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Seismic interferometry using non-volcanic tremor in Cascadia Chaput, Julien 2006

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SEISMIC I N T E R F E R O M E T R Y USING NON-VOLCANIC T R E M O R IN CASCADIA by Julien Chaput B . S c , Universite de Moncton, 2004 A THESIS S U B M I T T E D IN P A R T I A L F U L F I L L M E N T OF T H E R E Q U I R E M E N T S F O R T H E D E G R E E OF M A S T E R OF S C I E N C E in T H E F A C U L T Y OF G R A D U A T E S T U D I E S (Geophysics) T H E U N I V E R S I T Y OF B R I T I S H C O L U M B I A September 2006 © Julien Chaput, 2006 Abstract T h e Green's function for a source and receiver located on the Ear th ' s surface over a heterogeneous medium can be recovered by cross-correlating and integrating the transmission response of noise fields recorded at the two surface locations. T h i s assertion relies on the assumption that the noise field is generated by random, independent sources dis tr ibuted over a surface surrounding the heterogeneity, w i t h the dominant contributions to the integral over source location occur-r ing at stationary points of the integrand for a given structure. T h e majori ty of seismological research on seismic interferometry to date has focussed on surface wave applications, due in part to the general absence of deep, high-frequency noise sources. In this study, I inves-tigate the possibil i ty of using the recently documented, deep-seated, non-volcanic tremor on the Cascadia subduction zone as a noise source for seismic interferometry to recover scattered body wave contr ibu-tions to the surface Green's function. Tremors i n the v ic in i ty of the P O L A R I S - B C array for 2004 and 2005 were documented, and data for stations T W K B , M G C B and L Z B were filtered and cross-correlated for a l l components of stations pairs T W K B - M C G B and T W K B - L Z B . T W K B and M G C B correlations are generally superior, generating a ii large highly reproducible arrival at 4.5 s in 2004 and 2005 for combi-nations of vertical with radial or transverse components. T W K B and L Z B correlations are less reproducible, but still yield, for the same components, a strong arrival at 3.5 s for 2005. Upon consideration of source/receiver geometry, polarity and appearance at positive ver-sus negative lags, I interpret these arrivals to represent contributions travelling as S-to-P-to-S en route from source to free-surface to scat-ter er to receiver. Arrival times suggest that these signals originate at depths between 9 and 12 km, coincident with an interval of strong reflectivity imaged in the 1987 Lithoprobe Vancouver Island transect. i i i Contents A b s t r a c t i i C o n t e n t s iv L i s t o f F i g u r e s v 1 I n t r o d u c t i o n 1 2 T h e o r e t i c a l B a s i s 3 2.1 Deterministic derivation 3 2.1.1 Acoustic derivation 4 2.1.2 Elastodynamic expansion and practical approximations 8 2.2 Par t ia l source sampling 11 3 E x p e r i m e n t a l G e o m e t r y 15 4 D a t a P r o c e s s i n g 18 5 R e s u l t s a n d I n t e r p r e t a t i o n 22 5.1 Cross-Correlation Results . . . . : 22 5.2 S P S reflection/conversion 25 5.3 Comparison wi th Lithoprobe Reflection Profiles 27 5.4 Limitat ions and points of interest 27 6 C o n c l u s i o n s 32 iv List of Figures 1 Model l ing of "ghost signals" wi th relation to source distribu-t ion (Wapenaar, 2006). a) A uniform source distribution along dV leads to a coherent integration of contributions from out-side the closed domain of interest, b) A randomized source distribution wi th respect to dV causes the ghost signals to break while not affecting physical signals 9 2 a) Schematic model involving a single horizontal reflector be-tween two surface stations A and B wi th a sources to one side only. Sources wi thin the first Fresnel zone of the station-ary point wi l l contribute to the true reflected arrival, whereas other sources wi l l produce non-stationary non-physical arrivals, b) Signals recorded at stations A and B . T ime reversing sig-nal A in the cross-correlation wi l l result in a non-zero causal contribution on the correlation 13 v Geographical setting. Black arrow indicates direction of E T S path progression across southern Vancouver Island. The lo-cation of Lithoprobe Line 2 is indicated on the inset. Whi te circles indicate tremor locations for 2005, grey squares indicate tremor locations for 2004, and white triangles represent P O -L A R I S and C N S N stations. The dashed ellipses indicate the spatially clustured sources which contribute to reproducible arrivals for both years a) 8 hours of raw tremor data featuring artificial transients (time domain), b) Result of a wavelet transform of the raw data; tremor noise is removed, c) Data wi th transients re-moved v ia wavelet transform, d) F ina l de-spiked data after hard threshold a) Typica l tremor power spectrum featuring anomalous fre-quency content, b) Non tremor-related reproducible signal at 3.43 Hz. c) Notch filter impulse response, used to remove anomalous frequency content in b) v i 6 Examples of correlated data displaying large coherent arrivals. M a i n variables denote correlated components, * designates complex conjugation, subscripts define stations involved ( T = T W K B , M = M G C B , L = L Z B ) and —a or — c defines the acausal or causal portion of the correlation 23 7 Grey lines in a), b), represent correlations between T W K B and M G C B for the 2005 E T S event, and the black plots rep-resent correlated data for the 2004 E T S event. Labels -a or -c indicate whether the causal or acausal portion of the cor-relation is plotted, c) Stacked data for correlations between stations T W K B and L Z B for 2005. Grey traces display causal correlated data from 2005, black traces show acausal corre-lated data for 2005. Note 3.5 s arrival appearing on causal lags. 24 8 Reflection survey data for line 2 from Lithoprobe 1987 South-ern Vancouver Island transect. Dominant arrivals in our ap-plication would seem to correspond to conversion/reflections from the B a n d C layers. 28 v i i Synthetic model from V a n Manen et al (2005). The left figure represents two receivers A and B embedded in an inhomoge-neous medium, wi th an impulse source distribution on dV. The right figure shows the cross-correlation of the wavefield for each individual source location. M a i n contributions to the integral over dV as denned by (10) occur at stationary points of the integrand, where sequential sources produce flat sig-nals wi th little moveout. Note that for any given source, the causal and acausal portions of the correlations are not sym-metric, but the final stack of al l the data produces the full two sided Green's function. v i i i 1 Introduction Determination of an accurate Green's function from recordings of scattered seismic waves has been the subject of much research over the years, and various means have been developed to accomplish this task. For example, reflection seismology often makes use of V ib rose i s© technology to impart elastic energy in the form of a frequency sweep into the ground. Since the source is known to a good approximation, an accurate reflection impulse re-sponse can be obtained through deconvolution or matched filtering. The use of anthropogenic sources place limits, however, on the depth of investigation. Moreover, the logistical effort of deploying truck convoys to the target region can be challenging, not to mention that the V ib rose i s© experiments are also costly. In teleseismic earthquake seismology, powerful natural sources, earthquakes, are used to probe structure to greater depths. In this case, the "receiver function" approximation (Vinnik, 1977; Langston, 1979) is made to remove the effect of the source, thereby introducing some degree of error, in particular regarding scattered P-waves (Mercier et al, 2006). Also, since the distribution of earthquakes tends to be concentrated along plate bound-aries, there are geometrical constraints placed on the imaging of subsurface structure. 1 A third and independent approach to extracting scattered wave Green's functions was presented by Claerbout (1968), who demonstrated that the subsurface reflection profile could be recovered through cross-correlation of seismic noise recorded at the surface from noise sources at depth. Motivat ion for this approach resides in the fact that no source estimate is required, as cross-correlation largely eliminates the source signature. Pract ical demon-stration of this concept has been accomplished in various settings (and fre-quency bands) including helioseismology (Duvall et ai, 1993), ultrasonics (Lobkis and Weaver, 2001), and solid earth seismology (Campillo and Paul 2003, Shapiro et al, 2005, Shapiro and Campil lo, 2004, Roux et al, 2005). Most solid earth applications have involved surface waves since the dominant noise sources are located close to the surface, and surface waves suffer less geometric loss and attenuation than body waves. The work of Roux et al, (2005) represents an exception in that these authors identified the directly transmitted P-wave from correlations at seismic stations near Parkfield Ca l -ifornia. To-date, however, there has been little practical demonstration that weaker, scattered body-wave phases can be recovered from cross-correlations. The goal of this thesis is to investigate the feasibility of using the re-cently documented non-volcanic Episodic Tremor and Slip (ETS) events in 2 the northern Cascadia subduction zone (Dragert et al, 2003) as a novel, deep-seated noise source to recover the scattered body wave Green's func-t ion wi thin an active subduction zone through cross-correlation. I wi l l begin by laying out a general derivation for acoustic seismic interferometry as de-veloped by Wapenaar and Fokkema (2005), then proceed to note the approx-imations required for practical application, including the stationary phase argument and its implications to Green's function recovery. I shall then briefly describe the Episodic Tremor and Slip (ETS) events on the Cascadia subduction zone, and state some justifications as to why these tremor events satisfy the requirements of seismic intereferometry. I wi l l then describe the experimental geometry used here, and proceed to lay out the results and give interpretations yielded by the data. 2 Theoretical Basis 2.1 Deterministic derivation In this section, I wi l l provide a brief overview of the governing theory for seismic interferometry based on derivations from works by Wapenaar and Fokkema (2005) and Snieder (2004), and then develop some physical argu-3 merits pertaining to our experimental geometry. 2.1.1 Acoustic derivation Claerbout (1968) demonstrated that the acoustic reflection profile of a hori-zontally stratified 1-D medium could be obtained through autocorrelation of the transmission response of a white noise source in the subsurface. I wi l l adopt the simplest scenario, as layed out by Wapenaar and Fokkema (2005), to develop the governing equations for the 3D acoustic scenario, and worry about the elasto-dynamic case later. The following derivation is entirely in the frequency domain, and I've chosen to replace p wi th p, where p normally defines the fourier transform of p . This applies to al l variables, and is imple-mented to simplify notation. For a lossless inhomogenous open fluid medium (i.e. no free surface), the acoustic pressure p and the particle velocity v obey the equation of motion and the stress-strain relation where / j denotes the external volume force density, q volume injection rate density of source distribution, j the imaginary unit, K the compressibility, 4 j u p v i + d t p = f i (1) j u K p + d i V i = q , (2) and to the angular frequency. Given two states A and B (may be viewed as two receiver points within the medium), the subsitution of. (1) and (2) into the following identity yields, when integrated over a closed spatial domain V and modified through the divergence theorem, / \PAQB ~ vi}Afi,B ~ QAPB + /i,A^i,s]rf3x ( 3 ) = \PAVZ,B ~ vitApB}nid2x:. This expression is the acoustic reciprocity theorem of the convolution type. Since the wave equation is invariant for time reversal, the complex conjugates of p and v also obey (1) and (2), yielding in a similar fashion / \p*A,qB + vZAfitB + q*APB + fUvi,B]d3X ( 4 ) = Jgv\P*Avi,B + < I A P B ] M 2 X , which is the reciprocity theorem of the correlation type. Intuitively, these theorems may be viewed as 3 D generalizations of the ID vertical power flux conservation theorem. In order to obtain expressions for acoustic Green's functions from these theorems, qA<B is denned as an impulse source in (2). We define therefore: qAtB(x.,u) = <5(x - XA,B) , where states A and B are both in V. In this case, the pressure measurement at a spatial point x is chosen to be strictly equal to the Green's function at that point, such that: pAtB(x,u) = G ( X , X A , B , W ) , (5) and from the equation of motion (1): * M , B ( X , W ) = -0 'wp (x ) ) - 1 diG (x ,x A ] B , u ; ) . (6) As the Green's function in this description obeys the wave equation, we may substitute (5) and (6) into the reciprocity theorems. Substi tut ion into the convolution type reciprocity theorem yields the source-receiver reciprocity relation: G ( x B , x A , w ) = G(xA,xB,u), (7) 6 whereas substitution of (5) and (6) into the correlation type reciprocity the-orem yields a different result; 2U[G{xA,xB,u)} (8) = / -l/jup(x)(G*(x.A, x, u)diG(xB, x, u)-(diG*{xA, x, CJ )G(X b , x, cu))rijd2: J av where 3ft denotes real part, * represents complex conjugate, UJ is frequency, j is the imaginary unit and p is density. Equat ion (8) is the basis for acoustic seismic interferometry, though it is not well suited for practical applications. As writ ten, it requires the presence of both monopole and dipole sources, and the spatial integral implies that we must have perfect knowledge of source locations over dV in order to measure their responses individually. Also, this equation is exact, in that it encompasses al l possible ray paths, including reflections from scatter points inside and outside the closed domain denned by dV. This last statement can however be subjected to a useful approximation if the source distr ibution on the surface dV is fairly random with respect to the normal vector to dV, noted (n*). From an intuitive standpoint, should the source distr ibution not be random, reflections from scatter points outside dV which are the product of an out-going source ray to the reflector and in-going source ray to the receiver wi l l be coherently integrated into (8) (figure 7 1). Note that the t iming of such arrivals depends heavily on the contributing source's exact location around n* and corresponds, once cross-correlated, to non-physical signals. Should the source distribution be random, these non-physical signals are not coherently integrated without affecting the true arrivals, and thus for a single reflector, it is possible to recover structural signals from outside the source distribution. Snieder (2006) however noted that for multiple reflectors, there exist ghost signals that cannot be cancelled unless we have a source distribution that extends beneath the reflectors. In any case, should the source distribution be fairly random on dV, (8) can be approximated as: 2 K [ G ( x A , x B , u)] = I - l/jup(x)(G*(xA, x , u)diG{xB, x, u ; )n i ( i 2 x. (9) J dV 2.1.2 E l a s t o d y n a m i c e x p a n s i o n a n d p r a c t i c a l a p p r o x i m a t i o n s Naturally, when one deals wi th an applied scenario, recovering the pressure Green's function is impractical, and the acoustic case is incomplete. The elastodynamic generalization can be derived in much the same fashion by including force and deformation into the source description. Note also that the recovered Green's function is a velocity Green's function, which is far 8 Figure 1: Model l ing of "ghost signals" with relation to source distribution (Wapenaar, 2006). a) A uniform source distribution along dV leads to a coherent integration of contributions from outside the closed domain of in-terest, b) A randomized source distribution wi th respect to dV causes the ghost signals to break while not affecting physical signals. 9 more suited to practical applications. In the elastodynamic case: 2 K [ G ^ . ( x A , x f l ; UJ)] = 2/jup f [diGl'^A, x , u)]*Gvq>%{-KB) x , ^)n^ 2 x J dV (10) « 2 / p C p ( ^ * ( x A , a ; ) i ; f (xB,u;)>, where cp is P-velocity. The frequency domain Green's functions are defined as follows: G ^ ( x A , x B , a;) is the particle velocity in the pth direction at point x A due to an impulsive body force in the qth direction at point x#, whereas Gp'xfaA, x , u>) is the particle velocity in the pth direction at xA due to a modal source generating P (K = 0) or S (K = 1, 2, 3) waves wi th different polariza-tions at point x . The surface integral in (10) is taken over a closed surface dV with normal n . that includes the free surface and the locations of independant random noise sources in the subsurface. The Green's functions are thereby re-lated to cross-correlations (multiplication wi th complex conjugate in the fre-quency domain) of observed particle velocities v°bs*(x.A, u>)v°bs(x.s, UJ) due to the same random noise sources. Extract ion of the real part 3?[Gp^(x A , x B , ui)] implies equivalence between the causal and acausal portions of the correla-tion in the time domain. Note also that the velocity Green's function obeys the reciprocal relation: 10 G£j(xA,xB,a;) = G££(xB,xA >a;), (11) as derived from the reciprocity theorem of the convolution type. The approximation in (10) requires a few assumptions. To begin with, a high frequency approximation is applied, thereby reducing the dipole re-sponse to an expression involving only a monopole response, such that: d i G p ^ X A , x , uj)ttjoj/cKGvp'*K(x.A, x , w ) Moreover, a perfect mapping of source locations as required by the spatial integral in (10) is generally not readily available. A solution to this prob-lem arises when we replace the impulse sources on dV wi th a distribution of uncorrelated noise sources. The approximation in (10) implies that transmis-sion responses from all sources can be read simultaneously, thereby reducing the spatial integral to a simple correlation. 2.2 Partial source sampling It is useful to note for interpretation purposes that the main contributions to the Green's function occur at stationary points of the integrand within the strict equality of (10) (see figure 2) (Snieder, 2003)), and this fact can 11 be exploited to gauge the effect of an incomplete sampling of sources on the resulting estimates of Green's functions. Figure 2a displays a simpli-fied scenario that wi l l help illustrate several points important to subsequent discussion. Consider 2 stations A and B symmetrically located at the free surface above a narrow horizontal reflector segment wi thin an otherwise ho-mogeneous medium. Idealized seismograms (high frequency, single scatter-ing, acoustic) recorded at both stations for an impulsive source located below the reflector segment to the left of both stations are shown in figure 2b. Ig-noring the effect of edge diffractions, one would expect the seismogram at station A to be dominated by the direct arrival from the source, whereas the recording at station B wi l l display both the direct arrival and an additional stationary, scattered arrival (specular reflection) from the reflector afforded through reflection of the direct wave at the free surface. Cross-correlation of the two seismograms (i.e. convolution of the seismogram at B wi th the time reversed seismogram at station A ) largely removes the time delay associated wi th the propagation of the first upgoing transmitted wave. Moreover, the cross-correlation is one sided, wi th al l energy appearing at positive (causal) lags. Under the assumption that the second pulse on the cross-correlation is stationary for this particular source-receiver geometry, it w i l l represent the 12 a) A B / / / ^ \ , ? x / Free surface - ' ' ' •/ ' * ' '/ ' ' ft ' \ N / ' / ' * / ' * ' '/ \ \ / / s \ / Reflector • / / , - © Stationary point source • Non-stationary source — Stationary ray paths - - Non-stationary ray paths b ) A B (A*)(B) 0 0 Causal Figure 2: a) Schematic model involving a single horizontal reflector between two surface stations A and B with a sources to one side only. Sources wi thin the first Fresnel zone of the stationary point wi l l contribute to the true reflected arrival, whereas other sources wi l l produce non-stationary non-physical arrivals, b) Signals recorded at stations A and B . T ime reversing signal A in the cross-correlation wi l l result in a non-zero causal contribution on the correlation. 13 primary contribution to the reflection appearing in the Green's function for a source at A and a receiver at B (or vice versa due to (11)). B y extension then, if the available source distr ibution were l imited to the left-hand side of the surface dV in figure 2, a reasonably complete reflec-t ion Green's function would be recovered from only the one (causal) side of the correlation. For elastic waves one faces the added complexity of excita-t ion/observation component directions. Since the source/receiver geometry defines both the port ion (causal or acausal) of the correlation on which sta-t ionary arrivals wi l l occur and the basic ray geometry, the polarization di-rection of the wavefield on both the up-going (receiver side) and down-going (source side) portions of the raypath can be readily inferred. Should we have instead a more complete, two-sided distr ibution of sources over a surface dV as defined by (10), we would expect to recover a correla-t ion for which both sides were symmetric and corresponded to the Green's function that would be recorded if a source were located at one station and recorded at the other. This assertion is, however, dependent on the sources uniformly exciting al l modes (P,S), a condit ion that, if not met, wi l l also lead to a break in the symmetry implied in (10). The main points to take from this simple analysis are: i) true reflections 14 within the Green's function wi l l be built up from free surface reflections of transmitted waves created at depth from stationary points in the integrand of (10), ii) if gradients in material properties are dominantly vertical and if the source distribution is dominantly to one side of the station pair, we expect to see meaningful contributions to the Green's function on only one side of the cross-correlation, and iii) the vectorial components of up and downgoing waves that constitute a particular scattered signal on the recovered Green's function can also be inferred from the source-receiver (transmission) geom-etry or, equivalently, from the portion (causal/acausal) of cross-component correlations on which that signal appears. 3 Experimental Geometry The map in figure 3 displays the epicentral distribution of E T S events in northern Cascadia for episodes in July 2004 and September 2005, as deter-mined using the Source-Scanning Algor i thm (Kao et al, 2005, pers. comm.). E T S events occur every 13 to 16 months, and last from 10 days to a month as they move from the south-east in northern Washington to the north-west along southern Vancouver Island (Rogers and Dragert, 2003, K a o et al, 15 Tremor locations for July 2004 and September 2005 Figure 3: Geographical setting. Black arrow indicates direction of E T S path progression across southern Vancouver Island. The location of Lithoprobe Line 2 is indicated on the inset. Whi te circles indicate tremor locations for 2005, grey squares indicate tremor locations for 2004, and white triangles represent P O L A R I S and C N S N stations. The dashed ellipses indicate the spatially clustured sources which contribute to reproducible arrivals for both years. 16 2005). I employed 3 stations of the P O L A R I S - B C array (Eaton et al, 2005; Nicholson et ai, 2005) on Vancouver Island to recover tremor data for the July 2004 and September 2005 E T S events. The precise mechanism of E T S is not yet understood, and tremor depths can vary from 10 to 60 km. Tremor data satisfy several key requirements for recovery of scattered body wave Green's functions using seismic interferometry, namely: i) a quasi-random source signature wi th near constant power spectrum in the frequency band of interest (1.5-10 Hz); ii) a source distribution that extends to depths below the target levels of interest, and iii) a wavenumber spectrum that is domi-nated by body wave energy (La Rocca et al, 2005). A l l tremor events wi thin the near vicinity of P O L A R I S - B C stations L Z B , M G C B , and T W K B were identified from epicenter compilations (see figure 3) and corresponding seis-mograms were accessed using the Geological Survey of Canada automated server. O n the basis of factors discussed in section 2, this station-event ge-ometry was judged to afford the best likelihood of revealing structural signals using seismic interferometry. 17 4 Data Processing The first task in preparing the data for analysis was to remove artificial high-amplitude transients using a combination of wavelet transform (Donoho et al) and thresholding techniques. Figure 4 displays the removal of high ampli-tude transients v ia wavelet transform and hard thresholding. The wavelet transform technique convolves the raw data (figure 4a) wi th a wavelet of ar-bitrary order, and finds the time lags at which the data matches the wavelet, for a user defined threshold of correlation. These transient wavelets (figures 4b,c) are then removed from the original data. However, some transients do not display wavelet-like signatures, and thus are not removed through a wavelet transform. The effect of these non-wavelet transients is dimin-ished through the use of a simple hard threshold, applied at eight times the standard deviation of tremor data (figure 4d). For data relating to the 2005 E T S events, an additional notch filter is applied to remove a particularly reproducible harmonic contribution at 3.43 Hz which dominates the data. This signal is apparently not related to the tremor signature as it is visible throughout the entire year of 2005 and ap-pears on every station of the Polar i s -BC array (thus also eliminating the pos-sibility of a local phenomenon). Figure 5a shows a typical 2005 tremor power 18 a) 1.5 1 0.5 0 -0.5 -1 -1.5 x 10 Raw data b) c) 0 2 4 6 Hours of data Data with transients removed 2 4 6 Hours of data 1.5 1 0.5 0 -0.5 -1 -1.5 x 10 Wavelet matched tansients d) 1000 500 -500 -1000 2 4 6 Hours of data Final thresholded data 2 4 6 Hours of data Figure 4: a) 8 hours of raw tremor data featuring artificial transients (time domain), b) Result of a wavelet transform of the raw data; tremor noise is removed, c) Data with transients removed via wavelet transform, d) Final de-spiked data after hard threshold. 19 x 10 Tremor power spectrum a) 6 4 2 0 b) 0.04 0.03 0.02 0.01 ^^ ^^ ^^ ^ 4 5 6 7 Highly reproducible transient ...i . . . i i t _ j, • L . 1 . - - I . - . . . - . .. . . . . . c) 3.34 3.36 3.38 3.4 3.42 3.44 3.46 Notch filter impulse response 3.48 3000 2000 1000h -100 'Hz 100 200 300 400 500 10 3.5 H _ 3.52 600 Figure 5: a) Typica l tremor power spectrum featuring anomalous frequency content, b) Non tremor-related reproducible signal at 3.43 Hz. c) Notch filter impulse response, used to remove anomalous frequency content in b). 20 spectrum between 1.5 and 10 Hz wi th a few frequency spikes, the largest of which is the problematic 3.43 Hz signal (figure 5b). Figure 5c shows the impulse response of the notch filter used to remove the frequency spike. The fact that this particular frequency spike appears more strongly on coastal stations suggests a sea to land conversion, possibly of US navy submarine communications, which employ the noted Extremely Low Frequency band (3-30 Hz) (See Wikipedia , on E L F frequency band). Other frequency spikes noted in figure 5a seem to be local, as they appear randomly throughout power spectra of various tremor events. The data were then divided into 30 minute segments, tapered, and fi l-tered using a 1.5-10 Hz band-pass Butterworth filter in order to isolate the tremor signature. I detrended the filtered data, rotated them into a ra-dial (R), transverse (T) and vertical (Z) coordinate system as defined by the station locations, and cross-correlated the results for a l l components of sta-tion pairs T W K B - M G C B and T W K B - L Z B . Same-station, cross-component correlations and autocorrelations were also computed. I opted to always time reverse components of station T W K B in the correlations. Correlated data were then amplitude normalized and stacked to investigate the presence of possible structural arrivals. 21 5 Results and Interpretation 5.1 Cross-Correlation Results Figure 6 shows several panels of the first 10 s of cross-correlated 30 minute data segments prior to stacking. These examples display several sig-nals exhibiting little moveout as observed for most combinations of cross-correlations involving component Z wi th components R or T. Figure 7 shows examples of cross-correlations after stacking for which these same strong ar-rivals persist.A remarkable aspect of many correlations involving T W K B and M G C B is their reproducibility between the tremor events of 2004 and 2005 (Figures 7a and 7b). This observation, especially relevant for same-station correlations but also for some cross-station correlations, strongly suggests that the tremor signature has been removed, and that we are left wi th some form of structural response. The most prominent later arrival for stations T W K B and M G C B occurs at 4.5 s, and is evident in both same-station and cross-station cross-correlations for combinations of component Z wi th components R or 77. For cross-correlations between L Z B and T W K B , (Fig-ure 7c) an arrival occurs at 3.5 s and although not as reproducible between years as results from T W K B - M G C B , it appears strongly on correlations of 22 2005 event, FijZj-a Ui I 4 o <_) a. 6 E 8 10 I 2 4 20 40 60 2005 event, flT2,, -a to o •2- 6 <u E 8 10 20 40 60 (0 C o o at E 2 4 6 8 10 2005event, 20 40 f - - :V IFTCTloitr 60 2 Ui pu 4 o o CD in. 6 CD E P 8 10 2005 event, ZTJ< — -i 20 40 60 80 Figure 6: Examples of correlated data displaying large coherent arrivals. M a i n variables denote correlated components, * designates complex conju-gation, subscripts define stations involved ( T = T W K B , M = M G C B , L = L Z B ) and —a or —c defines the acausal or causal portion of the correlation. 23 a) b) 0.5 0 -0.5 [ 0.5 0 -0.5 0.5 | ol -0.5 [ 4/ R^Z^-a ~ — v M - a 0.5 0 -0.5 05 0 -0 5 4f JIMlv 0 2 4 6 Time (s) 2 4 6 8 Time (s) c) 0.5 0 -0.5 I 0.5 0 -0.5 2 4 6 Time (s) 8 10 Figure 7: Grey lines in a), b), represent correlations between T W K B and M G C B for the 2005 E T S event, and the black plots represent correlated data for the 2004 E T S event. Labels -a or -c indicate whether the causal or acausal portion of the correlation is plotted, c) Stacked data for correlations between stations T W K B and L Z B for 2005. Grey traces display causal correlated data from 2005, black traces show acausal correlated data for 2005. Note 3.5 s arrival appearing on causal lags. 24 Z wi th both R and T for the 2005 sequence. For both station combinations in 2005, the strong arrivals emerge from spatially clustered tremor events to the northeast of the stations as shown in figure 2. If the tremor source moves in a stable, steady fashion, we would expect strong arrivals exhibiting little moveout in the cross-correlations to correspond to stationary points of the integral in (10), and thus to represent physical signals, e.g. specular reflections (Van Manen et al, 2005, Snieder 2004). 5.2 SPS reflection/conversion To develop a physical interpretation for these signals we must examine their temporal, spatial and directional attributes. Consider first the 4.5 s arrival for T W K B - M G C B . Its presence on cross-component correlations suggests that it represents a conversion-reflection mode. Moreover, it is most clearly exposed on causal portions of correlations Z ^ R M and Z ^ T M and acausal portions of correlations R ^ Z M and T ^ Z M , where subscripts T, M , L denote stations T W K B , M G C B , L Z B , respectively. The source-station geometry (see earlier discussion in section 2) along with these combinations of components and t iming imply a dominantly vertically polarized wave downgoing at station T W K B which is converted-reflected in the subsurface to produce an upgoing 25 wave polarized in the horizontal plane at station M G C B (see figure 2). This analysis, combined wi th the observation that E T S generates dominantly S waves (La Rocca et al, 2005), suggests an S-P conversion at the free surface followed by a P-S conversion-reflection from the heterogeneity, or an S-P-S wave path. The t iming of the signal at 4.5 s places the likely depth of the reflector at approximately 10 km. A s previously mentioned, the T W K B - L Z B arrival at 3.5 s is less well defined. Here we note that the source/station geometry is rather different from that for T W K B - M G C B . The 2005 tremor sequence, for which the 3.5 s arrival is most pronounced, extends further to the N E than the 2004 sequence, which is distributed more nearly parallel to the line joining T W K B and M G C B (figure 3). Sources further to the N E may be more suitably positioned therefore to produce stationary arrivals that are not represented in the 2004 tremor sequence. The 3.5 s arrival for the 2005 sequence is best defined on the causal portions of correlations Z ^ R L , Z^TL and a little less clearly on Z ^ Z L . This combination of components and source-receiver geometry is once more consistent wi th interpretation as an S-P-S wave path. We also note that the greater distance between sources stations and the earlier arrival time (3.5 s versus 4.5 s) are both consistent with an origin from shallower structure. 26 5.3 C o m p a r i s o n w i t h L i t h o p r o b e R e f l e c t i o n Pro f i l es For additional insight into the nature of subsurface structure responsible for these arrivals, we compared results wi th seismic reflection data collected as part of the Lithoprobe southern Cordil lera transect (Clowes et al, 1987). Seismic lines 2 and 4 are located a few k m to the south-west and east of our station pairs L Z B , T W K B , M G C B (see figure 3). The corresponding reflection profiles image a sequence of strong reflectors between 9 and 14 k m depth that dip at approximately 20 degrees in a northerly direction. From basic calculations using a simple velocity model (Nicholson et al, 2005) it was noted that the t iming of the 3.5 s and 4.5 s arrivals would be consistent wi th origins from the depth interval corresponding to the B and C layers (figure 8). 5.4 L i m i t a t i o n s a n d p o i n t s o f in te res t To conclude our discussion we consider the limitations of the imperfect source distribution represented by the tremor events. We generally note short lag (i.e. [-0.5 s,0.5 s]) large amplitude signals on the correlations for T W K B -M G C B for both 2004 and 2005, that probably signify the presence of un-cancelled (i.e non-stationary) contributions from deep sources near stations. 27 Figure 8: Reflection survey data for line 2 from Lithoprobe 1987 Southern Vancouver Island transect. Dominant arrivals in our application would seem to correspond to conversion/reflections from the B and C layers. 28 These signals are too early to correspond to the true, first arrival wi thin the Green's function that should arrive near ± 0.8 s for this station pair. More-over, from the arguments made in section 2, we would expect the true first arrival to emerge from stationary contributions corresponding to shallow, near-surface sources on either side of the station pair. Symmetries implied by (10) and (11) are not realized in cross-station correlations, as the source distribution is incomplete, nor, surprizingly, are they realized for same sta-tion cross-component correlations. This fact may potentially be explained by preferential source excitation, as the tremor sources seem to generate mainly 5-waves, and the fact that causal and acausal ray paths correspond to inverted source and receiver components. (Figure 2). Another interest-ing point concerns the correlations for T W K B - L Z B . The E T S distribution for 2005 from K a o (pers. comm.) places the sources dominantly to the N E of the station pair. A s predicted for this geometry, the spatially clustered tremors for 2005 generate a large coherent arrival on the causal portions of correlations, while the acausal portions display mainly incoherent energy (figure 7c). Finally, we do not observe any large scale moveout around the flat arrivals, as is noted clearly in synthetic experiments. In such models, a regular progression of sources along dV, as depicted in figure 9, produces 29 an equally regular moveout about the stationary arrivals. In our case, the source distribution is likely neither l imited to a 2D surface, nor is it reg-ularly varying. Moreover, tremor locations often appear random, wi th the possibility of several tremors occuring simultaneously. It is conceivable that the lack of moveout points to a redundant source cluster that could very well correspond to a non-stationary arrival. Several clues, however, suggest otherwise: i) Reproducibili ty of arrivals for two apparently different source distributions strongly suggests the recovery of a structural signal, ii) l im-ited localized moveout is nonetheless observed, as one would expect even for tightly clustered sources, which discounts the possibility of a single prolonged redundant source and iii) stationary points represent the slowest varying sec-tions of the integrand, and thus there is a greater likelihood of reproducing a stationary point than a non-stationary point. Also, arrivals wi thin the first Fresnel zone interfere constructively wi th the true arrival, thus further broadening the spatial range of potential stationary sources. 30 Figure 9: Synthetic model from Van Manen et al (2005). The left figure represents two receivers A and B embedded in an inhomogeneous medium, wi th an impulse source distribution on dV. The right figure shows the cross-correlation of the wavefield for each individual source location. M a i n con-tributions to the integral over dV as defined by (10) occur at stationary points of the integrand, where sequential sources produce flat signals wi th little moveout. Note that for any given source, the causal and acausal por-tions of the correlations are not symmetric, but the final stack of a l l the data produces the full two sided Green's function. 31 6 Conclusions Stacked correlations of E T S tremor data from recordings at P O L A R I S - B C stations T W K B and M G C B show remarkable consistency between E T S events in 2004 and 2005 for same station correlations and, to a lesser degree, cross-station correlations. This consistency suggests the emergence of a struc-tural signal which is related to the "surface Green's function" that would be recorded at one station due to a point source at the other, as predicted from the theory of seismic interferometry (Wapenaar and Fokkema, 2005). Cross-station correlations from stations T W K B and L Z B are less reproducible but, for the 2005 E T S sequence, nicely demonstrate the predicted emergence of signal at positive lags for sources located to the northeast of the stations. Approximate knowledge of the source-receiver geometry allows us to inter-pret strong, structural arrivals observed at 4.5 s ( T W K B - M G C B ) and 3.5 s ( T W K B - L Z B ) as S'-to-P-to-5 reflection conversions. The t iming of these ar-rivals places the scattering structure at depths between 9 and 12 km, which corresponds to the interval at which reflectors B and C were identified in seismic reflection profiles over the same region (Clowes et al., 1987). If my interpretation proves correct, it would represent an important practi-cal demonstration of the retrieval of scattered body wave contributions to 32 the surface Green's function using seismic interferometry and deep, passive sources. Because E T S events occur at regular and frequent 14 month in-tervals, it may prove feasible to tailor future seismic experiments for the investigation of subsurface structure using this approach. 33 Acknowledgments I would to thank first and foremost Dr . Michael Bostock for his patience and insight, and my supervisory committee for their input. I thank Honn K a o for supplying unpublished tremor locations for the 2005 sequence. I also gratefully acknowledge the technical assistance of Issam A l - K h o u b b i , Isa Asudeh and the P O L A R I S technical team. Denoising of data was accom-plished using the Wavelab wavelet transform package for Mat lab . This work was supported by a Natural Sciences and Engineering Counci l of Canada Discovery Grant to M G B . 34 References [1] Campil lo, M . , Paul , A . (2003), Long-range correlations in the diffuse seismic coda, Science, 299, 547-549 [2] Clowes, R . M . , Brandon, M . T . , Green, A . G . , Yorath, C . J , Suther-land Brown, A . , Kanasewich, E . R . , Spencer, C. (1987), L I T H O P R O B E -southern Vancouver Island: Cenozoic subduction complex imaged by deep seismic reflections, Can. J. Earth Sci.,, 24, 31-51 [3] Donoho, D . , Maleki , A . , Morteza, S., Wavelab for Mat lab , Stanford U n i -versity, http://www-stat.stanford.edu/ wavelab/WaveLab701.html [4] Eaton, D . and 10 of hers (2005), Investigating Canada's Lithosphere and Earthquake Hazards wi th Portable Arrays, E O S , Transactions of the American Geophysical Union, 86(17), 169-176 [5] Kao , H . , Shan, S.J., Dragert, H . , Rogers, G . , Cassidy, J .F . , Ramachan-dran, K . (2005), A wide depth distribution of seismic tremors along the northern Cascadia margin, Nature, 436, 841-844 [6] L a Rocca, M . , McCausland, W . , Galluzzo, D . , Malone, S., Saccorotti, G . , Del Pezzo, E . (2005), Array measurements of deep tremor signals in the 35 Cascadia subduction zone, Geophysical Research Letters, 32, 3011-3017 [7] Langston, C. A . (1979), Structure under Mount Rainier, Washington, inferred from teleseismic body waves, J. Geophys. Res., 84, 4749-4762 [8] Lobkis, O., Weaver, R. (2001), O n the emergence of the Green's function in the correlations of a diffuse field, Acoustical Society of America, 110, 3011-3017 [9] Mercier, J.P., Bostock, M . G . , Baig, A . M . (2006), Improved Green's func-tions for passive source structural studies, Geophysics, In Print [10] Nicholson, T . , Bostock, M . , Cassidy, J .F . (2005), New constraints on subduction zone structure in northern Cascadia, Geophys. J. Int., 161, 849-859 [11] Rogers, G . , Dragert, H . (2003), Episodic tremor and slip on the Cascadia subduction zone: the chatter of silent slip, Science, 300, 1942-1943 [12] Roux, P., Sabra, K . G . , Gerstoft, O., Kuperman, W . A . , Fehler, M . C . (2005), P-waves from cross-correlation of seismic noise, Geophysical Re-search Letters, 32, LI9303 36 [13] Shapiro, N . M . , Campil lo, M . , Stehly, L . , Ritzwoller, M . H . (2005), High-resolution surface-wave tomography from ambient seismic noise, Science, 307, 1615-1618 [14] Shapiro, N . M . , Campil lo, M . (2004), Emergence of broadband Rayleigh waves from correlations of the ambient seismic noise, Geophysical Research Letters, 31, L07614 [15] Snieder, R. (2004), Extract ing the Green's function from the correlation of coda waves: A derivation based on stationary phase, Physical Review E, 69, 046610 [16] Snieder, R. , Wapenaar, K . , Larner, K . (2006), Spurious multiples in seismic interferometry of primaries, Geophysics, 71, SI111-SI124 [17] V a n Manen, D . , Robertsson, J . , Curtis, A . (2005), Modeling of wave propagation in inhomogeneous media, Physical Review Letters, 94, 164301 [18] Vinn ik , L . R (1977), Detection of waves converted from P to S V in the mantle, Phys. Earth planet. Int., 15, 39-45 [19] Wapenaar, K . , Fokkema, J . (2005), Green's function representations for seismic interferometry, Geophysics, Special issue on seismic interferometry 37 [20] Wapenaar, K . (2006), Seismic interferometry for passive and exploration data employing the coda, EAGE Workshop 3 38 

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