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P coda evidence for a layer of anomalous velocity in the upper crust beneath Leduc, Alberta. Somerville, Paul Graham 1971-12-31

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P CODA EVIDENCE FOR A LAYER OF ANOMALOUS VELOCITY IN THE UPPER CRUST BENEATH LEDUC, ALBERTA by Paul Graham Somerville B.Sc. (Hons.) University of New England, 1969 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in the Department of GEOPHYSICS We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September, 1971 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 representatives. It is understood that copying or publication of this thes.is for financial gain shall not be allowed without my written permission. Department of The University of British Columbia Vancouver 8, Canada i ABSTRACT Previous seismic studies of crustal structure using short-period P coda recorded in the vicinity of Leduc, central Alberta have indicated that serious discrepancies between the. experimental observations and those based on a horizontally layered model of,the crust exist in both the time and frequency domains. This 'Standard' crustal model is based on well log data for the sedimentary section, and on seismic refraction work in southern Alberta for the lower layers. The principal discrepancy lies in the large amplitude radial motion on the experimental seismograms which lags, vertical arrivals by approxi mately two seconds. It is concluded that this radial motion, which is absent from synthetic seismograms generated using the 'Standard' crustal model, represents the generation of large-amplitude shear waves within the crust. This; large radial motion.is manifested in the frequency do main by experimental vertical-radial spectral ratios which are consider ably, lower than .those, computed using,the 'Standard' crustal model. Using vertical-radial spectral.ratios-and.synthetic seismograms, a modified crustal model has been derived which gives much better agreement between experimental and theoretical results. This model involves the insertion of a layer several kilometers thick having large velocity con trast with respect to. the surrounding media at the base of the Precam-brian basement (12 km deep). The new crustal, model is discussed in the light of widespread evidence for a low velocity zone in the upper crust in continental regions. Several important.discrepancies, between, experimental and synthetic seismograms remain unresolved: among-these, are the small onset amplitude and the .character of the delayed motion of the radial component. ii CONTENTS Abstract (i) Contents (iiList of Tables (iiiList of Figures (ivAcknowledgments (vi) Chapter 1: Introduction 1.1 Previous studies. 1 1.2 Data collection and preparation. 2 Chapter 2: Analysis 2.1 Deficiency of 'Standard' crustal model in explaining the character of the earthquake seismograms. 10 2.2 Some explanations of the experimental results. 17 2.3 Effect of the sedimentary section of the crust. 8 2.4 The influence of wavelet shape on the synthetic seismograms. 25 2.5 Modes of generation of shear waves at depth. 26 2.6 Investigations into layers of large velocity contrast. 31 2.7 Comparison of experimental and model seismograms. 49 Chapter 3: Discussion 3.1 Evidence for a low velocity zone in continental regions. 54 3.2 Discussion and interpretation of results. 58 Chapter 4: Concluding Remarks 4.1 Summary. 61 4.2 Conclusions. 3 4.3 Suggestions for further work. 64 References 65 Appendix: Homomorphic deconvolution 68 iii LIST OF TABLES Table I Parameters of the earthquake events. A Table II Layer parameters of the 'Standard' crustal sections beneath the three stations. 8 Table III Layer parameters of the detailed sedimentary section. 23 Table IV Layer parameters of the low velocity layer and high velocity layer crustal models. 35 Table V Radial-vertical amplitude ratios of the experimental and synthetic Kurile seismograms. 50 iv LIST OF FIGURES Fig. 1. A map of the seismic stations and oilwell locations by which the crustal section was determined. 3 Fig. 2(a) The sedimentary crustal section obtained by interpolation between oilwell geophysical logs. 6 (b) Crustal model for southern Alberta (after Cumming and Kanasewich, 1966). 7 Fig. 3. Vertical and radial components of the Leduc seismograms for the Kurile and Honshu events. 11 Fig. 4. Radial-vertical cross correlations of experimental, standard crust and low velocity layer crust seismograms. 12 Fig. 5. Comparison of the 'Standard' crust seismogram with the experimental Kurile seismogram. 13 Fig. 6. Spectral vertical-radial ratios for the 'Standard' crustal model compared with experimental spectral ratios for i at (a) 20° and (b) 35°. m 15,16 Fig. 7. Impulse response of the 'Standard' crustal model with the major arrivals identified. 21 Fig. 8(a) Synthetic seismogram for a crust having a detailed sedimentary section. 24 (b) Synthetic seismogram for the 'Standard' crustal model using a long wavelet.Fig. 9. Large velocity contrast layer models. 27 Fig.10. Transfer function of a large velocity contrast layer. 28 Fig.11. Generation of shear waves at the boundaries of a large velocity contrast layer. 30 Fig.12(a) Profiles of 'Standard', low velocity layer, and high velocity layer crustal models. 2 (b) Sections of 'Standard', low velocity layer, and high velocity layer crustal models. 33 Fig.13. Radial components of impulse responses for the 'Standard', low velocity layer, and high velocity layer crustal models. 34 Fig.14. Vertical-radial spectral ratios of thick (2.75 km) and thin (1.7 km) 5.3 km/sec low velocity layer crustal models, compared with experimental and 'Standard' results for i at (a) 20° and (b) 35°. m 37,38 Fig.15 Synthetic seismograms for thick (2.75 km) and thin (.1.7 km) 5.2 km/sec low velocity layer crustal models. 39 V Fig.16. Synthetic seismograms for the 5.2 km/sec and 5.5 km/sec low velocity layer crustal models compared with the experimental seismogram. 40 Fig.17. Vertical-radial sepctral ratios for the 5.2 km/sec and 5.5 km/sec low velocity layer crustal models, compared with experimental results for i at (a) 20° and (b) 35°. 41,42 Fig.18. Vertical-radial spectral ratios for perturbed thickness of 5.2 km/sec low velocity layer model for i , at (a) 20° and (b) 35°. m 43)44 Fig.19. Synthetic seismogram for 7.0 km/see high velocity layer crustal model. 46 Fig.20. Vertical-radial spectral ratios for the 7.0 km/sec high velocity layer model, compared with experimental results for i at (a) 20° and (b) 35°. 47,48 m Fig.21. Azimuth deviations plotted against azimuth for the 15 earthquake events, and..36 of the events. of Ellis and Basham (1968). 52 Fig.22. Crustal section through, the Rhinegraben. rift system (after Mueller et al, 1969). 5 Al(a) Canonic representation of the homomorphic filtering process. 70 (b) Characteristic system for a homomorphic deconvolution filter.A2 Synthesis of.a signal using a wavelet and an impulse pair. 72 A3 Complex cepstrum and recovered wavelet from the signal of Fig. A2. 74 A4 The Kurile seismogram, its. complex cepstrum, and the deconvolved impulse-series and wavelet. 75. vi ACKNOWLEDGEMENTS I wish to thank Dr R. M. Ellis for his valuable guidance and assistance with this work, and for his critical review of its presentation as a thesis. I am much indebted to Dr 0. G. Jensen for his continual discussions and criticisms of the work, and for his guidance in computer analysis techniques. His computer program, together with wavelets deconvolved from earthquake events by Dr T. J. Ulrych, made.possible the computation of synthetic seis mograms. I am also grateful to Dr R. M. Clowes for his discussions concern ing crustal structure in Alberta, and to Dr H. J. Greenwood for his guidance in petrological interpretations. I would also like to acknowledge the contribution of the Department of Geophysics staff, in the preparation of the.seismic field equipment and in the recording and. digitization of the data. Field equipment was made avail able by the Earth Physics. Branch,,Department of Energy, Mines and Resources and both equipment and. .facilities, were provided by the University of Alberta. This research.was supported by the Defence Research Board of Canada (Grant 9511 -76). I would like to thank.Miss. Wei Hsien Ho for her typing of the manuscript. 1 Chapter One INTRODUCTION 1.1 Previous studies. In an earlier P coda study using seismograms recorded in central Alberta, Ellis and Basham (1968) compared vertical-radial spectral ratios (V/H) with theoretical ratios calculated using the Thompson-Haskell ma trix formulation. Although moderate success was achieved in matching curves at several stations, particularly large deviations between the experimental and theoretical curves were observed for seismograms re corded on the portable seismograph designated LED located in the Univer sity of Alberta Edmonton Seismological. Observatory. Anomalously large horizontal amplitudes were noted and attributed to shear conversion and scattering within the crust. . For their, theoretical, model,, velocity, logs, from deep wells were used to determine sedimentary P, wave velocities. S.wave velocities were obtained using the relationship vg = v while the formation densities were obtained from the P wave density curves of Nafe and Drake (Grant and West, 1965). Beneath the sedimentsthe crustal layering and velocities used were those of Cumming and Kanasewich (1966) for southern Alberta extrapolated along regional geological strike. 2 1.2 Data collection and preparation. During October and early November 1968, a 15 km-sided tripartite ar ray of seismographs was operated in central Alberta* One system (LED) was located in the University of Alberta Edmonton Seismological Observatory while the other two, CHA and LAR, were installed in the basements of abandoned farm houses (Fig. 1). During this period, 15 teleseismic events of high signal-to-noise ratio were recorded and have been used in time domain studies.. The parameters of these events are presented in Table I. For frequency domain studies,, the experimental V/H curves of Ellis and Basham (1968) computed for seismograms recorded at LED were used. In their studies of 41 events, many fell in the same range of incidence angles, i^, at the Mohorovicic discontinuity. In particular, 11 were in the range 18°< i 22° and 22 were in the range 31° < i ^ 45°. They m m were therefore able to average over these events to obtain smoother and presumably more representative experimental V/H curves than those which could be obtained from the more limited selection of data used in this work. In both studies, the same seismograph system was used at LED, and the CHA station is of identical design. The three components of ground motion were detected by seismometers with a natural frequency of 0.5 hz, amplified with phototube-galvanometer amplifiers with a natural frequency of 5 hz, and recorded on an FM tape recorder. For a detailed description of the system and the response, the reader is referred to Bancroft and Basham (1967). The LAR system had similar characteristics. The seismograms were digitized at. a sampling interval of 0.05 second, which corresponds to a Nyquist frequency of 10 hz. Since there is little teleseismic energy at this frequency, and since it is well beyond the cutoff frequency of the seismograph (5 hz), aliasing effects due to sam pling are minimal. The ground motion amplitude frequency response for each seismograph was established from transient calibration pulses in the manner described by Deas (1969). The sensitivity of the seismographs varied from one cali bration to the next: in particular, the value of the transducer constant K exhibited random fluctuations of the order of 5% superimposed upon a de crease in value of the order of 5% over the fifty day period of recording. 7 26 25 24 23 2 2 21 20 RGE ' W4 Fig. 1 A map of the seismic stations and oilwell locations by which the crustal section was determined (after Jensen, 1971) TABLE I Parameters of the earthquake Event Region Lat. (deg 1 Bonin Is. +26.3 2 Hokkaido +42.0 3 Venezuela +10o7 4 Fiji Is, -20.9 5 Chile-Bolivia -19.6 6 Kurile Is. +49*7 7 Honshu +-31*2 8 Alaska +65o4 9 Alaska +65.4 10 Peru -16.3 11 Novaya Zemlya +73.4 12 Illinois +38.0 13 Alaska Pen. +57.3 14 Honshu +40.1 15 Ryukyu Is. +-27.5 events Long. Depth Date (deg.) (km) Y M D +140.6 516 68 10 7 +140.6 32 68 10 7 - 62.6 80 68 10 12 -178.8 607 68 10 12 - 68.9 107 68 10 24 +155.8 35 68 10 24 +141.6 17 68 10 29 -150.1 7 68 10 29 -150.1 16 68 10 31 - 73.3 67 68 10 31 + 54.9 0 68 11 7 + 88.5 19 68 11 9 -155.3 59 68 11 11 +143.0 35 68 11 11 +128.4 48 68 11 12 H M S 19 20 20.3 6.1 20 49 01.3 5.7 19 19 29.3 4.8 19 17 39.9 5.7 01 29 42.6 5.3 22 35 50.9 5.5 04 06 04.1 5.7 22 16 15.6 6.0 00 25 45.1 4.5 09 15 46.9 5.7 10 02 05.3 6.0 17 01 41.1 5.3 08 53 52.0 5.3 14 41 15.9 5.5 00 44 12.8 5.8 -A im Azimuth (deg.)(deg.) (LED-event) 78 23 298.2 65 27 307.2 59 30 116.9 93 19 238.4 82 21 138.2 53 31 305.6 74 24 300.5 22 45 318.0 22 45 318.0 77 23 140.7 53 31 004.2 23 44 121.6 24 43 296.7 66 26 305.4 83 21 308.0 5 A similar characteristic in the variation of K with time was noted, with out explanation, by Deas (1969), A decreasing magnetization of the mass may contribute to the decline, while the fluctuations are probably errors in measurement of parameters of the K. test records (although a fluctuating damping constant could also be contributing to this). Accordingly, a least-squares straight line was fitted to the K vs time curves and used in the calculation of the sensivity for each calibration. The sensivity curves were standardized to. the same gain at 1 hz, the center of the frequency band of .interest, ,and the appropriate corrections were applied to the seismograms., .The response of the three components at each station were thus rendered almost identical, since for a given station, the sensitivity curves for the three components have very similar form. The records were digitally filtered using a Lanczos bandpass filter (Basham, 1967) at 0.5 and 3.0 hz.. .With .the responses of the three compo nents standardized as described above, the radial and transverse components of horizontal motion were computed from the North and East components using the great circle station-.to-event azimuth, . Since excellent frequency and time, domain data are both available at LED, the emphasis in this, study has. been, .concentrated on the crustal section beneath this station., In the ensuing discussion, the 'Standard' crust is that portrayed in Figs. 2(a) and 2(b).. and Table II, The sedi mentary P wave velocities and layer thicknesses of Jensen and Ellis (1971) based on well logs have been used and the S wave velocities and densities obtained in the same manner as Ellis and Basham (1968). For. the sub-sedimentary crustal structure, the model of Cumming and Kanasewich (1966) for southern Alberta, extrapolated in a direction paral lel, to the Rocky Mountains, has been used [Fig. 2(b)], It is in general conformity with the more recent work of Clowes et al (1968) and of Chandra and Cumming (1971) in southern Alberta, Both Cumming and Kanasewich (1966) and Chandra and Cumming (1971) have, noted that the base of the Precambrian basement varies in depth and lacks continuity. The latter workers also discern a considerable variability in.the thickness of the sub-sediment layers, and a crustal thickening which trends eastward from 7 P velocity (km/sec) * Thickness (km) surface }/. jtfr/*>*>*s**s'f SEDIMENTS PRECAMBRIAN 6.1 10 SUB-LAYER I ' 6.5 24 SUB-LAYER II 7.2 11 mohorovicic ________ discontinuity . _ o. Fig. 2(b) Crustal model for southern Alberta (after Cumming and Kanasewich, 1966). TABLE II Layer parameters of the 'Standard' crustal sections beneath the three stations Layer Formation (top) Thickness (km) P Velocity i (km/sec) Density (gm/cc) LED CHA LAR LED CHA LAR LED CHA LAR 1 Post Alberta 0.62 0.58 0.71 2.7 2.7 2.7 2.16 2.16 2.16 2 Alberta 0.46 0.49 0.49 3.0 3.0 3.1 2.20 2.20 2.22 3 Blairmore 0.31 0.28 0.35 3.7 4.1 4.1 2.32 2.38 2.38 4 Wabumum 0.16 0.23 0.21 5.5 5.6 5.6 2.60 2.62 2.62 5 Ireton 0.17 0.22 0.19 4.0 4.2 4.5 2.36 2.40 . 2.44 6 Cooking Lake 0.26 0.27 0.30 5.3 5.4 5.5 2.58 2.59 2.60 7 Elk Point 0.19 0.19 0.18 4.6 4.7 4.7 2.46 2.48 2.48 8 Cambrian 0.42 0.40 0.37 4.1 4.2 4.2 2.38 2.40 2.40 9 Precambrian 10.0 10.0 10.0 6.1 6.1 6.1 2.70 2.70 2.70 10 Sub-layer I 24.0 24.0 24.0 6.5 6.5 6.5 2.77 2.77 2.77 11 Sub-layer II 11.0 11.0 11.0 7.2 7.2 7.2 2.88 2.88 2.88 Mantle boundary 8.2 8.2 8.2 3.04 3.04 3.04 9 the Rocky Mountains. In the frequency band of interest, such variations in thickness have very little effect on the first few seconds of the seis mogram, and the effect on the vertical-radial spectral ratios is also small. 10 Chapter Two ANALYSIS 2.1 Deficiency of the 'Standard' crustal model in explaining the character of the earthquake seismograms„ A striking feature of all the seismograms is the apparent delay of approximately two seconds in the major arrivals in the radial component compared with the vertical. For events with simple waveforms, a detailed correlation of character with this delay is evident for at least the first minute of the P coda. For illustration purposes, two earthquakes: a Kurile Island event of October 24, 1968 and a Honshu event of October 29, 1968 will be used (Fig. 3). For the Kurile Island event, the delay of the major arrivals in the radial component is clear. Even detailed character is replicated with delay for the Honshu event. The radial-vertical ratio of the peak amplitudes is. approximately one-half when averaged over all seismograms. To quantitatively confirm this visual observation, cross-correlations between the vertical and radial components were, computed for 6.5-second lengths of data. The. delay of the peak cross-correlation, value generally fell between 1.8 and 2.0 seconds for all events at all stations [Fig. 4(a)]. For the vertical and radial time series normalized to the same power, the value of the cross-correlation is close to 0,5, indicating the large similarity in character. A large discrepancy between the experimental results and theoretical computations based on the 'Standard' crustal model is evident in both the, frequency and time domains. A synthetic seismogram for the Kurile Island event shown in Fig. 5, has been generated by the linear systems technique (Jensen and Ellis, 19 7.1.) using an input wavelet provided by T„J„ Ulrych. This wavelet was obtained using, the non-linear homomorphic filtering technique (Ulrych, 1971) outlined in the Appendix. An angle of incidence i of 31.4° upon the Mohorovicic discontinuity is assumed for this and m all subsequent synthetic seismograms, as it corresponds to the value ap propriate to the Kurile earthquake. The synthetic seismogram does not show the large delayed radial ar rival which is a prominent feature of the Kurile seismogram. At a delay KURILE IS Fig. 3 Vertical and radial components of the Leduc seismograms for the Kurile Is. and Honshu events. 12 1.0 0.5 0.0 -3.0 (a) Experimental -7.0 0.5 -6.0 -5.0 -4.0 -3.0 'TIME SHIFT (SEC) 2.0 1.0 0.5 (b) 'Standard' crustal model 0.0 -3.0 -7.0 -6.0 0.5 -5.0 T -4.0 -3.0 TIME SHIFT (SEC) 1.0 0.5 (c) Low velocity layer model 0.0 -3.0 -7.0 -6.0 0.5 n i v—>'—T— -5.0 -4.0 -3.0 TIME SHIFT (SEC) Fig. 4 Radial-vertical cross-correlations of (a) experimental, (b) 'Standard' crustal model, and (c) low velocity layer model seismograms. KURILE IS - LE D SYNTHETIC - STANDARD CRUST V J I ,5 SEC t WAVELET Fig. 5 Comparison of the 'Standard' crust seismogram with the experimental Kurile seismogram. 14 of about two seconds, it does, however, exhibit an arrival that has ap proximately 1.5 times the amplitude of the radial onset motion. Similarly, the cross-correlation of the synthetic seismogram [Fig. 4(b)], while not having a large maximum at. a 2.0 second lag, does have its maximum near there, although it is not very much greater than values at other lags. It was found that these properties in the synthetic seismogram and its vertical-radial cross-correlation are basically unchanged if one considers only the sedimentary section of the crust. This suggested that the sedimentary section might be producing the observed effects. However, a comprehensive examination of this, possibility, within the constraints imposed by well log information, failed to produce signifi cantly better agreement. This investigation is the subject of Section 2.3. The deficiency of radial motion on the synthetic seismograms calculated for the 'Standard' crustal model is also evident in the vertical-radial spectral ratios for angles of incidence i close to 20° and 35°. In Fig. 6, m the theoretical curves for the'Standard' crust are compared with the experi mental results of Ellis and Basham (1968) for two different angles of inci dence. A slightly different crustal section and smoothing operator accounts for the difference between the 'Standard' crust curves presented here and the theoretical curves of their work. The crustal section of Jensen (1971) was preferred since it was based on a more detailed net of wells around Leduc. Although the peak positions for the two sets of curves of Fig. 6 correspond, the amplitudes of the theoretical curves are too large, indi cating that more radial motion is present in the earthquake seismograms than is predicted by the .'Standard' crustal model. Ellis and Basham (1968) used the presence of large transverse motion to substantiate their inter pretation of this radial motion as representing the conversion of P to S by crustal inhomogeneities and topographic scattering. 15 < X CO A -o • m o —i 3D ID 13 CZ a 70° Q experimental 'Standard' crust Q.Q 0.5 l.Q n 1.5 2.0 1 2.5 FREQUENCY (HZ) Fig. 6(a) Spectral vertical-radial ratios for the 'Standard' crustal compared with experimental ratios for i «= 20°. m experimental 'Standard' crust 17 2.2 Some explanations of the experimental results. As there are no large amplitude vertical arrivals coincident with the horizontal motions on the simple waveform events (Fig. 3), these displace ments cannot be attributed to the horizontal component of P motion. The two seconds delay of the prominent horizontal arrivals at all stations for all azimuths and epicentral distances rules put the possibility that the radial motion consists of scattered P waves. The small delayed arrival on the radial component of the synthetic seismograms for the 'Standard' crust is produced by the reverberations of waves between the surface and the top of the Wabumum (layer 4), and between the surface and the Precambrian basement. These reverberations are sep arated in time in such a way as to mutually reinforce a wave whose fre quency content is dominantly 1 hz. The reverberations are shear waves in the upward going leg, thus producing large horizontal motion. A de tailed analysis of the impulse response of the crust, and its correlation with the crustal section and the synthetic seismograms, is given in Section 2.3. As will be seen in that section, well log information pro hibits the adoption of a sedimentary model which could enhance this re verberation effect to a level adequate to explain the appearance of the seismograms. Another possible explanation depends upon shear wave generation, not within the sedimentary section but at a greater depth. In this model, the delay arises not from reverberation times between layers, but in the travel-time difference between S and P waves from the source of shear wave generation. The two-second delay then represents shear wave generation at a depth of approximately 12 km in the 'Standard' crustal; model, corresponding to the lower boundary of the crystalline basement. This model provides an immediate explanation of the similarity in character and the delay between the vertical and radial motions. Modes of shear wave generation at this depth are examined in Section 2.5, and models obtained which best fit the experimental results are presented in Section 2.6. 18 2.3 Effect of the sedimentary section. The construction from well log information of a sedimentary section appropriate to studies of short period P coda involves a considerable amount of interpretation. Firstly, the representation of a continuously varying velocity profile as a small number of discrete velocity intervals requires subjective judgement. Secondly, the determination of P wave velocities at approximately 1 hz must be made on the basis of high frequency sonic log measurements. Information upon which to base S velocities and den sities for the particular section is absent. The sedimentary section of Jensen (1971) was based on a closer net of wells than that of Ellis and Basham (1968) and was preferred for this reason. For the purposes of this Investigation, a detailed, accurate sedimentary section at LED was required. For this reason, a slightly dif ferent set of criteria were used in compiling the section from those used by Jensen (1971). Firstly, whereas Jensen's section was based predomin antly on geological formations, the new model was based on velocity con trasts alone. In particular, the actual magnitude of each velocity con trast was preserved, adjusting the thickness to take account of any fluc tuations in velocity within a layer. Secondly, rather than compiling an average section from many wells, a single well, G (Fig. 1), the CNS As sociation Petroleum Corporation Roily View Well, has been used, as it is within two miles of LED. Correlations between it and wells H (Big Hay) and I (Imperial Dinant) have been used to complete the section at the upper and lower ends. An empirical study of the relationship between sonic log velocities and those obtained by the conventional 'check shot1 technique was made by Gretener (1961). Sonic logging tools obtain the average velocity of the rock in a vertical direction over an interval of between three and five feet and at a frequency in the vicinity of 12 khz. The study of Gretener pertains to measurements made with the Shell sonic logging tool in 50 wells scattered throughout the Alberta plains. The travel time for each check shot interval was computed for both the sonic log and check shot measurements. The times computed conventionally were system atically greater than those from the sonic log by an average of 1.7 ms/1000 ft. with a standard deviation of 1,8 ms/1000 ft. For a material of P wave velocity 3.5 km/sec, this corresponds to a difference of 2% in velocity. Gretener concluded that there existed two principal causes of this systematic delay. Firstly, he found that at shallow depth a 10% apparent anisotropy was present, consisting of real anisotropy and the effect of layering (ignored in correcting the check shot times for offset), producing errors in the conventional survey. Secondly, he assumed that dispersion was contributing to the deviation between conventional and sonic log mea surements, whose frequencies are separated by a factor of several hundred. Dispersion was studied experimentally by McDonal et al (1958) and by Wuenschel (1965). McDonal et al found that in the range 25 to 400 hz, the phase velocity varies by 2.6% in the Pierre Shale. Wuenschel, using the theory of Futterman (1962) relating the real and imaginary parts of the propagation constant, obtained a theoretical dispersion relation in which the phase velocity depends logarithmically on frequency. Using this and the observed dispersion for Pierre Shale, one obtains a difference of the order of 10% for phase velocities at 1 hz and 10 khz, corresponding to the frequencies of short-period teleseismic signals and the sonic logging instrument respectively. It is clear from this that the discrepancies between the phase ve locities at the two frequencies are much greater in the Pierre Shale study than in the findings of Gretener (1961). This may be due to the difference in Q values of the two sedimentary sections: a higher Q would produce less dispersion. Wuenschel estimates the Q 'of Pierre Shale to be 30, which is lower than estimates of the Q of the Alberta sediments. Jensen (1971) chose a meanQ of 45 from reports in the literature on lab oratory studies. This is in contrast with a Q of 300 for the southern Alberta sediments as determined by Clowes and Kanasewich (1970) from a comparison of observational and theoretical reflection seismograms. Strick (1971) has found that Q values between 50 and 150, which he considers appropriate to the Alberta sandstones and shales, provide travel-time discrepancies which are compatible with Gretener1s observations when used in his PL attenuation function"*" describing the absorption of Strick's power law(PL) attenuation model describes the real and imaginary parts of the propagation constant as having a frequency dependence slightly different from linear, thus complying with the Paley-Weiner causality condi tion requiring them to increase slower than the first power of the frequency as the frequency becomes infinite. The demand of constant Q (independent of frequency), with its requirement that the real and imaginary parts of the propagation function be linear functions of frequency, is slightly relaxed. 20 seismic energy in the earth. With this substantiation of the small dis persion values found by Gretener, it can be assumed that these values are the most appropriate ones available for the Alberta sediments. This dis persion is so small as to be negligible, and velocities obtained from sonic logs can be used in the study of short-period P coda. The appearance of a synthetic seismogram can be explained in terms of its impulse response: the impulse response of the 'Standard' crustal model, with its major arrivals identified, is shown in Fig. 7. The large delayed arrivals on the vertical represent reverberations of P-waves between the sedimentary interfaces and the surface. On the radial compo nent there are two groups of strong arrivals. The first group, arriving at delays between one quarter and one-half second, are shear waves gen erated at the sedimentary interfaces, and the second group, arriving between one and two and a half seconds, are reverberations between the surface and sedimentary interfaces, with the upward path as shear motion, and the downward path either as compressional or as shear motion as in dicated. It is the association of this second group of arrivals that produces the large delayed amplitude in the radial component. Dominant among them are the PS reverberation with the base on the sedimentary section, and the PS and SS reverberations with the top of the Wabamum (interface 3). These constructively interfere when the input wavelet has its fre quency content centered at about 1 hz. The impulse response was used as a diagnostic aid in the designing of sedimentary Sections that would enhance the delayed radial motion. As has already been seen, the expected effect of dispersion upon the velocities of a sedimentary section determined from sonic logs can be assumed to be negligible in Alberta. Nevertheless, as a check against gross systematic error in the sonic logs, sedimentary sections were con structed whose velocities deviated 10% on either side of the sonic log velocities. It was found that delayed radial amplitudes were not en hanced, and spectral ratios remained unchanged in level and shape, and were only shifted slightly along the frequency axis. The most accurate model derived from the well log data is presented in Table III. It has layers as thin as 12 meters: as was anticipated, 21 P-P reverberations between the surface and the interface numbered. 1 sec Shear conversion from interface numbered. P-S and S-S reverberations between the surface and the interface numbered. Fig. 7 Impulse response of the 'Standard' crustal model with the major arrivals identified. 22 the effect of these in both time and frequency domains is small, because of the high frequency nature of their effects. The synthetic seismogram for a crust with this sedimentary section [Fig. 8(a)] is seen to differ only slightly from that of the 'Standard* crustal model (Fig. 5). Several other models were tried, in which the boundaries of layers were slightly altered, and the number of layers varied. On the suggestion of E. R. Kanasewich (personal communication), a value of Poisson's ratio of 0.3 was used in the sedimentary section. However, none of these models enhanced the delayed radial motion notably, now was any improvement made in the fit of the spectral ratio curves. The reason is presumably that the delayed arrival is indeed due largely to the impulses already described, and the reflection coefficients of the two interfaces that generate them cannot be increased beyond the restraints of well log data. TABLE III Layer parameters of the detailed sedimentary section. Layer P-Velocity S-Velocity Density Thioknet • 1 2.40 1.39 2.10 0.242 V.;. 2.80 .; 1.62 2.17 0.558 . 3 3.20 1.85 2.24 0.107 ." 4 2.80 ;! i.62 2.17 0.149 3.72 2.15 2.31 , 0.034 6 2.82 • 1.63 2.17 0.021 7 • ' 3.82 2.21 2.34 0.207 ' 8 .;. 5.65 ;. ''^'.y- 3.27 2.62 0.168 9 ... ; 4.93 2.95 2.50 0.040 10 . 4.02 2.32 2.36 0.034 11 v 3.77 2.18 2.33 0.052 12 V 4.02 2.32 2.36 0.030 13 4.77 2.76 2.48 0.015 14 4.02 2.32 2.36 . 0.022 15 5.26 3.04 2.58 0.015 16 4.02 • 2.32 2.36 0.012 17 :. 5.26 3.04 2.58 0.030 18 5.87 3.39 2.67 ' 0.241 19 4.60 2.66 2.46 0.192 20 4.10 2.37 2.38 0.421 Basement 6.10 3.52 2.70 24 R -t-INPUT: PULSE ... j • Fig. 8(a) Synthetic seismogram for a crust having a detailed sedimentary section. 5 sec R INPUT PULSE Fig, 8(b) Synthetic seismogram for the 'Standard' crustal model using a long wavelet. 25 2.4 The influence of wavelet shape on the synthetic seismograms. The possiblity that a different wavelet might produce the observed effect in the sedimentary section was also examined. The choice of a wavelet is restricted both in dominant frequency and in duration. A wavelet whose dominant frequency is inappropriate gives a very much diminished resemblance with the Kurile seismogram in the vertical component. Also, the appearance of the vertical component of the Ku rile seismogram (Fig. 3) indicates that a long, 'ringing' wavelet of several cycles duration is not an appropriate representation of the motion at the base of the crust. If constructive interference phenomena within the sediments are dominant in producing the delayed radial motion, then a longer wavelet would enhance this effect. Accordingly, a synthetic seismogram was generated using Ulrych's wavelet with an additional cycle added onto the tail. The five seconds length of this improbably long wavelet ex ceeds the duration of the dominant radial arrivals of the impulse re sponse (Fig. 7). The result [Fig. 8(b)] does not display any signif icant enhancement of the delayed radial motion. It can be concluded that the Ulrych wavelet is the best available representation of the motion at the base of the crust. In the light of these experiments with the sedimentary section of the crust and with the wavelet, it is difficult to believe that the sedimentary section is entirely responsible for the observed de layed radial motion on the earthquake seismograms. 26 2.5 Modes of generation of shear waves at depth. The amplitude of radial motion is far greater than that which could be generated at a single velocity discontinuity of reasonable velocity contrast. For example, if a P wave is incident upon a velocity decrease of 25% at an angle of 30°, the ratio of shear to compressional refracted energy is approximately 0.15. McCamy et al (1962), from whose curves this value is obtained, have shown that variations in Poisson's ratio and density produce very small changes in the Zoeppritz coefficient curves. Thus, in order to explain the experimental data, the effects of inter ference phenomena within a layer of considerable velocity contrast with the bounding media were examined. Firstly, reverberation effects within a layer were studied. The layer was chosen to have velocity greater than or less than the veloc ities of the surrounding media, as indicated in Fig. 9. In this case, the reflection coefficients at the upper and lower boundaries for waves within the layer have the same sign. For normal incidence of a wave within a layer whose one way travel time isT, the transmission function varies with frequency as illustrated in Fig. 10, with peaks every JTT7 corresponding to frequencies at which an integral number of two-way re verberations represent a travel path of one wavelength. Models were tested which had layers whose thicknesses were chosen so as to optimize the transmission of shear waves at ~jpp hz. At the same time, the transmission of P waves is near a minimum, as can be seen from Fig. 10. This effect, however, cannot adequately explain the observed shear amplitudes: synthetic seismograms obtained even for extreme Velocity contrast models showed peak radial-vertical ratios of about one-quarter, in contrast with the experimental ratios of one half. A second interference effect has provided good quantitative agree ment: it involves the constructive interference between shear waves gen erated at the upper and lower boundaries of a layer of suitable thickness. For non-critical angles, body waves are transmitted through velocity discontinuities without change of phase, except for the case of shear waves generated by a compressional wave entering a medium of higher veloc ity, which suffer a 180° change of phase with respect to the parent com pressional wave. 27 high velocity low velocity layer high velocity low velocity high velocity layer low velocity Fig. 9 Large velocity contrast layer models. Fig. 10 Transfer function of a large velocity contrast layer. 29 For interleaved layers of alternately high and low velocity (Fig. 9), the phase difference between P and S travel paths within a layer must be (n + 0.5) cycles, n integer, for maximum constructive interfer ence of generated shear waves for a given harmonic set of frequencies f (see Fig. 11). For a given angle of incidence of upgoing P waves i at the upper boundary of a layer, the travel path must be a fraction r of a P wave length for constructive interference of S waves to occur, where r is given by r cos ip = (r + n + 0.5)X^ cos is (1) where and are P and S wavelengths respectively for the nth fre-harmonic, respectively at the upper boundary. The thickness of the layer h is then given by quency harmonic, and i and ig are the incident angles of P and S motion , \ (n + 0.5) cos in cos is h = rAjcos l = — '—— - * b P A^ cos ip - A^ cos is C2) For near-normal incidence, (n + o.5) (3) tn oC - P where f is the frequency of the waves, and JL and ft are P and S wave velocities in the layer. Fig, 11 Generation of shear waves at the boundaries of a large velocity contrast layer. 31 2.6 Investigations into layers of large velocity contrast. A modeling investigation was undertaken with the object of exploiting the interference effect that has just been described. Basic crustal mod els were developed using synthetic seismograms, and these were adjusted to give the best fit to the experimental data by the use of vertical-radial spectral ratios, which are more sensitive to variations in layer parameters than are synthetic seismograms. Using the delay time of 1.9 seconds obtained from the experimental vertical-radial cross-correlations, the upper surface of the. large ve locity contrast layer was set. at a depth of approximately 12 km below the surface of the 'Standard1 crustal model. Equation 3 was used to calcu late the thickness of the layer which would optimize the deepening of one or other of the two troughs, at 1.3 hz and 2.1 hz, in the experimental spectral ratio curves (Fig. 6). The layer which was inserted between the crystalline basement (P velocity 6.1 km/sec) and sub-layer I (P velocity 6.5 km/sec) was allowed to have velocities both lower and higher than those of the surrounding media. The large contrast layer contributes to the large amplitude delayed radial motion by shear wave conversion at its upper and lower boundaries. The largest amplitude is obtained if these arrivals reinforce the rever berations within the sedimentary column. Thus the optimum depth for a low velocity layer is 12.2 km, and that for a high velocity layer is 14.3 km. These depths affect the amplitude of the radial motional critically. Profiles and sections of the 'Standard', low and high velocity layer models are shown in Fig. 12, and their radial impulse responses in Fig. 13. The layer parameters of these models, are presented in Table IV. The two impulses representing shear conversion constitute the only significant difference between the high contrast layer and 'Standard' models in the first few seconds. Models chosen to optimize shear generation at either 1.3 hz or 2.1 hz are comparable in their results. The thin layer gives appreciably better spectral ratio curves for im = 35° [Fig. 14(b)], especially at the fre quency of 2.1 hz for which it is designed. However, Ellis and Basham (1968) found that for increasing angles of incidence, the coherency 32 10 20 Depth (km) 30 40 50 P velocity (km/sec) 4 • 6 low velocity layer 'Standard' high velocity layer Fig. 12(a) Profiles of 'Standard', low velocity layer, and high velocity layer crustal models. 33 'Standard' model Low velocity layer High velocity layer model model P vel. h P vel. h P vel. h (km/sec) (km) (km/sec) (km) (km/sec) (km) ^3.v•) 3 • S 2• 39 •••« •••• 6.1 10 ' ... 9.6 .... 11.7, 5.2 2. 75 ; 7.0 3.7 6.5 24 ... 21.65 ... 18.6 7.2 11 8.2 Fig. 12(b) Sections of 'Standard', low velocity layer, and high velocity layer crustal models. 34 'Standard' model Low velocity layer model 1 sec Fig. 13 Radial components of impulse responses for the 'Standard', low velocity layer, and high velocity layer models. TABLE IV Layer parameters of the low velocity layer (LVL) and high velocity layer (HVL) crustal models Layer Formation (top) P Velocity S V/ilo Density . Thickness (km/sec) (km / sec) (gm/cc) (km) LVL HVL LVL HVL LVL HVL LVL HVL 1 Post Alberta 2.7 2.7 1.56 1.56 2.16 2.16 0.62 0.62 2 Alberta 3.0 3.0 1.73 1.73 2.20 2.20 0.46 0.46 3 Blairmore 3.7 3.7 2.14 2.14 2.32 2.32 0.31 0.31 4 Wabumum 5.5 5.5 3.18 3.18 2.60 2.60 0.16 0.16 5 Ireton 4.0 4.0 2.31 2.31 2.36 2.36 0.17 0.17 6 Cooking Lake 5.3 5.3 3.06 3.06 2.58 2.58 0.26 0.26 7 Elk Point 4.6 4.6 2.66 2.66 2.46 2.46 .0.19 0.19 8 Cambrian 4.1 4.1 2.37 2.37 2.38 2.38 0.42 0:42 9 Precambrian 6.1 6.1 3.52 3.52 2.70 2.70 9.60 11.70 10 Large vel. contrast 5.2 7.0 3,00 4.05 2.54 2.93 2.75 3.70 11 Sub-layer I 6.5 6.5 3.75 3.75 2.77 2.77 21.65 18.60 12 Sub-layer II 7.2 7.2 4.31 4.31 2.88 2.88 11.00 11.00 Mantle boundary 8.2 8.2 4.73 4.73 3.04 3.04 :i j • '-i j -• ^ ~* 4 1 \ <J1 36 between seismograms for an earthquake event recorded at different stations tended to decrease, implying an increasing amount of scattering. It can be concluded, therefore, that the experimental spectral ratio curves for i = 35° are less reliable than those for i = 20°, and so the better agreement of the thin layer model for i = 35° may not be very significant. Further more, since the Kurile wavelet has a dominant frequency of approximately 1.5 hz, the synthetic seismogram for the thick layer model (optimizing shear motion at 1.3 hz) shows a larger delayed radial amplitude than that for the thin layer, as is evident-in Fig. 15. The profile of the thick 5.2 km/sec model is shown in Fig. 12. A comparison between the synthetic seismogram for this model and the Kurile earthquake shows that the relative amplitudes of peak radial to vertical motion are equal (Fig. 15). However, while it is evident that the model produces considerable improvement in the spectral ratio curves, there is still a large amount of radial energy that remains unexplained: it may be partially due to scattering caused by inhomogeneities in the crust. Because the peak amplitude motions should be less subjected to scattering than the spectral ratios computed from 20 sec. lengths of record, they are chosen as the criterion for selecting the best model. Increasing the velocity contrast of the layer was found to improve the fit of model results to experimental ones. For example, in Figs. 16 and 17, the results for thick low velocity layers of velocities 5.2 km/sec and 5.5 km/sec are compared. The improvement of the 5.2 km/sec layer model over the 5.5 km/sec one is clear in both time and frequency domains. The shape of the spectral ratio curves suffers rapid degradation when the layer thickness is perturbed from its optimum value. In Fig. 18, curves are presented for crusts with the thickness of the 5.2 km/sec low velocity layer perturbed by 0.2 km, or less than 10% about the optimum value. For these perturbations, the synthetic seismograms show a cor responding decrease in delayed radial amplitude. Equally good agreement between model and experimental results is obtained for a high velocity layer modelwith comparable velocity con trast with the surrounding media. A synthetic"seismogram'and spectral ratio curves for a 3.7 km thick layer of"P wave velocity 7.0 km/sec are presented in Figs. 19 and 20, and the profile of the model is shown in 37 Fig. H(a) Vertical-radial spectral ratios of thick (2.75 km) and thin (1.7 km) 5.2 km/sec low velocity layer crustal models, compared with experimental and 'Standard' results for imra20c. 38 experimental 'Standard' crust —-—•— thin low velocity layer thick low velocity layer o —H ID So r~ i-—i —i c: a rnN-. X) o o 0.5 "T~~ 1.0 "~1 2.0 0.0 "T-1.5 I 2.5 FREQUENCY (HZ) Fig. 14(b) Vertical-radial spectral ratios of thick (2.75 1cm) and thin (1.7 km) 5.2 km/sec low velocity layer crustal models, compared with experimental and 'Standard* results for in"35* 39 Fig. 15 Synthetic seismograms for thick (2.75 km) and thin (1.7 km) 5.2 km/sec low velocity layer crustal models. V . « Standard' crust 5.2 km/sec low velocity layer R V R 5.5 km/sec low velocity layer Fig. 16 Synthetic seismograms for the 5.2 km/sec and 5o5 km/sec low velocity layer crustal models compared with the espsriscantol seismogram. 41 Fig. 17(a)Vertical-radial spectral ratios for the 5.2 km/sec and 5.5 km/sec low yelocity layer crustal models, compared with experimental results for at 20°. 42 Fig. 17(b) Vertical-radial spectral ratios for the 5.2 km/sec and 5.5 km/sec low velocity layer crustal models, compared with experimental results for im -35°. 43 — experimental — 2.75 km 2.95 km 2.55 km 1—~ 1 1 —-i— r~ 0.5 1.0 1.5 2.0 2.S FREQUENCY (HZ) ' Fig. 18(a) Vertical-radial spectral ratios for perturbed thickness of 5.2 km/sec low velocity layer model for. i^ • 2Q°. 0.0 44 experimental 2.75 km ; 2.95 km 2.55 km °-| , . , , 1— 1 0.0 0.5 1.0 1.5 2.0 2.5 FREQUENCY (HZ) Fig. 18(b) Vertical-radial spectral ratios for perturbed thickness of 5.2 km/sec low velocity layer model for im • 35°. Fig. 12. The results are comparable with those of the roughly analogous case of a 5.5 km/sec low velocity layer. Notwithstanding this equivalence of results using high and low ve locity layers, the following chapters will concentrate attention on the low velocity model, as it appears to conform with other evidence. Using the time-domain amplitude criterion discussed above, the low velocity model that will be examined consists of the standard crust, perturbed so as to contain a layer of velocity 5.2 km/sec and thickness 2.75 km situated below the Precambrian basement at a depth of 12.2 km, as portrayed in Fig. 12 and Table IV. 46 5 sec V R Fig. 19 Synthetic seismogram for the 7.0 km/sec high velocity layer crustal model. Fig. 20(a) Vertical-radial spectral ratios for the 7.0 km/sec high velocity layer model, compared with experimental results for im - 20°-48 Fig. 20(b) Vertical-radial spectral ratios for the 7.0 km/sec high velocity layer model, compared with experimental results for im •=> 35°. 49 2.7 Comparison of experimental and model seismograms. The vertical component of the synthetic seismogram for the low velocity model gives good qualitative and quantitative agreement with the Kurile earthquake for the first few seconds. Beyond this point, however, motion of considerable amplitude on the earthquake seismogram is absent from the synthetic seismogram. This is understandable since the wavelet used in the computation of the synthetic seismogram must be much shorter and simpler than the Kurile event, which, occurring at a depth of 35 km, must be complicated by motion generated near the source. Furthermore, the synthetic seismogram is free of scattered energy which is considered to be partially responsible for the large horizontal amplitudes of the seismograms. The radial motion of the synthetic seismogram does not agree in character with that of the earthquake. Inaccuracies in both the crustal model and the wavelet could be contributing to this. However, the relative amplitudes of peak vertical and radial arrivals for the low velocity layer crust are equal to the experimental ones, in con trast with those of the 'Standard' crust, as indicated^in Table V. This difference in delayed radial amplitude is evident if the vertical-radial cross-correlation of the Kurile seismogram is compared with those computed from the 'Standard' and low velocity layer synthetic seismograms (Fig. 4). The correlation maxima of the experimental and low velocity layer model seismograms are equal in value, being almost twice that for the 'Standard', crust case. The delay of the correlation peak for the synthetic seismogram is 2.0 sec, or 0.2 sec. greater than that for the Kurile seismogram. This, delay is controlled by the P-S reverberation between the surface and the basement: any attempt to decrease the delay by raising the low velocity layer results, in diminishing radial amplitudes. In order to obtain the observed delay, it appears that a 10% reduction in the P travel time through the sediments is. required. As was seen in Section 2.3, such a deviation from known sedimentary profiles is hardly toler able. The discrepancy in correlation lag thus remains unresolved. Pos sibly, a more complex large velocity contrast structure might resolve TABLE V Radial-vertical amplitude ratios of the experimental and synthetic Kurile seismograms Peak Onset Peak Radial Radial/Vertical Radial/Vertical Onset Radial Ratio Ratio Ratio Kurile Earthquake 0.47 0.13 3.5 'Standard' Crust Synthetic 0.27 0.17 1.6 Low velocity Crust Synthetic 0.46 0.17 2.7 51 both this discrepancy and the lack of similarity in character between the synthetic and experimental radial motions. The main remaining disagreement between all the model seismograms and experiment is in the vertical-radial onset ratio: experimentally, this is approximately eight, while that calculated (assuming the velocity immediately below the Leduc vault to be 2.7 km/sec) is 5.0. Even if a velocity of 2.3 km/sec is assumed, the ratio is only increased to 5.9. A surface lay er of very low velocity and thickness at least one wavelength could cause such an effect. However, the Leduc vault is situated on bedrock. The low radial onset amplitude is common to all events at all three stations: the vertical-radial onset ratio is commonly eight to ten, and often cannot be estimated with good accuracy because the noise is of com parable amplitude to the radial onset motion. One explanation of low radial onset amplitudes is the possibility that seismic waves are traveling upward more steeply than expected. The empirical curve of Ichikawa (Basham, 1967) gives an angle of incidence at the Moho i of 31.4° for the Kurile event: this is confirmed by the m value of 32.75° extrapolated from the angle of incidence at the surface using the tables of Banghar (1970). However, a vertical-radial onset ratio of eight,, as observed for the Kurile event, requires an i of m 22.5°, for a horizontal Moho, and a dip of 30° of the Moho toward the epicenter for i = 31.4°. The effect of such a dip on the azimuth m deviations (which: would be. very conspicuous) is not observed, and furthermore, the vertical-radial onset ratio does not show any pro nounced azimuthal dependence. A systematic east-of-north trend was found in the azimuths cal culated from the horizontal components compared with the great circle azimuths. The discrepancy was of the order of 10° on the average, which is in accord with the measurements by Ellis and Basham (1968) of an analogous discrepancy averaging 18° for forty events recorded at the same location. The origin of such a consistent discrepancy for various azimuths is very difficult to explain. Nevertheless, large discrepancies in azimuth can be expected in view of the large dips found by Kanasewich et al (1969) in southern Alberta. 0 30 25 20 -I 15 10 Somerville Ellis and Basham (1969) N A e 60°^ dip \ DEVIATION (East of North): \ observed az. - great circle az. ^ A A A A 4 A 4 4 l 0© / A A' A to 10 o — /-© — A \ 9 \ 4 / \ .ft 30 60 90 120 -5 \ 180 \ AZIMUTH \{deg.) N 210 A 240 274 A 300 330 360 Fig. 21 Azimuth deviations plotted against azimuth for the 15 earthquake events and 36 of the events of Ellis and Basham (1968). 53 The distribution of azimuth deviation with azimuth is shown in Fig. 21, which shows the events of both the present seismograms and those of Ellis and Basham (1968). Superimposed upon the systematic deviation there appears to be a pseudo-sinusoidal distribution. Interpreted using the tables of Niazi (1966), this represents a dip of the order of 10° in a direction 60° E. of N. Local dips of this magnitude have been determined by Kanasewich et al (1969) for the Mohorovicic and shallower reflectors in southern Alberta. In the same region, Robertson (1963), using explor ation seismograms, determined a reflector dipping at 8° to the southeast, from a depth of 8 km to 12 km over a distance of 30 km. 54 Chapter Three DISCUSSION 3.1 Evidence for a low-velocity zone in continental regions. The assumption that seismic velocities increase continuously or dis-continuously with depth in the crust was first challenged by Gutenberg (1950). Among other evidence, he observed that P velocity measured for shallow earthquakes was 5.5 - 5.6 km/sec, in conflict with the velocity of 6.0 km/sec found in explosion studies. Mueller and Landisman (1966) summarized evidence from world-wide refraction surveys of large second arrivals, termed P , which closely c follow the refracted arrival P in observations 50 - 150 km from the g shot-point. Further, they presented evidence of strong reflection ar rivals at an echo time of 4.0 sec. in West Germany. They concluded that an explanation of these reflections and refractions required the presence of a well developed low velocity channel which overlay a zone of velocity markedly greater than that in the channel and at least 0.2 km/sec high er than that above the channel. Landisman and Mueller (1966) showed how the presence of such a layer brought the previously conflicting evi dence of reflection and refraction determinations of the depth of the discontinuity into accord. More recent seismic reflection and refraction work in the Rhine-graben by Mueller et al (1969) has delineated two velocity inversions in the upper crust, which entail velocity contrasts as great as those of the 5.2 km/sec low velocity model proposed in this thesis. A section through the Rhinegraben rift system, taken from the paper of Mueller et al (1969) is shown in Fig. 22. A recent refraction survey in southern Norway by Sellevoll and Warwick (1971) has indicated the possible existence of a low velocity zone a few km thick at a depth of about 6 km beneath the west coast. The low velocity channel (6km/sec) is overlain by a layer of velocity 6.22 -6.32 km/sec and overlies a layer of velocity 6.51 km/sec. By the inversion of surface wave modes in southern Africa, Bloch et al (1969) found that a common characteristic of their models was the presence of two low velocity channels beginning at depths of 12 km 55 Fig. 22 Crustal section through the Rhinegraben rift system (after Mueller et al, 1969). 56 and 24 km. However, models without such channels can be chosen which provide dispersion curves within the error of the experimental data, so their analysis cannot definitely establish the existence of low velocity channels. Short-period surface wave, data in central Europe obtained by Schnei der et al (1965) is consistent with the presence of a low velocity chan nel. Observed group velocity maxima were found to be very close to the results of theoretical dispersion computations for a model which includes a low velocity layer. In North America, comparison between surface wave dispersion data and theoretical calculations for models based on seismic refraction results have shown discrepancies greater than the uncertainty in experimental values [Press (1960), Oliver et al (1961), and Dorman and Ewing (1962) J.. At least part of this discrepancy could be resolved by the inclusion of a low velocity zone. The zone should also provide a very efficient channel for the transmission of guided waves such as P" and L . g Evidence from other branches of geophysics lends support to the ex istence of a low velocity layer. Steinhart et al (.1962) have shown that temperature coefficients of the seismic wave, velocities determined in the laboratory and the known temperature gradients in the crust make it prob able that seismic velocities decrease with depth. This has led to the suggestion that a low velocity channel of thermal origin might be the site of shallow earthquake activity. A study by Cleary et al (1964) in the moderately stable seismic region of south-eastern Australia has shown a very prominent peak at 10 km in the depth distribution of shallow earthquakes. It has been found by Mueller and Landisman (1966) that the seismic delay between P^ and P^ measured in widely separated continental areas is approximately proportional to the heat, flow through the Earth's sur face. It appears that the P -P^ delay may be related to the thermal re gime in the low velocity channel. The smallest delays are found in shield areas, and the largest occur predominantly in tectonically active regions. Notwithstanding the above observations,, it is difficult to understand how thermal effects alone could cause the sharp velocity contrasts that most observations require of the low velocity channel. 57 Evidence for a low velocity channel has recently been obtained from seismic refraction experiments in Superior Province, Quebec by Berry (1971). The channel, at a depth of approximately 6 km, has a markedly lower ve locity than the surrounding material. Furthermore, deep reflection results at Yellowknife, N.W.T., by Berry (personal communication, 1971) show re flections from a depth of approximately 6 km. While evidence for a low velocity layer in the continental crust accumulates, there appears to be no evidence for a layer of high velocity. 58 3.2 Discussion and interpretation of results. By investigating synthetic seismograms and vertical-radial spectral ratios, a definite preference is obtained for the large velocity contrast model over the 'Standard' crustal model. The inversion is, by its nature, non-unique, and the solutions proposed cannot be considered the best pos sible ones because parameters such as Poisson's ratio and deusity were kept fixed and only the gross P wave velocity structure of the upper crust was varied. Nevertheless, in view of the wide geographic occurrence of the shear wave generation phenomenon, it seems unlikely that an alterna tive kind of explanation could prove equally adequate, particularly when the well-defined nature of the sedimentary section is taken into account. The synthetic seismograms do not show large arrivals at the travel time of approximately five seconds for P reverberations between the sur face and the large velocity contrast layer. Hence an independent test of the presence of the layer (provided by searching the experimental seismograms for these arrivals) would not be fruitful. No crustal refraction work has been done in the Leduc region. The refraction work of Cumming and Kanasewich (1966) in southern Alberta does not show any evidence for a large contrast layer. However, Robertson (1963) detected a well defined, continuous reflector over a 30 km profile in southern Alberta, and the work of Kanasewich et al (1969) in the same region, while designed for lower crustal levels, does indi cate reflectors at a depth of approximately 15 km in the vicinity of the base of the Precambrian. It may be, however, that these reflections are due to the velocity increase from 6 1 km/sec to 6.5 km/sec at the base of the Precambrian layer. In view of the evidence for a low velocity zone in a number of con tinental regions, and the absence of evidence for a'high velocity zone at this depth, it seems that the large velocity contrast layer proposed in this thesis is most likely to be a low velocity layer. For thi:, reason, in the ensuing discussion of the possible composition of the layer, a low velocity layer will be assumed. This presents more dif-ficulties in interpretation than does a high velocity layer, to which could be ascribed the composition of some basic material such as gabbro which has a P wave velocity of approximately 7;0 km/sec at the appropri ate depth (Clark, 1966). 59 By virtue of its P wave velocity of 6.1 km/sec, it appears likely that the basement material underneath central Alberta is of granitic composition. The pressure at a depth of 15 km below the earth's surface is of the order of four kilobars: at this pressure, granite has an aver age P wave velocity of 6,2 km/sec (Clark, 1966). It does not seem possible that the velocity changes entailed in the low velocity layer model can be explained without resorting to a compo sitional difference. The possible velocity inversion in granite due to temperature effects proposed by Steinhart et al (1962) does not seem capable of providing .the sharp velocity decrease that is required by the observations. H.J. Greenwood (personal communication) has pointed out that the only phase change that could occur in the upper crust is the JL~P transition of quartz, which, occurring as temperature is increased, entails a volume increase of 5%. However, for this transition to occur at a depth of 15 km would require a temperature of 700° C (Yoder, 1950) whereas the temperature at this depth is unlikely to be in excess fof 400° C. Thus the presence of a quartz phase transformation causing a low velocity in the upper crust must be discounted; Turning to a compositional change as an explanation of the low velocity layer, one finds that there are very few materials whose P wave velocities are less than 6.0 km/sec at 4 kb pressure. Greenwood (per sonal communication) has. suggested the possibility that the material of the low velocity layer might be a greenstone comppsed of chlorite and serpentine derived by the hydration of a rock of gabbroic composition. The work of Fawcett and Yoder (1966) indicates that chlorite is stable at the pressures and temperatures prevailing at the proposed depth. The gabbro may have been implaced as a sill at a depth where the hydrostatic pressure equalled that in the parent magma chamber.. P. wave velocities as low as 5.8 km/sec at 4 kb pressure have been measured for serpentinite (Clark, 1966). This is, of course, still considerably larger than the low velocity layer velocities reviewed and proposed in this thesis. Support for the hypothesis of a hydrated layer is lent by recent magnetotelluric work in Alberta. : In a magnetotelluric study at Leduc, Rankin and Reddy (1969) proposed a resistivity model in which a downward 60 decrease in resistivity of one or two orders of magnitude occurs at a depth of 5.5 km in a highly anisotropic material. The resistivity in-' creases again at a depth of 14.5 km. Rankin and Reddy (1969) interpret the results of Vozoff et al (1963) at the Kavanaugh station (13 km from Leduc, see Fig. 1) as suggesting a low resistivity zone. The other stations operated by Vozoff et al (1963), which all lie to the north of the region of the present study, do not indicate the presence of this low resistivity zone. Chapter Four CONCLUDING REMARKS 4.1 Summary Using synthetic seismograms and vertical-radial spectral ratios, the 'Standard' crustal model for central Alberta has been shown to be inadequate in explaining prominent features of teleseismic events re corded in the vicinity of Leduc. The crustal model, based on the gross crustal structure of Cumming and Kanasewich (1966) for southern Alberta and the sedimentary section of Jensen (1971) does not predict the large delayed radial arrivals that characterize the seismograms. An investigation was made into the possible modes of generation of this radial motion. . Although reverberations within the sediment ary section cause a considerable amount of shear motion at the observed delay, a detailed examination of the velocity logs in the vicinity showed it unlikely that this could be the sole source of the radial motion. The generation of. shear waves at depth was then studied, and the most favourable mechanism was the constructive interference of shear waves generated at the boundaries of a layer of large velocity contrast situated about 13 km below the surface. A layer of low velocity (5.2 km/sec) inserted at the base of the crystalline basement (6.1 km/sec) and overlying sub-layer I (6.5 km/sec) produced delayed radial motion of the required amplitude on the synthetic seismograms and considerably improved the fit between theoretical and experimental vertical-radial spectral ratios. The choice of a low velocity layer was made in view of the mount ing evidence in favour of the presence of a low velocity zone of world-wide extent in the upper continental crust. This evidence has recently been augmented by Canadian observations obtained in Superior Province, Quebec (Berry, 1971) and Yellowknife, N.W.T. (Berry, personal communication). The possible, composition of the proposed low velocity .layer is extremely problematic. Petrological and magnetotelluric evidence is in favour of a hydrated basic zone as a possible explanation. 62 The anomalously large vertical-radial onset ratios characteristic of the earthquakes recorded in the vicinity of Leduc remains unexplained. 63 4.2 Conclusions. The applicability of non-normal incidence synthetic seismograms to crustal studies has been illustrated. Using a wavelet obtained from the Kurile earthquake by the hompmorphic deconvolution technique developed by Ulrych (1971) a synthetic seismogram was obtained whose vertical com ponent agreed very well with the Kurile seismogram for the first few sec onds after onset. This lent confidence to the use of synthetic seismo grams in discriminating against unacceptable crustal models. The vertical-radial spectral ratio curves for models served as a sensitive test of layer parameters. With this integrated approach, a crustal model was obtained which fitted both synthetic seismograms and spectral ratios much more closely than the 'Standard' model. The model entails a layer of large velocity contrast with its surrounding layers at a depth of about 12 km. The use of synthetic seismograms lends a considerable amount of confidence to crustal modelling investigations. It has been demonstrated that at Leduc a horizontally layered crust can give fairly good agree ment with the experimental results. It should now be possible to de lineate more clearly the limitations of a horizontally layered model in crustal descriptions, and it can be expected that the quantity and origin of scattered energy in the crust may thereby be rendered more susceptible to description. 64 4.3 Suggestions for further work. The most direct way of confirming the existence of the proposed large velocity contrast layer would be to examine exploration seismograms re corded near Leduc for deep reflections in the manner of Robinson's work (1963) in southern Alberta. Such records may not be available, or may be of such poor quality that reflections, if observed at the appropriate depth, may not resolve the high or low velocity nature of--the-layer. A deep reflection survey would probably provide this resolution. Seismic refraction studies could lead to a clearer definition of the velocity of the layer. The areal extent of the proposed layer could be delineated by in spection of short period seismograms recorded at other locations, such as those of Ellis and Basham (1968). However, the characteristic delayed radial motion could be absent in spite of the presence of the layer, since some values of the layer thickness would cause destructive interference of shear waves at about 1 hz. In that case, vertical-radial spectral ratios could be used, although these are always subject to uncertainty as to the quantity of radial motion originating from scattering. In order to find a material having a P wave velocity as low as that suggested for a low velocity zone by many workers (5.5 km/sec), measure ments of P wave velocity in hydrated chloritic greenstones of various compositions should be conducted at about 4 kb pressure and 400° C. 65 REFERENCES Bancroft, A.M. and Basham, P.W. 1967. An FM magnetic tape recording seismograph. Pub. Dom. Obs. 35_, pp. 199 - 217. Banghar, A.R. 1970. New tables of angles of incidence of P waves as a function of epicentral distance. Earthquake Notes, 40, pp. 45 -58. Basham, P.W. 1967. Time domain studies of short period teleseismic P phases. M.A.Sc. Thesis, University of British Columbia. Berry, M.J. 1971. Velocity-depth profile in Superior Province. Physics in Canada, 2_7, 4, (Abstract). Bloch, S., Hales, A.L. and Landisman,M. 1969. Velocities in the crust and upper mantle of southern Africa from multi-mode surface wave dispersion. Bull. Seism. Soc. Am., 59_, pp. 1599 - 1629. Chandra, N.N. and Cumming, G.L. 1971. Crustal structure in western Canada. Physics in Canada, 2_7, 4, (Abstact). Clark, S.P. (ed). 1966. Handbook of physical constants. Geol. Soc. Amer. Memoir 97. Cleary, J.R., Doyle, H.A. and Moye, D.G. 1964. Seismic activity in the Snowy Mountains region and its relationship to geological structures. J. Geol. Soc. Aust., 11, p. 89. Clowes, R.M. .Kanasewich,. E.R. and Cumming, G.L. 1968. Deep crustal seismic reflections at near vertical incidence.. Geophysics, 33, pp. 441 - 451. Clowes, R.M. 19.69.. Seismic reflection, investigations of crustal structure in southern Alberta. Ph. D. Thesis, University of Alberta. Cumming, G.L. and Kanasewich, E.R. 1966. Crustal structure in west ern Canada. Priject Vela Uniform, Final Report AFCRL-66-519. Deas, A.T. 1969. A crustal study using teleseismic P phases recorded near Port Arthur, Ontario. M.Sc. Thesis, University of British Columbia. Dorman, J. and Ewing, M. 1962. Numerical inversion of seismic sur face wave dispersion data and crust mantle structure in the New York - Pennsylvania. Area. J. Geophys. Res.., 67, p. 5227. Ellis, R.M. and Basham, P.W. 1968.. Crustal characteristics from.short period P waves. Bull. Seism. Soc. Am., 5_8, pp. 1681 - 1700. Fawcett, J.J. and Yoder, H.S. 1966. Phase relationships of chlorites in the system MgO-Al^-SiO^^O. Am. Mineral., 59_, pp. 353 - 380. Futterman, W.I. 1962. Dispersive body waves. J. Geophys. Res., 67, pp. 5279 - 5291. 66 Grant, F.S. and West, G.F. 1965. Interpretation theory in applied geo physics. McGraw-Hill, New York. p. 200. Gretener, P.E.F. 1961. An analysis of the observed time discrepancies between continuous and conventional well velocity surveys. Geophy sics, 26_, pp. 1 - 11. Gutenberg, B. 1950. Structure of the earth's crust in the continents. Science, III, p. 29. Jensen, O.G. 1971. Linear systems theory applied to a horizontally layered crust. Ph.D. Thesis, University of British Columbia. Jensen, O.G. and Ellis, R.M. 1971. Generation of synthetic seismograms using linear systems theory. Submitted to Can. J. Earth Sci. Kanasewich, E.R., Clowes, R.M. and McCloughan, C.H. 1969. A buried Precambrian rift in western Canada. Tectonophysics, JS, pp. 513 -527. Landisman, M. and Mueller,. S and Fuchs, K. 1967. Further evidence for the sialic low-velocity zone in continental areas. Geophys. J. R. Astr. Soc, 13, pp. 367 - 368. Landisman, M. and Mueller, S. 1966. Seismic studies of the earth's crust in continents and adjacent shelf areas. Geophys. J. R. Astr. Soc., 10, pp. 539 - 548. McCamy, K., Meyer, R.P.., and Smith, T.J. 1962. Generally applicable solutions of Zoeppritz' amplitude equations. Bull. Seism. Soc. Am., 52, pp. 923 - 955. McDonal, I.J., Angona, F.A., Mills,R.L., Sengbush, R.L., Van Nostrand, R.G. and White, J.E. 1958. Attenuation of shear and compressional waves in Pierre Shale. Geophysics, 2_3, pp. 421 - 439. Mueller, S. and Landisman, M. 1966. Seismic studies of the earth's crust in continents, Part I: Evidence for a low-velocity zone in the upper part of the lithosphere. Geophys. J. R. Astr. Soc, 10, pp. 525 - 548. Mueller, S., Peterschmitt, E.,,, Fuchs, K. and Ansorge, J.. 1969. Crustal structure beneath the Rhinegraben from seismic refraction and reflec tion measurements. Tectonophysics, J5, pp. 529 - 542. Niazi, M. 1966. Corrections to apparent azimuths and travel-time gra dients for a dipping Mohorovicic discontinuity. Bull. Seism. Soc. Am., 56, pp. 491 - 509. Oliver,. J., Kovach, R. and Dorman, J... 1961. Crustal structure of the -New York - Pennsylvania area. J. Geophys. Res. 66, p. 215. Press, F. 1960. Crustal structure, in the California - Nevada region. J. Geophys. Res., 6\5, p. 1030. Rankin, D. and Reddy, I.K. 1969. A magnetotelluric study of resistiv ity anisotropy. Geophysics, _34_, pp. 438 - 449. 67 Robertson, G. 1963. Intrabasement reflections in southwestern Alberta. Geophysics, 18, pp. 910 - 915. Schneider, G., Mueller, S. and Knopoff, L. 1966. Gruppengeschwindig-keitsmessungen an Kurzperiodischen Oberflachenwellen in Mitteleuropa, Z. Geophys., 32, pp. 33 - 57. Sellevoll, M. A. and Warwick, R. E. 1971. A refraction study of the crustal structure of southern Norway. Bull. Seism. Soc Am., 61, pp. 457 - 471. Steinhart, J.S., Green, R. , Asada,. T., Rodrigues, A., Aldrich, L.T. and Tuve, M.A. 1962. The earth's crust: seismic studies. Carnegie Institution of Washington Year Book, 61_, pp. 221 - 231. Strick, E. 1971. An explanation of observed time discrepancies between continuous and conventional well log surveys. Geophysics, _36^ pp. 285 - 295. Ulrych, T.J. 1971. Application of homomorphic deconvolution to seis mology. Geophysics, 3_6, pp. 650 - 660. Vozoff, K., Hasegawa, H. and Ellis, R.M. 1963. Results and limitations of magnetotelluric surveys in simple geologic situations. Geophysics, 28, pp. 778 - 792. Wuenschel, P.C. 1965. Dispersive body waves - an experimental study. Geophysics, 3i0_, pp. 539 - 551. Y6der, H.S. 1950. High-low quartz inversion up to 10,000 bars. Trans. Amer. geophys. Union, _31, pp. 827 - 835. 68 APPENDIX Homomorphic deconvolution. The wavelet used in the generation of synthetic seismograms was ob tained by Ulrych (1971) by applying the homomorphic deconvolution tech nique to the experimental Kurile seismogram. This appendix describes the principles of this non-linear filtering technique. When approaching the problem of filtering signals that have been ad-ditively combined, we usually choose a linear system because of the ana lytic convenience of the fact that linear systems satisfy the principle of superposition. This principle requires that if <fi is the system trans formation, then for any two inputs x^(t) and x^(t) and any scalar c, 0 [ X;L(t) + x2(t) ] = jrJ [ xr(t) ] + <f> [ x2(t) j and $ [ c.x(t) ] = c.^ [ x(t) ] This principle, as it stands, applies only to signals that have been additively combined. For this reason, when a filtering procedure to sep arate signals that have been combined by other means (such as by multipli cation or convolution) is to be chosen, it is usually more difficult, and often less meaningful, to use a linear system. In our case, the seismogram is conceived as being generated by the convolution of a wavelet with an impulse series.. Without making prior assumptions, the separation of these two components is not possible using the concept of linear filtering that has been described. Nevertheless, we can expand the concept of linear filtering so that it encompasses signals combined in ways other than by addition. Our first step is to generalize the principle of superposition so that it applies to operations other than addition of inputs, and multiplication' of inputs by scalars. Such a general principle of superposition is 4> [ x±(t) „ x2(t) ] = <f>[ X;L(t) ] 0 <f> [ x2(t) ] 69 and ^1 cAx(t) J = c*f[ x(t) J , where ° and * are generalized operations. We now. regard the linear super position principle as the one in which ° corresponds to + , and * corres ponds to •. The second step in linearizing our problem is to find a transforma tion of the inputs into a vector space in which the rule of combination of inputs becomes the rule of vector addition, and the rule of combina tion of inputs and scalars becomes scalar multiplication. (The equivalent requirements for the set of outputs is guaranteed by the requirement that the inputs constitute a vector space .and that the transformation satisfy the principle of superposition). We are thus selecting from the group of all systems which satisfy the principle of superposition the subgroup of homomorphic systems which are those ones which can be represented as linear transformations between vector spaces. A non-linear homomorphic filtering process is one which: i) by A, transforms the space of input vectors into one in which the law of combination of vectors is addition (corresponding to a linear space). ii) by L, performs the required, filtering operation, linearly, and iii) by A \ inverts from the additive space back to the original one. Thus a canonic representation of the non-linear homomorphic filtering process can be depicted as shown in Fig. Al(a). The filter A is character istic of the class in that it depends only on the operations ° and *, and hot on the details of the required filtering operation. A is such that A[ x1»x2 ] = A[ x1 ] + A[ x2 ] and A[ c*x ] = c.A[ x ] A_1 is such that A_1[ A[ x(t) ] ] = x(t) 70 o + h + A L A"1 1 • • 1 Fig. Al(a) Canonic representation of the homomorphic filtering process. Pi 7 tts. + + + + + ,+ +/ + log 7 In L • * Fig. Al(b) Characteristic system for a homomorphic deconvolution filter. / 71 A common approach to deconvolution is the method of inverse filtering, which requires a detailed description of the component to be removed. In the case of seismic deconvolution, this description is obtained by: i) assuming a random series of spikes to represent the reflecting layers, so that the wavelet autocorrelation can be obtained from the trace autocorrelation; and ii) in ignorance of the phase spectrum of the wavelet,, assuming it to be minimum phase, so that it can be obtained easily from,its power spec trum. The homomorphic. method of deconvolution obviates the..need of making such assumptions. The characteristic system for two convolved signals s and n can be represented as. in Fig. Al(b) . The third operation within the characteristic filter A produces the 'complex cepstrum' of the input n*s : although it may appear to. be. operationally superfluous ...to. the filter ing process, it has great analytic convenience. Consider the. echoed signal.generated by the convolution of:a. wavelet with a pair of impulses as shown in.Fig. A2, This signal can be written: x(t) = s(t) +. s(tVr) = s(t) * [ J(t) +4<J<t-V)] Taking its Fourier transform, X(w) = S(W) [ .1 +-(e"1Wr ] The complex logarithm of this is log[ X(w) J = log|s(W)| + log( 1 +o<e"i<0r) The second term in this expression is periodic in with a repetition rate proportional to the delay time . The spectrum of this term would therefore exhibit a peak at this delay time, and would thus prove useful in interpretation. Because we are thereby thinking in spectral terms while we are really in a time domain, this is called the complex 'cepstrum'. The cepstrum is the inverse Fourier transform of the complex logarithm of the Fourier transform of the function x(t), i.e. F"1 ( log[ F( x(t) •)] j 72 Input wavelet Impulse series Convolution of wavelet with impulse series Fig. A2 Synthesis of a signal using a wavelet and an impulse pair. 73 The complex cepstrum of the signal of Fig. A2 is shown in Fig. A3, In this case, because the spectrum of the wavelet is of lower frequency content than that of the impulse pair, the spike series in the complex cepstrum is well separated from the complex cepstrum of the wavelet, which appears at the central part of the cepstrum. By low-pass filtering the complex cepstrum and applying the inverse characteristic, filter A: \ the wavelet is recovered (Fig. A3). Similarly, by applying a high-pass filter and then the inverse filter, the impulse pair is obtained. The Kurile earthquake seismogram recorded at Leduc,. its complex cepstrum, and the deconvolved wavelet and impulse series are shown in Fig. A4. 74 Deconvolved wavelet Fig. A3 Complex cepstrum and recovered wavelet from the signal of Fig. A2. 


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