe combining the results from mineral physics to a combined normal mode + body wave tomographic study could provide useful constraints on C M B topography. From mineral physics, one could apriori fix the radial profiles of both [dh\Vs /d\nVP) , and (dlnp/dlnVp)p, and consequently remove the tradeoff between [d\nVs/d\nVP)p and inferred C M B topography via S-sensitive normal modes. The resulting constrained C M B Chapter 9, page 1034 topography is then "sharpened " by absolute PcP, PKP(ab), and PKP(bc) traveltimes, which themselves no longer suffer from a strong trade off between C M B topography and D" velocity heterogeneity. Chapter 9, page 1035 9.15 References Flanagan, M.P., and Shearer, P.M., 1998. PP Precursors: Another way to image Upper Mantle discontinuities. EOS Transactions of the American Geophysical Union, Fall meeting, F641. He, X . , and Tromp, J., 1996. Normal mode constraints on the structure of the Earth. Journal of Geophysical Research, vol., 101, 20,053-20,082. Laske, G., and Masters, G., 1998. Surface-wave polarization data and global anisotropic structure. Geophysical Journal International, vol., 132, 508-520. L i , X .D. , Giardini, D. and Woodhouse, J.H., 1991a. Large scale three-dimensional even degree structure of the Earth from splitting of long-period normal modes. Journal of Geophysical Research, vol., 96, 551-577. L i , X . -D . , Giardini, D. and Woodhouse, J.H., 1991b. The relative amplitudes of mantle heterogeneity in P velocity, S velocity and density from free oscillation data. Geophysical Journal International, vol., 105, 649-657. Morelli, A. , and Dziewonski, A . M . , 1987a. Topography of the core-mantle boundary and lateral homogeneity of the liquid core. Nature, vol., 325, 678-683. Pulliam, R.J., and Stark, P.B., 1993. Bumps on the core-mantle boundary: Are they facts or artifacts? Journal of Geophysical Research, vol., 98, 1943-1955. Resovsky, J.S., and Ritzwoller, M.H. , 1994. Characterizing long-period seismic effects of long-wavelength elastic and anelastic models. Geophysical Journal International, vol., 117,365-393. Richards, M.A . , and Hager, B.H. , 1984. Geoid anomalies in a dynamic Earth. Journal of Geophysical Research, vol., 89, 5987-6002. Ritzwoller, M . H . , and Lavely, E .M. , 1995. Three-Dimensional Seismic Models of the Earth's Mantle. Reviews of Geophysics, vol., 33, 1-66. Rodgers, A. , and Wahr, J., 1993. Inference of core-mantle boundary topography from ISC PcP and PKP traveltimes. Geophysical Journal International, vol., 115, 991-1011. Rodgers, A. , and Wahr, J., 1994. The trade-off between volumetric and topographic structure for seismic traveltimes: 660 km topography and mantle structure. Geophysical Journal International, vol., 117, 19-32. Chapter 9, page 1036 Shearer, P .M. , 1994. Constraints on inner core anisotropy from PKP(DF) travel times. Journal of Geophysical Research, vol., 99, 19,647-19,659. Shearer, P .M. , and Toy, K . M . , 1991. PKP(BC) versus PKP(DF) differential travel times and aspherical structure in the Earth's inner core. Journal of Geophysical Research, vol., 96, 2233-2247. Vasco, D.W., Pulliam, R.J., and Johnson, L.R., 1993. Formal inversion of ISC arrival times for mantle P-velocity structure. Geophysical Journal International, vol., 113, 586-606. Vasco, D.W., Johnson, L.R., Pulliam, R.J., Earle, P.S., 1994. Robust inversion of IASP91 travel time residuals for mantle P and S velocity structure, earthquake mislocations, and station corrections. Journal of Geophysical Research, vol., 99, 13,727-13,755. Vasco, D.W., Johnson, L.R., and Pulliam, J., 1995. Lateral variations in mantle velocity structure and discontinuities determined from P, PP, S, SS, and SS-S^S travel time residuals. Journal of Geophysical Research, vol., 100, 24,037-24,059. Vasco, D.W., and Johnson, L.R., 1998. Whole Earth Structure estimated from seismic arrival times. Journal of Geophysical Research, vol., 103, 2633-2671. Widmer, R., Masters, G., and Gilbert, F., 1991. Spherically symmetric attenuation within the Earth from normal mode data. Geophysical Journal International, vol., 104, 541-553. Widmer, R., Masters, G., and Gilbert, F., 1992a. Observably split multiplets- Data analysis and interpretation in terms of large-scale aspherical structure. Geophysical Journal International, vol., I l l , 559-576. Woodward, R.L., and Masters, G., 1992. Upper mantle structure from long-period differential traveltimes and free-oscillation data. Geophysical Journal International, vol., 109, 275-293. Chapter 9, page 1037 9.16 Future work: Other Chemically layered models While this thesis has focussed on evaluating only two end-member compositional models, there exist a number of alternative chemically layered models which have been proposed (Agee, 1993; Javoy, 1995, Gasparik, 1997; Karato, 1998; Grand, 1998; Hager et al., 1998; Kellogg et al., 1998; van der Hilst et al., 1998). However, none have been subjected yet to quantitative mineral physics tests where the predicted properties, calculated along geotherms appropriate for chemically layered states, are compared against the seismic observations. For example, Agee (1993) forward models the elastic properties of the transition zone of the mantle using the elastic data set of Duffy and Anderson (1989). He concludes that a chemically layered transition zone with a strong chemical gradient across it gives a better fit than an isochemical composition to the velocity gradients and absolute velocities for this region. The chemical gradient is hypothesized to form due to gravity settling and floatation of various minerals which have crystallized from a primordial magma ocean. However, as noted in chapter 3, the Duffy and Anderson (1989) data set is largely based on semi-quantitative guesses for the bulk of entries, and thereby, it is unclear i f it provides a useful database for quantitative modeling of the density and velocity properties of minerals. Second, Agee (1993) calculated both the isochemical and chemically layered compositional models along identical adiabatic geotherms. As emphasized throughout this thesis, this approach is invalid when calculating the properties of a chemically, and hence, convectively isolated layer in the mantle. Furthermore, the seismic model which Agee (1993) adopted as his seismic reference with which to judge the fit between predicted and observed comes from the Gulf of California (GCA of Walck, 1985), and significantly, does not include Chapter 9, page 1038 a 520 km seismic discontinuity in the transition zone. Consequently, this seismic model has a near-constant velocity gradient in the transition zone, which is not consistent with recent regional oceanic models (PA5; Gaherty et a l , 1996). Thus, the misfit between predicted and observed velocity gradients for the uniform pyrolite composition, which Agee (1993) used as evidence to reject the isochemical model, is an artifact which reflects shortcomings of the seismic, but not the compositional models. Lastly, the chemical layering invoked by Agee (1993) is postulated to form by gradual sinking or floating of silicate liquids and crystals, respectively, reflecting density crossovers in a quiescent global magma ocean. However, convection calculations for such a magma ocean indicate that at the high thermal Rayleigh number for a planetary scale magma chamber (>109), the convective mixing is highly chaotic and hence it is unlikely that crystal fractionation will occur (Tonks and Melosh, 1990). Indeed, Miller et al., (1991) calculate that crystals 60 meters in diameter would be required for crystal segregation to occur within such a turbulent magma ocean. They stress that while equation of state predictions on density crossovers between silicate liquid and crystals may suggest crystal floatation or settling during crystallization of a magma ocean, when the flow characteristics of such a magma ocean are considered, such a process is emphatically precluded. Indeed, I suspect that when all of the recent chemically layered transition zone models (Agee, 1993; Gasparik, 1997; Karato, 1998) are subjected to quantitative testing, as performed in this thesis, they will all have difficulty satisfying the seismic observations. This work is presently underway. Recently, a number of workers (e.g. Grand, 1998; Hager et al., 1998; Kellogg et al., 1998; van der Hilst et al., 1998) have advocated a chemically layered model of the mantle where the boundary is placed at approximately 2000 km depth (see Chapter 9, page 1039 figure 9.12). The motivation behind such a model is to reconcile seismological observations for flow across the 660 km seismic discontinuity with isotopic interpretations of long-lived and isolated reservoirs (e.g. Jacobsen and Wasserburg, 1979). They rationalize the complete lack of any seismic signature of this boundary (an invisible boundary at 2000 km) by claiming that the large amplitude of topography on the boundary effectively scatter reflected waves (e.g. ScS waves) such that fortuitously, no coherent signal from this boundary is ever seen. Hager et al. (1998) further argues that the high temperatures within the chemically distinct lower layer reduces its inferred chemical-density anomaly of +5% down to only +1% greater than the overlying mantle, with the consequence that such a.mantle density structure is able to satisfy surface geoid observations, as estimated via viscous flow calculations. However, inspection of figures 9.3 and 9.4 reveals that such a chemically distinct, deep layer is implausible from a mineral physics perspective. Assuming that such a chemical boundary exists at « 2000 km depth, figure 9.3 shows that a piclogite layer would be less dense than the overlying mantle, a convectively unstable situation which is in stark conflict with the requirement that such a layer be more dense, to exist as a long term, stable lower layer. Furthermore, even i f one adjusts the chemical composition of the purported lower layer such that the density requirement is satisfied, the results of figure 9.4 demonstrate that at 2000 km, a chemical layer will have a large and distinct velocity jump at its boundary (a negative jump for both Vs and Vp across the « 2000 km boundary) underlain by extremely slow Vs and Vp velocity profiles within the body of the layer. Note that the mineral physics experiments of Mao et al. (1991) and Wang et al., (1994) indicate that the iron content of Mg-perovskite does not have a resolvable effect on its bulk modulus or pressure or Chapter 9, page 1040 temperature derivatives, indicating that an Fe-enriched Mg-perovskite will have a similar predicted velocity to that estimated here. Specific mineral physics calculations of the particular model proposed by Hager and co-workers are underway. Such mineral physics models could then be easily tested by collaborative work with seismologists who specifically focus on the seismic properties of the D" layer and adjacent regions. These workers routinely ray trace through this region and given the large velocity perturbations indicated in figure 9.3 and 9.4 compared to the uniform pyrolite mineral physics model, could detect such differences (Wysession personal communication). 9.17 Preliminary Conclusions This thesis focused on testing only two endmember models proposed for the bulk composition of the mantle. While this was deliberately done to limit the scope of the thesis and because self-consistent models of the mineral assemblages for both of these endmembers are available. Inspite of the numerous difficulties in rationalizing a layered mantle with the seismic and mineral physics evidence for whole mantle flow, it is evident by the number of additional layered models that the siren call of a layered model is too difficult for some Earth scientists to ignore. Unfortunately, virtually none of the proposed layered models have been quantitatively tested by calculating their density and velocity profiles and then comparing these against seismological observations. In addition, many studies which are invoking a layered mantle are arguing such models are required to satisfy isotopic requirements of long lived isolated reservoirs within the mantle (e.g. Hager et al., 1998; Kellogg et al., 1998; and van der Hilst et al., 1998). Unfortunately, the conclusions for an isotopically layered mantle, Chapter 9, page 1041 which were drawn from the early isotopic modeling studies, are not robust, and as I show in later sections, do not support a layered mantle, but instead, demand that the whole mantle is isotopically uniform and furthermore, that the melting events responsible for producing the depleted whole mantle must have occurred very early in Earth's history, likely within the first 200 Myr or so of Earth's history). This highlights a potential limitation of mineral physics modeling in that the predictions are compared against present day observations of the Earth and hence, can not be used to distinguish between hypothesis that the Earth was layered for much of its history, but has only recently switched over to a whole mantle convective style (e.g. Allegre, 1997). To test such hypothesis requires techniques and information (such as isotopic modeling of crust-mantle evolution) that are outside the confines of mineral physics. Nevertheless, it is critical that such independent fields as mineral physics and isotopic inferences on the chemical structure of the mantle be simultaneously evaluated since the two provide different, but complimentary lines of evidence on mantle structure. Mineral physics, when combined with seismic observations, constrains the present day composition and dynamics of the mantle, while isotopic studies have the capability to place time dependent constraints on the mantle's structure over Earth's history. Towards this end initial results of new Sm-Nd modeling of crust mantle evolution have been completed (Calderwood, 1997a, b, c, 1998). These isotopic projects have been expanded to include He, Ar, and Ne rare gases because these tracers offer independent and unique constraints on mantle structure unavailable to the lithophile tracers such as Sm-Nd. Lastly, these isotopic studies are also currently being complimented by independent calculations on the volume of the depleted mantel utilizing Nb/U and Ce/Pb ratios of oceanic basalts. Chapter 9, page 1042 Collectively, these isotopic and trace element studies provide independent constraints on mantle structure which, unlike the mineral physics modeling presented in this thesis, incorporate the element of time, since the radioactive daughter elements (e.g. l 4 3 Nd, 8 7Sr, 2 0 7 Pb, 4 He, 4 0 Ar , 2 1Ne, 1 2 9 Xe) explicitly reflect the decay of radioactive parent elements. Chapter 9, page 1043 9.18 References Agee, C.B., 1993. Petrology of the Mantle Transition zone. Annual Reviews of Earth and Planetary Science, vol., 21, 19-41. Agee, C.B., 1998. Phase Transformations and seismic structure in the upper mantle and transition zone. IN: Ultrahigh Pressure Mineralogy: Physics and Chemistry of the Earth's Deep Interior. Hemley, R.J., ed. Mineralogical Society of America, Reviews of Mineralogy, vol., 37, pp. 165-200. Allegre, C.J., 1997. Limitation on the mass exchange between the upper and lower mantle: the evolving convection regime of the Earth. Earth and Planetary Science Letters, vol., 150, 1-6. Calderwood, A.R., 1997a. Sm-Nd Isotopic modeling of the Evolution of the Earth's Depleted Mantle and Crust revisited: 1) the Time of Crust-Mantle Differentiation and the Mass of the Depleted Mantle. In Seventh Annual V.M. Goldschmidt Conference, p. 39, LPI Contribution No 921, Lunar and Planetary Institute, Houston. Calderwood, A.R., 1997b. Sm-Nd Isotopic modeling of the Evolution of the Earth's Depleted Mantle and Crust revisited: 2) The Age of Crust-Mantle differentiation and the mean Samarium-147/ Neodymium-144 and Neodymium-143/Neodymium-144 ratios of the Depleted Mantle. Seventh Annual V.M. Goldschmidt Conference, p. 40, LPI Contribution No 921, Lunar and Planetary Institute, Houston. Calderwood, A.R., 1997c. Sm-Nd Isotopic modeling of the Evolution of the Earth's Depleted Mantle and Crust revisited: 3) Testing Crustal Growth Models with and without Recycling Against a Hadean to Recent s N d(0 database. In Seventh Annual V.M. Goldschmidt Conference, p. 40, LPI Contribution No 921, Lunar and Planetary Institute, Houston. Calderwood, A.R., 1998. Sm-Nd isotopic modeling of the evolution of the Earth's depleted mantle and crust: Estimates of Continental Recycling and accretion rates. In Geological Society of America Annual National Meeting, Toronto, Canada, vol., 30, no. 7, p. 207. Duffy, T.S., and Anderson, D.L., 1989. Seismic velocities in mantle minerals and the mineralogy of the upper mantle. Journal of Geophysical Research, vol., 94, 1895-1912. Gasparik, T., 1997. A Model for the Layered upper mantle. Physics of the Earth and Planetary Interiors, vol., 100,197-212. Chapter 9, page 1044 Grand, S.P. 1998. Two barriers to Flow in the Deep Mantle. EOS Transactions of the American Geophysical Union, Fall meeting, F586. Hager, B .H. , Kellogg, L .H . , and van der Hilst, R., 1998. A compositionally distinct Deep Mantle - Comparison of Model predictions and Seismological Observations. EOS Transactions of the American Geophysical Union, Fall Meeting, F599 Jacobsen, S.B., and Wasserburg, G.J., 1979. The Mean age of mantle and crustal reservoirs. Journal of Geophysical Research, vol., 84, 7411-7427. Javoy, M . , 1995. The integral enstatite chondrite model of the Earth. Geophysical Research Letters, vol., 22, 2219-2222. Karato, S.I., 1998. Seismic anisotropy in the Deep Mantle, Boundary layers and the Geometry of Mantle Convection. Pure and Applied Geophysics, vol. 151, 565-587. Kellogg, L . H . , Hager, B.H. , and van der Hilst, R., 1998. A compositionally distinct Deep Mantle - reconciling chemical, Geodynamical, and seismological Constraints on Mantle Layering. EOS Transactions of the American Geophysical Union, Fall Meeting, F599. Mao, H.K., Hemley, R.J., Fei, Y . , Shu, J.F., Chen, L.C. , Jephcoat, A.P., Wu, Y. , and Bassett, W.A., 1991. Effect of Pressure, Temperature, and Composition of Lattice Parameters and density of (Fe,Mg)Si03-Perovskites to 30 GPa. Journal of Geophysical Research, vol., 96, 8069-8079. Miller, G.H., Stolper, E .M. , and Ahrens, T.J., 1991. The Equation of State of a Molten Komatiite 2. Application to Komatiite Petrogenesis and the Hadean Mantle. Journal of Geophysical Research, vol., 96, 11,849-11,864. Tonks, W.B., and Melosh, H.J., 1990. The Physics of crystal settling and suspension in a turbulent magma ocean. IN: Origin of the Earth. Newsom, H.E., and Jones, J.H. (eds.) Oxford University Press, New York, pp. 151-174. van der Hilst, R.D., Karason, H. , and Bruneton, M . , 1998. Do Chemically Distinct Domains Exist in the Bottom 1000 km of Earth's Mantle? EOS Transactions of the American Geophysical Union, Fall meeting, F986. Walck, M.C. , 1985. The upper mantle beneath the north-east Pacific rim: a comparison with the Gulf of California. Geophysical Journal of the Royal Astronomical Society, vol., 81,243-276. Chapter 9, page 1045 Wang, Y. , Weidner, D.J., Liebermann, R.L., and Zhao, Y. , 1994. P-V-T equation of state of (Mg,Fe)Si03 perovskite: constraints on composition of the lower mantle. Physics of the Earth and Planetary Interiors, vol., 83, 13-40. Chapter 9, page 1046 Hager.grf Figure 9.12. Illustration of a recent compositionally layered mantle structure where the chemical layer lies deep in the lower mantle (after Hager et al., 1998).
Thesis/Dissertation
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Mineral physics constraints on the chemical composition and temperature of the earth’s mantle
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