The Vertical Component P-Wave Receiver Function

Transcription

1 The Vertical Component P-Wave Receiver Function By Charles A. Langston John K. Hammer* Center for Earthquake Research and Information University of Memphis Memphis, TN *Shell Deepwater Development, Inc. One Shell Square P.O. Box New Orleans, LA Submitted to the Bulletin of the Seismological Society of America July 20,

2 Abstract The vertical component P-wave receiver function is an important source of data in studies of the crust/mantle transfer function for determining earth structure under isolated receivers or under receiver arrays. This waveform illuminates a missing aspect of the wave propagation in receiver function studies that employ only the horizontal components of motion and yields complementary constraints on near-receiver heterogeneity and P-wave propagation. The vertical component P-wave receiver function is formed using an array estimate for the effective teleseismic source function that is then deconvolved from all vertical and horizontal components of ground motion at each station in the array. 1D, 3D and stochastic wave propagation models are used to test the robustness of the technique. Breakdown of single-station receiver function deconvolution occurs because of high levels of non-correlated noise between ground motion components. Receiver functions for stations of the southern California TERRAscope array are investigated using the array technique. Vertical receiver functions for stations in the Los Angeles Basin and Long Valley Caldera show high amplitude secondary arrivals which cannot be explained by simple 1D structures but probably reflect wave propagation in 3D basin structures. Three component receiver functions from the station at Mammoth Lakes, CA, (MLAC) show pathological behavior where horizontal components of ground motion exceed the amplitude of vertical components suggesting extreme topographic and 3D velocity heterogeneity. Use of all three components of the receiver function in modern passive array experiments is encouraged to reduce the problems of non-uniqueness in determining earth models. 2

3 Introduction The purpose of this paper is to emphasize the importance of considering the vertical component of the wave field in broadband receiver function studies. The receiver function is an approximation of the crust/mantle transfer function for an incident teleseismic or deep event regional P wave (Burdick and Langston, 1977; Langston, 1977; 1979; Zhang and Langston, 1995). As they are usually formed, P wave receiver functions contain information only on the converted S wave field. In particular, the vertical component of motion, which should contain independent information on P wave multiples and other scattering effects, is lost since it is used as the initial (and final) estimate for the teleseismic source function. The receiver function technique for determining crust and mantle structure under arrays of broadband stations has evolved along two complementary paths. Deployment of large passive experiments (e.g., Dueker and Sheehan, 1997) has facilitated imaging methods where the transmitted Ps wave field is migrated into depth sections using a velocity model similar to methods developed in reflection seismology. Laterally coherent Sp arrivals on these sections can then be interpreted as a direct representation of interface geology. Alternatively, individual receiver functions or suites of receiver functions at a single station may be the object of formal data inversion to determine the best velocity model by directly fitting radial and, sometimes, tangential receiver function waveforms (e.g., Owens et al. 1984; Zhang and Langston, 1995). In both kinds of studies, radial and tangential component receiver functions are usually formed by deconvolving the vertical component of ground motion from the horizontal components for a particular event. This removes the effective teleseismic 3

4 source function of the earthquake so that the Ps conversions can be seen more clearly and receiver functions from many different earthquake events can be compared directly (Langston, 1979). Unfortunately, this also removes most of the wave field information concerning P wave multiples in the structure. Both imaging and modeling approaches can suffer if the local receiver structure is complex. Indeed, the technique was originally developed to examine pathological structure for a station located on Mt. Rainier, a major stratovolcano in the Pacific Northwest (Langston, 1979). Subsequent studies at other receivers have shown that nearreceiver scattering can be a significant component of the wave field in receiver functions and mask coherent Ps conversions (e.g., Langston, 1989; Langston and Ammon, 1991; Hammer and Langston, 1996). When large scattering effects do occur in the data, it becomes a difficult job to infer what kinds of waves are giving rise to the scattering. Clues for deciphering the wave field are limited when only the horizontal components are available. We show here that additional, important information is available from the vertical component (i.e., the vertical receiver function ) if a better estimate of the teleseismic source function is available for deconvolution. The character of the vertical receiver function can be used to quickly investigate the level of scattering evidenced by the amplitude of the P wave coda compared to expected amplitudes of Ps arrivals from plausible plane layered structures. In all cases, the vertical receiver function itself becomes an interesting data waveform that can be used to model P wave structure or to provide important constraints on major 3D wave propagation effects. Having all three 4

5 components of the structure transfer function is much more informative than having only two. We also show how single-station receiver function deconvolutions break down because of uncorrelated signal-generated noise between ground motion components. In fact, it was this failure of the method in studying receiver functions from southern California that motivated us to investigate ways of getting a better estimate of the teleseismic source function. A suite of receiver functions from the TERRAScope array in southern California (Figure 1) is presented to motivate the simple array deconvolution technique and to display obvious complexity in the receiver function waveforms. Detailed study of receiver functions at individual stations is left for future reports. Failure of the Deconvolution at TERRAScope Stations P waveforms from 20 teleseismic earthquakes recorded at broadband stations of the TERRAScope array were collected from the IRIS and SCEC data centers as part of a larger study of crust and mantle structure in southern California (Figure 1, Table 1). In the course of processing these data in the usual way of deconvolving the vertical component from the horizontals, it was found that deconvolutions at some stations were exceptionally poor. For example, pre-event noise was as high or higher than the signal, even for apparently good signal-to-noise ratios in the data. Figure 2 shows a typical example of data recorded at the USC (University of Southern California) and PAS (Pasadena) stations. It has been known for some time that structure under PAS is quite complex and not amenable to characterization with a 1D structure (Langston, 1989). Horizontal particle motions shown in Figure 2 for PAS are 5

6 complex, as expected, showing large tangential (off-plane) motions. The data at USC are even more complex showing elliptical particle motions in the horizontal plane and a definite time lag between vertical and horizontal components where the horizontals seem to arrive a few seconds after the vertical P wave arrival. This is characteristic of wave propagation in structure with low velocity sediments near the surface, certainly the case for USC located in the midst of the Los Angeles basin. The P wave is primarily polarized in the vertical direction because near-surface velocity is very low. The Ps conversions arrive later and are purely horizontal, thus giving an apparent arrival time difference between components. Using the water level method of deconvolution (Helmberger and Wiggins, 1971), it was found that USC and other stations in the array had unsatisfactory deconvolutions. Figure 3 shows an example for an event recorded at USC where both radial and tangential deconvolutions were poor. It is well known that deconvolution can be an unstable process (Oldenburg, 1981; Ligorria and Ammon, 1999). In our attempt to improve the quality of the deconvolutions, we reinvented a technique similar to that proposed by others. The importance here is showing that the result yields an important addition to the usual receiver function technique in yielding the vertical receiver function and in gaining practical insight on why the deconvolution process breaks down for teleseismic body waves. 6

7 Array Deconvolution Here, we assume the usual concept of the teleseismic source function as the time history of the P wave before interacting with structure immediately below the receiver. The teleseismic source function includes the source function of the source, near-source reverberations, and the effects of attenuation encountered through the mantle. It is the major unknown in receiver function studies and changes from event to event, and receiver to receiver. Several authors have suggested ways to treat teleseismic P waveform data to remove common source function and instrument responses to examine later arrivals in more detail. In particular, Der et al. (1987) developed a method to examine the response of individual vertical component array stations by iteratively using the array stack as the estimate for the teleseismic source function. Houard and Nataf (1992) used a similar method in their study of lower mantle structure by empirically stacking time-lagged P waveforms over distance to find an estimate of the teleseismic source function. Recently Li and Nabelek (1999) included this method in their more general study of deconvolution methods, as applied to receiver functions, that included homomorphic methods (Bostok and Sacchi, 1997). Notably, Li and Nabelek (1999) show a profile of vertical receiver functions over the subduction zone in the Pacific Northwest to demonstrate how individual station responses change dramatically. Thus, these methods have been available in the literature for some time and are starting to be used for receiver function work in special cases. Because receiver function studies have become routine and because the usual method of deconvolving the vertical component from horizontal components is 7

8 commonplace even in imaging studies, it seems useful to present some details of theory and to demonstrate how receiver function deconvolutions fail. A surprising inference is that signal-generated noise appears to be decoupled between components and causes the most problems for deconvolution rather than spectral holes that may appear in the vertical component spectrum. The usual convolution model for ground displacement for an incident P wave with constant ray parameter at a single station is (Langston, 1979): D () t = It () St () E () t V D () t = It () St () E () t R D () t = It () St () E () t T V R T (1) where I(t) is the instrument response, S(t) the teleseismic source function, and the E(t) functions the vertical (V), radial (R), and tangential (T) component crust/mantle transfer functions. For a single station, the teleseismic source function is combined with the instrument response and is commonly approximated by: Dt () = It () St () D () t (2) V For a three-component seismic array with n elements the best array beam is used (Li and Nabelek, 1999) and is given by: n 1 S() = n V ( + ) i i i= 1 D t D t τ (3) so that 8

9 Dt () D () t (4) where, the τ i are the relative time lags of the direct P wave at each station across the array. These time lags are determined using correlation on the direct P wave (e.g. VanDecar and Crosson, 1990). Using the array beam has the well-known advantage of increasing the direct P wave signal-to-noise ratio by reducing the effect of microseismic noise. Once D(t) is determined deconvolution can be performed to find the two horizontal component earth responses (for a single station) or the three earth responses for each station of the array: S E E E Vi Ri Ti D Vi ( ω) ( ω) D ( ω) D Ri ( ω) ( ω) D ( ω) D Ti ( ω) ( ω) D ( ω) (5) Here we use the water-level method of deconvolution suggested by Helmberger and Wiggins (1971). Effect of Teleseismic P Wave Coda in Receiver Function Deconvolution Langston (1989) and Langston and Ammon (1991) examined the nature of P wave coda for teleseismic P waves and found that the data are often dominated by scattering near the receiver. Coda after direct P decays exponentially with time and generally seems to be homogeneously distributed between ground motion components. That is, coda amplitude levels are comparable on all three components of motion but phase relationships are complex showing non-rectilinear motions. In fact, the character of P 9

10 wave data at some stations is more indicative of random scattering rather than wave propagation in simple layered earth structures. These observations suggest that a realistic model for the ground motion from an incident P wave can be given by the following equations: D () t = adt () δ( t τ ) + Dt () N () t + N () t Vi i i Vi mvi D () t = bdt () δ( t τ ) + Dt () N () t + N () t Ri i i Ri mri D () t = cdt () δ( t τ ) + Dt () N () t + N () t Ti i i Ti mti (6) The N V (t), etc, represent signal generated noise through wave scattering in the local i earth structure and N mvi (t) the background microseismic noise for each station component. The coefficients a i, etc, represent the causal effects of wave propagation on the direct P wave. The Fourier spectrum of the vertical component is iωτ iϕv ( ω) i i iϕm( ω) DV ( ω) = ad( ω) e + D( ω) NV ( ω) e + NmV ( ω) e (7) i i i i If N mvi (t) contains microseismic noise uncorrelated between array sites, then the summation in equation (3) will tend to increase the signal-to-noise ratio, where the signal is the teleseismic source function. The N V (t) contains signal generated noise which i includes almost all of the vertical earth response, E vi (t). If each element of the array has a different vertical earth response, then the phases of these differing responses will tend to destructively interfere when summed which will increase the signal-to-noise ratio once again. Obviously, the effects of a common structure across the array cannot be resolved. 10

11 However, we will show with simple model experiments below that this is not a significant problem for realistic structures. The signal model described above nicely explains why some receiver function deconvolutions breakdown. The phase spectrum of the direct wave is ϕω ( ) the group delay is = ωτ and ϕ ω = τ (8) Stacking over the array using equation (1.3) removes this group delay. However, the group delay spectrum of microseismic noise is generally distributed over all lag times and that of the signal generated noise over late time lags relative to direct P. In a standard receiver function deconvolution, these phases are added to the deconvolution spectrum and can distribute themselves over the entire signal, even before the arrival of the direct P wave. Figures 3 and 4 demonstrate this behavior for data collected from the TERRAScope array for station USC within the Los Angeles basin. The bottom half of Figure 3 shows the amplitude spectrum for the TERRAScope array stack of vertical components and the USC vertical component for the teleseism shown in Figure 2. There are no prominent holes in either vertical component spectrum that might lead to instability in the deconvolution. Figure 4 shows the phase and group delay of these vertical component signals. The phase spectra for both are relatively smooth. However, the group delay spectra (lower half of Figure 4) show large differences in the principal signal bandpass between 0 and 10 Hz. The USC vertical component shows large excursions of the group delay over the signal bandpass of -200 to 200 seconds. The 11

12 array stack, on the other hand, is much smoother and has large excursions at high frequency (f > 1 Hz) and at the microseism peak at f ~ 0.2 Hz. Deconvolutions using these two source function estimates are shown in Figure 3. Zero lag time corresponds to the arrival of the direct P wave. Deconvolutions using the USC vertical component show signals before the P wave arrival and are generally noisy. Deconvolutions using the vertical array beam have clear onset times after the P arrival and show much lower pre-p wave noise. Now, if the noise were correlated between components at a single station, then the simple, single-trace deconvolution (based on equation 2) should work since the noise group delays should annihilate each other in the spectral division, no matter how complicated the group delay spectrum looks. The character of data at pathological stations is that the three components of motion do not look similar at all. In the case of USC station, the two horizontal components differ considerably and they appear to start significantly after direct P arrives on the vertical component. Thus, each component appears to have a different noise spectrum independent of the other. The deconvolution breaks down not because of spectral nulls in the vertical component, but because of differing microseismic and signal generated noise behavior between components. This behavior is shown in Figure 5 for a number of synthetic time series realizations of equations (6). Ignoring the effect of microseismic noise, we set a i = b i = 1 and constructed 100 different synthetic radial and vertical waveforms with the following coda models (and dropping the index i ): γ t N () t = Ce n () t V V V γ t N () t = Ce n () t R R R (9) 12

13 The coda decay is controlled by γ and was set to 0.02/sec, a typical decay rate seen in P wave data (e.g., Langston and Ammon, 1991). C V and C R are constants that control the coda amplitude relative to direct P. The n v (t) and n R (t) are differing realizations of white noise time series. A simple gaussian time function was assumed for D(t). Figure 5 shows that the receiver function deconvolutions become progressively worse as the level of coda increases on the vertical component even for these ideal data. Synthetic receiver functions were seen to breakdown when coda levels were comparable (C V ~ C R ) and when C V was greater than C R. Sometimes there was little pre-p wave signal in the receiver function but the receiver function result did not mimic the original synthetic radial response. Large levels (C V > 0.5) of vertical coda usually produced large pre-p wave signals. Clearly, the relative level of vertical P wave coda affected the deconvolution results and mimicked effects seen in processing of real receiver function data. Stacking vertical components over an array is warranted to remove this coda. Synthetic Earth Model Tests Additional tests of the array stacking method were performed to verify the assumption that differing vertical component structure responses usually are removed in the array stack. 1D models were investigated using synthetic waveforms produced by the propagator matrix method (Haskell 1962). The earth models used are those found in Mooney and Weaver (1989) for structure in California. Eleven radial and vertical component synthetic seismograms for an incident P wave were constructed from each of eleven different models. A ray parameter of 5.56 sec/degree was assumed. A complex far-field time function was assumed as shown in Figure 6. The array stacking technique 13

14 (equation 3) was then applied to the synthetics to estimate the teleseismic source function from the vertical components and then used to deconvolve every other component. Typical results are shown in Figure 6. Note the excellent recovery of the vertical and radial earth responses as well as the recovery of the teleseismic source function by the vertical stack. Synthetics for complex, 3D structure were generated using a 3D finite difference technique (Frankel and Vidale, 1992) to test array stacking for more realistic and complex structure. A 3D model of the Los Angeles basin was constructed and synthetics were taken for 10 different surface locations on the model. A Gaussian teleseismic time function was assumed. Typical results are shown in Figure 7. Again, all three components are recovered with only minor differences occurring between original and recovered waveform. It is interesting to note that even in these synthetic cases of complex 3D wave propagation effects, application of the simple one-station method for estimating the teleseismic source time function recovered the radial and tangential receiver functions almost as well as using the array stacking technique. In no case did a synthetic test behave as badly as real data. However, the single station technique does not recover the vertical receiver function, by definition. We did not attempt to investigate what kinds of model heterogeneity that could give rise to differing signal generated noise between ground motion components. Simple basin structures, while yielding complex particle motions, did not seem to cause problems for the single station deconvolutions nor produce long codas. Model studies have been performed to examine the character of teleseismic P wave coda (e.g., Wagner and 14

15 Langston, 1992) and show that scatterer density and anisotropy are important parameters in controlling coda decay and levels. We did perform a synthetic test (not shown) of the stacking procedure using the coda model (equation 9) and synthetic seismograms for a plane layered earth model. We added various levels of coda to the synthetics and produced receiver functions. Individual receiver functions were sometimes quite noisy. However, after stacking many synthetics we found that we could recover the original receiver function and significantly reduce the noise induced by the deconvolution. This showed that stacking many receiver functions as done in imaging studies of mantle structure can overcome problems in the data processing step due to deconvolution. Application of Array Stacking to TERRAScope Data The original intent of our project was to investigate structure throughout southern California using receiver functions determined from the TERRAScope array (Figure 1). We collected P waveforms for teleseisms recorded by TERRAScope (Table 1) and processed the data using the array stacking method. Figure 8 displays the resulting vertical, radial, and tangential receiver functions. We split up the results roughly by geological province with Figure 8A showing stations in the Penninsular Ranges, Figure 8B the Mojave block, Figure 8C the Los Angeles basin, and Figure 8D the Transverse and Sierra Nevada ranges. We emphasize that for some stations, like SBC, USC, and MLAC, processing the receiver functions this way was the only way we obtained useful results. In general, receiver functions for stations in the Penninsular Ranges and Mojave block (Figures 8A and 8B) are relatively simple, showing some phases after P on the 15

16 vertical receiver function and relatively small tangential components. However, in almost all cases, there is significant azimuthal variation in each of the components implying significant azimuthal variations in structure. This is a chronic problem in receiver function work and one which imaging methods with large numbers of receivers may be able to overcome. However, modeling studies of data such as these are always difficult. Receiver functions for the Los Angeles basin (Figure 8C) and Tranverse/Sierra Nevada ranges (Figure 8D) show increasingly complex behavior with large arrivals on vertical components, long ringing codas, and extreme azimuthal variations. Note, for example, the large arrivals after direct P on the vertical receiver functions at USC. These vertical arrivals are larger than those seen on horizontal components and are probably related to P wave focusing and defocusing within the sediments of the Los Angeles basin. A particularly pathological station is Mammoth Lakes, California, (MLAC) which shows complex vertical receiver functions and remarkably large tangential and radial motions. Indeed, it is hard to imagine a wave propagation effect that can give rise to this general behavior since these teleseismic P waves propagate nearly vertically. Geologically, MLAC sits within the Long Valley caldera, a potentially active volcanic center in central California. No doubt there are large wave propagation effects due to 3D structure and topography. However, all model simulations we have tried to this point have been unable to approximate the large amplitude ratios seen between horizontal and vertical components. 16

17 Discussion From its inception, the receiver function technique has only provided a partial window on the response of the crust and upper mantle beneath three component seismic stations. The non-uniqueness inherent even in simplified plane-layered interpretations of the radial data is well known (Owens and Crosson, 1988; Ammon, Randall et al. 1990) and wave field complexity has been seen in the data from the beginning (Langston 1977; 1979). The basic problem seems like a simple one, in terms of seismological wave propagation, in that an up-coming teleseismic P wave scatters in structure beneath a station. Unfortunately, both the processing technique and the modeling technique is largely based on the plane layered earth model that predicts simple behavior of the vertical component of motion with most of the interesting effects occurring on the radial component. As shown by the TERRAScope data, these assumptions can be easily and dramatically violated by real earth structure. This project was motivated early on by processing problems encountered in the TERRAScope data. Unfortunately, detailed modeling of the TERRAScope receiver function data has proven to be difficult because of azimuthal variations in the receiver functions, the large amplitudes of tangential receiver functions, and the large coda amplitudes of vertical receiver functions. The data show that structure in an active tectonic area is full of interesting complexities that affect even the propagation of teleseismic P waves. There are strong structure signals in the data that probably will yield additional, new information on the geology and tectonics of the area through detailed modeling and imaging. However, it is sobering to realize how limited plane 17

18 layered earth models are in explaining simple first order wave propagation effects in the data. A close examination of Figure 8 shows that at almost every station the vertical components have coda as large as the horizontal components. Our synthetic tests of the single station deconvolution method using the stochastic model (equations 6 and 9) suggests that single station deconvolutions under these circumstances can have significant problems by being dominated by the vertical component scattered wave field. Detailed waveform modeling of standard receiver functions will be difficult under these circumstances, yielding noisy plane layered models. Use of imaging methods that stack out the background and processing noise is recommended. The vertical receiver function is potentially a very useful snapshot into the nature of the teleseismic wavefield. At a minimum, it gives unique and additional information on the nature of seismic coda after direct P. Like the tangential receiver function, the amplitude and decay of P coda on the vertical component gives an immediate estimate of the nature of scattering under the receiver and how much of the signal can be realistically modeled using simple earth models (e.g., Langston, 1989; Langston and Ammon, 1991; Wagner and Langston, 1992). Large vertical P wave coda might be used as an indicator of structure complexity and station quality when performing receiver function stacks in imaging studies. Even in the ideal case of plane layered structure modeling, the vertical receiver function can give additional constraints on velocity structure. For example, identification of P multiples in the layered structure can be used in conjunction with the Ps conversion travel times to constrain Poisson s ratio. Identification of P wave reverberations in a 18

19 basin setting, such as suggested here for the USC receiver function data, may also constrain basin geometry through modeling of times and amplitudes. Increasing amplitudes with arrival time in the P coda is a strong indicator of multiple ray focusing within a 3D structure (e.g., Lee and Langston, 1983). Small arrays of three-component stations would be useful in examining these focusing effects in complex structure areas. As a processing technique, array deconvolution should develop to be the norm in receiver function experiments (Li and Nabelek, 1999), particularly in modern passive deployments of broadband stations that employ receiver function modeling or imaging. Improving the estimate of the teleseismic source function stabilizes the deconvolution and yields another dataset that can be investigated for structure. Conclusions Array deconvolution is a useful method for estimating the teleseismic source function and for providing stable, three-component receiver functions at array stations. The additional result of obtaining the vertical component receiver function finally gives an estimate of the full structure transfer function for an incident teleseismic P wave. This additional information is useful for examining the level of incoherent scattering in the P wave coda, placing constraints on Poisson s ratio through modeling of P wave reverberations, and examining complex wave propagation effects in the local structure. Structure under every TERRAScope station examined here appears to have varying complexity that makes interpretation with plane layered structure problematical. Some stations show extreme wave propagation effects associated with scattering in the Los Angeles basin and Long Valley caldera. 19

20 Acknowledgements We gratefully acknowledge the National Science Foundation for support under grants EAR# and EAR # We also thank Christine Powell and Paul Bodin for reviews of the manuscript. This is CERI contribution # XXX. References Ammon, C. J., G. E. Randall, et al. (1990). On the nonuniqueness of receiver function inversions. Journal of Geophysical Research 95(10): Bostok, M. G. and M. D. Sacchi (1997). Deconvolution of teleseismic recording for mantle structure. Geophys. J. Int. 129: Burdick, L. J. and C. A. Langston (1977). Modeling crustal structure through the use of converted phases in teleseismic body waveforms. Bull. Seism. Soc. Am. 67: Der, Z. A., R. Shumway, et al. (1987). Multi-Channel Deconvolution of P Waves at Seismic Arrays. Bull. Seismol. Soc. Am. 77: Dueker, K. G. and A. F. Sheehan (1997). Mantle discontinuity structure from midpoint stacks of converted P and S waves across the Yellowstone hotspot track. Jour. Geophys. Res. 102: Frankel, A. and J. E. Vidale (1992 ). A three-dimensional simulation of seismic waves in the Santa Clara Valley, California, from Loma Prieta aftershock. Bull. Seismol. Soc. Am. 82:

21 Hammer, J. K. and C. A. Langston (1996). Modeling the Effect of San Andreas Fault Structure on Receiver Functions Using Elastic 3-D Finite-Difference. Bull. Seism. Soc. Am. 86(5): Haskell, N. A. (1962). Crustal reflection of plane P and SV waves. Jour. Geophys. Res. 67: Helmberger, D. V., and R. Wiggins (1971). Upper mantle structure of midwestern United States, Jour. Geophys. Res., 76: Houard, S. and H.-C. Nataf (1992). Further evidences for the 'Lay discontinuity' beneath northern Siberia and the North Atlantic from short-period P waves recorded in France. Phys. Earth planet. Inter. 72: Langston, C. A. (1977). Corvallis, Oregon, crustal and upper mantle structure from teleseismic P and S waves. Bull. Seism. Soc. Am. 67: Langston, C. A. (1979). Structure under Mount Rainier, Washington, inferred from teleseismic body waves. Jour. Geophys. Res. 84: Langston, C. A. (1989). Scattering of teleseismic body waves under Pasadena, California. Jour. Geophys. Res. 94,: Langston, C. A. and C. J. Ammon (1991). Scattering of teleseismic body waves along the Hayward-Calaveras fault system. Bull. Seism. Soc. Am. 81: Lee, J.-J. and C. A. Langston (1983). Three-dimensional ray tracing and the method of principal curvature for geometric spreading. Bull. Seism. Soc. Am. 73: Li, X.-Q. and J. L. Nabelek (1999). Deconvolution of teleseismic body waves for enhancing structure beneath a seismometer array. Bull. Seism. Soc. Am. 89:

22 Ligorria, J. P. and C. J. Ammon (1999). Iterative deconvolution and receiver-function estimation. Bull. Seism. Soc. Am 89: Mooney, W. D. and C. S. Weaver (1989 ). Regional crustal structure and tectonics of the Pacific Coastal States; California, Oregon, and Washington. GSA Memoir 172, Geological Society of America: Oldenburg, D. W. (1981). A comprehensive solution of the linear deconvolution problem, Geophys. J. R. Astr. Soc., 65: Owens, T. J. and R. S. Crosson (1988). Shallow structure effects on broadband teleseismic P waveforms. Bull. Seism. Soc. Am. 78: Owens, T. J., G. Zandt, et al. (1984). Seismic evidence for an ancient rift beneath the Cumberland Plateau, Tennessee; a detailed analysis of broadband teleseismic P waveforms. Journal of Geophysical Research. B. 89(9): VanDecar, J. C. and R. S. Crosson (1990). Determination of teleseismic relative phase arrival times using multi-channel cross-correlation and least squares. Bull. Seism. Soc. Am. 80: Wagner, G. S. and C. A. Langston (1992). A numerical investigation of scattering effects for teleseismic plane wave propagation in a heterogeneous layer over a homogeneous half-space. Geophys. J. Int. 110: Zhang, J. and C. A. Langston (1995). Constraints on oceanic lithosphere structure from deep-focus regional receiver function inversions. J. Geophys. Res. 100:

23 Zhang, J. and C. A. Langston (1995). Dipping structure under Dourbes, Belgium, determined by receiver function modeling and inversion. Bull. Seism. Soc. Am. 85:

24 Figure Captions Figure 1: Map of southern California (top) showing the location of TERRAScope stations used in this study, major faults, and geological provinces. The lower map shows the location of teleseisms studied with distances from TERRAScope given in degrees. Figure 2: Example of data recorded at USC and PAS of the TERRAScope array. The records show the vertical (Z), radial (R), and tangential (T) components of the P waveform from the M7.0 8/23/95 Mariana Islands event. The bottom two plots show the horizontal particle motion of these records with the arrow showing the theoretical ray direction. Both stations display complex horizontal particle motions indicative of scattering in 3D earth structure. Figure 3: Horizontal receiver function processing for the 8/23/95 event data recorded at USC. The top panel compares the radial and tangential receiver function obtained from the standard, single-station method of deconvolution and the array deconvolution method described in the text. Note the large noise levels before the expected P arrival (at 0 seconds) in the standard deconvolution and the marked improvement in these noise levels using the array deconvolution. The bottom two panels show the amplitude spectra for the array stacked vertical waveform and the USC vertical waveform for this event. Figure 4: Phase and group delay spectra for the array stacked vertical waveform and USC vertical waveform. The phase spectra have been unwrapped to produce a continuous phase spectrum. The phase spectrum is dominated by a linearly decreasing phase due to a small time shift in the P waveform time series. The group 24

25 delay is computed by taking the derivative of the phase spectrum with respect to frequency. The array stack vertical component shows less variation in the signal bandpass used here, although the 0.2 Hz microseism peak is prominent. The USC vertical component shows large variation in the group delay spectrum. Figure 5: Synthetic receiver functions calculated using the stochastic wave propagation model (equations 6 and 9). Vertical and radial ground displacements were computed assuming a gaussian time history and a coda model with a decay rate of 0.02/sec. The left panel shows synthetic vertical components for one particular realization of the coda time series weighted by the factor C v. The right panel shows the result of deconvolving the vertical component from the radial. C R is the weight of the radial coda time series. A value of C R =1.5 was chosen for display purposes. Note how the deconvolution degenerates with increasing vertical coda levels. Figure 6: Comparison of the array deconvolution result with the theoretical vertical and radial component responses for four structures used in the 1D modeling test. The bottom panel shows the comparison between the assumed teleseismic source time function and the estimate obtained from the array stack. P wave crustal structures are shown to the right of each pair of seismograms. Figure 7: Comparison of the array deconvolution result with the theoretical vertical and horizontal component responses for four structures used in the 3D modeling test. Figure 8: Vertical, radial, and tangential receiver functions for stations of the TERRAScope array plotted as a function of backazimuth to the source. A) Stations within the Penninsular Ranges. B) Stations within the Mojave block. 25

26 C) Stations within the Los Angeles basin. D) Stations within the Transverse Ranges (SBC) and Sierra Nevada (ISA, MLAC). 26

27 Table 1 Event Parameters Region Date Origin Lat. Long. Depth Distance Backazimuth from SVD from SVD (m/d/y) Time (o) (o) (km) m b (o) (o) Fox Islands 08/14/91 12:53: N W Cuba Region 05/25/92 16:55: N 77.82W Svalbard Region 07/20/92 07:46: N 5.52E Fiji Islands 03/21/93 05:04: S W Fiji Islands 04/16/93 14:08: S W Western Brazil 05/06/93 13:03: S 71.49W Jujuy Province, ARG South of Fiji Islands 05/24/93 23:51: S 66.54W /07/93 17:53: S E Fiji Islands 10/11/93 13:07: S W Peru-Bolivia Border 01/10/94 15:53: S 69.45W Fiji Islands 03/09/94 23:28: S W South of Fiji Islands Santiago Del Estro Prov., ARG 03/31/94 22:40: S W / :11: S 63.25W Trinadad 05/03/94 16:36: N 60.76W Santiago Del Estro Prov. Northern Bolivia Southeast Coast of Russia Santiago Del Estro Prov., ARG Leeward Islands 05/10/94 06:36: S 63.10W /09/94 00:33: S 67.55W /21/94 18:36: N E /19/94 10:02: S 63.42W /08/95 3:45: N 59.56W Mariana Islands 08/23/95 07:06: N E