Multicomponent C3 Green s Functions for Improved Long-Period Ground-Motion Prediction

Transcription

1 Bulletin of the Seismological Society of America, Vol. XX, No. XX, pp., 27, doi:.78/273 E Multicomponent C3 Green s Functions for Improved Long-Period Ground-Motion Prediction by Yixiao Sheng, Marine A. Denolle, and Gregory C. Beroza Abstract The virtual earthquake approach to ground-motion prediction uses Green s functions (GFs) determined from the ambient seismic field to predict long-period shaking from scenario earthquakes. The method requires accurate relative GF amplitudes between stations and among components; however, the amplitudes of ambient-field GFs are known to be subject to biases from uneven source distribution. We show that multicomponent, higher order cross correlations are significantly less biased than the conventional first-order cross correlation, and we demonstrate that they provide a more reliable prediction of observed ground-motion amplitudes for a recent moderate earthquake on the San Jacinto fault in southern California. Electronic Supplement: Examples of observed and virtual earthquake-derived three-component velocity amplitude spectrum. Introduction Accurately predicting the strength of ground shaking in earthquakes, an essential part of seismic-hazard analysis, is typically carried out using empirical ground-motion prediction equations (GMPEs) (e.g., Boore and Atkinson, 28). GMPEs are constructed through fitting observations of ground-shaking intensity with parametric equations representing source, path, and site contributions. Lack of data in close to large earthquakes leads to significant uncertainty in GMPEs for events that pose the greatest threat. This situation motivated seismologists to develop physics-based approaches for scenario ground-shaking simulations (Olsen et al., 26; Day et al., 22) and to use such simulations for probabilistic seismic-hazard analysis (Graves et al., 2). Accurate ground-motion quantification requires both exceptional computational effort (Cui et al., 23) and comprehensive knowledge of 3D crustal structure (Shaw et al., 2). Denolle et al. (23) proposed an alternative groundmotion prediction method, the virtual earthquake approach (VEA), which does not require comprehensive knowledge of crustal structure, nor exceptional computational effort. VEA takes the surface impulse response (Green s function [GF]) proportional to the time derivative of cross correlation of the ambient seismic field and corrects it for source depth, source mechanism, and finite-fault effects of earthquakes of interest. This method captures long-period sedimentary basin amplification effects (Denolle, Dunham, et al., 24; Denolle, Miyake, et al., 24) and has shown promise for characterizing the strength of long-period earthquake shaking. Moreover, Viens et al. (24) coupled the deterministic low-frequency ground motion with a nonstationary stochastic model and successfully extended ground-shaking simulations to Hz. Accurate ambient-field GFs are foundational to reliable ground-motion prediction, and studies of the ambient field have shown steady progress and innovation resulting in steadily improving GF estimates. Snieder and Safak (26) pointed out that deconvolution can also be used to retrieve the impulse response of a system. Prieto and Beroza (28) used deconvolution to extract not only phase but also relative amplitude and showed that relative amplitudes of GFs reflected ground-motion amplification observed from earthquake records. Amplitude measurements can be difficult to interpret (Prieto et al., 2), and the uneven distribution of noise sources can bias such amplitude measurements (Tsai, 2; Stehly and Boué, 27). Typically, in southern California, noise signals generated by nonlinear interaction of the ocean swell dominate the s frequency band, forming a strongly directional noise wavefield (Longuet- Higgins, 9; Stehly et al., 26). Symmetry in the crosscorrelation function, a metric for stability of the GF amplitude, is affected by this directionality (Paul et al., 2; Yao et al., 26). Wapenaar et al. (28) showed that interferometry by multidimensional deconvolution can mitigate the effects of source irregularity. Campillo and Paul (23) demonstrated that it is also possible to use the diffuse waves of the earthquake coda to construct the station-to-station response. This is possible because the scattered waves of the coda form a diffuse wavefield with scatterers acting effectively as secondary sources. /

2 2 Y. Sheng, M. A. Denolle, and G. C. Beroza Such use of earthquake coda can be extended to the coda of correlation as well. Stehly et al. (28) used the correlation of the coda of the vertical vertical ambient-field correlation, which they referred to as C3, to demonstrate that the scattered waves of the correlation coda also form a diffuse wavefield even if the original-wave excitation (raw seismic noise) is highly directional. Froment et al. (2) further tested the C3 method and suggested that the relatively even distribution of secondary source stations would lead to more symmetric GF estimates. Ma and Beroza (22) and Spica et al. (26) showed that C3 can bridge seismic networks operating at different times by estimating the GFs between stations that did not record simultaneous seismic noise. Zhang and Yang (23) suggested that C3 greatly reduces amplitude bias. In this article, we construct C3 GFs using the east vertical and north vertical components, in addition to the vertical vertical component in correlation (C). We test the multicomponent C3 results with stations near the San Jacinto fault zone, California. Though noisier than C GFs, the estimated GFs from multicomponent C3 are comparable in shape and substantially more symmetric than those from C. We extend the vertical vertical GFs to nine-component Green s tensors and incorporate them into VEA to synthesize seismograms, which we compare with recorded strongmotion records of the 26 M w.2 Borrego Springs earthquake. We find that the virtual earthquake seismograms derived by the multicomponent C3 method lead to a more reliable estimate of the observed earthquake records. Data and Methodology The San Jacinto fault has a high long-term slip rate, indicating that the hazard from the fault is high (Rockwell et al., 99). Lozos (26) showed that the San Jacinto fault might rupture together with the San Andreas fault, leading to very large events. The San Jacinto fault zone (SJFZ) is one of the most seismically active regions in southern California with abundant microseismicity that includes five M w > earthquakes since 98. The most recent of these was the June 26 M w.2 Borrego Springs earthquake, which provides a good opportunity to use VEA to assess earthquake groundmotion hazard from SJFZ events. To represent the shaking from a real earthquake, VEA requires a reference broadband station close to the epicenter, such that GFs estimated from the reference station are representative of ground motion excited by the earthquake. We choose station YN.TR2 (from YN network; see Data and Resources), which is about 2. km away from the epicenter, as the earthquake virtual source. We use all 23 available broadband stations in the Southern California Seismic Network (CI network; see Data and Resources). We focus our ground-motion comparison on those stations closest to the Borrego Spring earthquake that have high-quality C results. This excludes five stations in the Salton trough that were characterized by strong acausal arrivals in the C results (Fig. ), possibly due to either local, or directionally biased, Receiver station Virtual earthquake source YN.TR2 June, 26 M w.2 Borrego Springs earthquake focal mechanism Background station noise sources. We use the seismic ambient-field data of all three components (vertical Z, north N, east E) recorded continuously for the year 2 to estimate GFs. To mitigate the bias in GFs estimated by C, we use the multicomponent C3 method to construct the Green s tensors as described below. Although we explain the methodology to obtain the vertical vertical (ZZ) C3, the approach is identical for the other eight components of a Green s tensor (ZE, ZN, EZ, EN, EE, NZ, NN, and NE). The instrumental responses are removed. We divide the data into 3-min-long time series and discard those with spikes larger than 8 times the standard deviation of the window. We first extract the ZZ GF between the virtual source YN.TR2, marked as R below, and a receiver station R2 (any inverted triangle in Fig. ) by taking the following steps (shown schematically in Fig. 2).. We select an intermediate station, denoted as S, different from R and R2, and from the network (stars as well as the rest of the inverted triangles in Fig. ) to act as a secondary source. We Fourier transform the selected data and compute the S-R and S-R2 noise correlations based on deconvolution interferometry to preserve their relative amplitudes (Prieto and Beroza, 28; Denolle et al., 23). The equation we use is EQ-TARGET;temp:intralink-;df;33;9C S Ri ω June 26 M w.2 YN.TR2 6 6 Figure. Reference map showing location and focal mechanism of the 26 M w.2 Borrego Springs earthquake and the stations used in this study. The epicenter is indicated by the focal mechanism of the event. The earthquake virtual source is marked with a triangle overlapped by the focal mechanism plot. Inverted triangles represent the receiver stations in this study. The other stations in the CI network are denoted as background stations, marked by stars in the figure. These background stations, along with most receiver stations, other than the chosen one, serve as secondary sources in constructing C Green s functions (GFs). The color version of this figure is available only in the electronic edition u xri ; ω u x S ; ω fju x S ; ω jg 2 ;

3 Multicomponent C3 Green s Functions for Improved Long-Period Ground-Motion Prediction 3 (c) CS-R CS-R2 coda S CS-R S CS-R R R C3 R-R2 CS-R2 coda x R2 CS-R2 Figure 2. Schematic diagram for multicomponent C3, showing vertical response at R2 from a vertical impulse at R. We first calculate the cross correlations (C) between a virtual source (S) and two receivers (R and R2). In addition to using vertical component, we also use north or east component of the virtual source. Note that we only use vertical components of R and R2. We use both the causal and anticausal parts of the C coda. The coda parts have been amplified by a factor of in the figure for clarity. (c) We compute the cross correlations between coda waves from two receivers, separately on causal and anticausal parts, and take average of them to estimate the GF from R to R2. The color version of this figure is available only in the electronic edition. R2 Z N E in which h i denotes stacking over all time windows, ω refers to the angular frequency, Ri is either R or R2, x Ri refers to the location of the station, asterisk denotes the complex conjugate, and f g represents points smoothing over the spectrum, with df : Hz. We use the vertical component recorded at R and R2 to get the ZZ GF but include the north, east, and vertical components for S. The notation C XZ S Ri ω stands for using the X component of S and the Z component of either R or R2. We take the inverse Fourier transform of C XZ S Ri ω and obtain the time series C XZ S Ri t. 2. Following Stehly et al. (28) and Froment et al. (2), we select a 2-s-long time window in the late coda of each C correlation, starting at twice the Rayleigh-wave travel time. The Rayleigh-wave velocity we choose is fixed at 3 km=s. By doing so, we ensure that the coda window starts well after the surface-wave arrival at all stations. 3. We cross correlate the positive part of the coda in the S-R correlation, with the positive part of the coda in the S-R2 correlation, as well as the negative part of the coda in the S-R correlation, with the negative part of the coda in the S-R2 correlation. We denote their average time series as C3 ZXXZ S t. We whiten the coda spectra between 4 and s and use Welch s method to speed the convergence of the estimated GFs (Seats et al., 22). We divide the 2-s-long time series into -s-long % overlapping windows. Cross correlation is then constructed in each subwindow and the average is kept as the result. 4. We repeat this process for all N (229 in our study) secondary sources from the network and stack all the C3 functions to obtain C3 ZXXZ t between R and R2: EQ-TARGET;temp:intralink-;df2;33;397C3 ZXXZ t X N C3 ZXXZ S N i t ; X fz; N; Eg: i 2 C3 ZXXZ t corresponds to the ZZ GF between R and R2 but with the excitation at the secondary source station taken in X direction.. To improve the signal-to-noise ratio (SNR), we further take the average of C3 ZZZZ, C3 ZEEZ, and C3 ZNNZ to obtain an improved estimate that we denote as C3 ZΣZ : EQ-TARGET;temp:intralink-;df3;33;29C3 ZΣZ t 3 C3ZZZZ t C3 ZNNZ t C3 ZEEZ t : 3 Through this processing, we preserved the amplitude for C3 by preserving the amplitudes for the individual C contributions. The relative amplitudes of C3 ZΣZ GFs are shown in Figure 3c. The difference between the C3 method from Stehly et al. (28) and Froment et al. (2) and our method is that instead of using only the vertical components at the secondary source stations, we incorporate all components, that is, we consider all the possible orientations of the virtual impulseforce sources that could contribute to the wavefield of the C coda. Figure 3 compares the ZZ GFs extracted by different

4 4 Y. Sheng, M. A. Denolle, and G. C. Beroza 2 C3 ZNNZ 2 C ZZ 2 C3 ZZZZ Distance (km) - 2 C3 ZEEZ 2 C3 ZΣZ (c).8.6 Amplitudes of causal parts C ZZ.4 C3 ZΣZ.2 Distance (km) Relative amplitude Amplitudes of anticausal parts Average amplitudes C ZZ C3 ZΣZ C ZZ C3 ZΣZ Number of stations Figure 3. Comparison of GFs retrieved using different methods. All waveforms are band-pass filtered between 4 and s and normalized to their peak amplitude. Comparison between C ZZ and multicomponent C3s (C3 ZZZZ,C3 ZEEZ, and C3 ZNNZ ). Note that multicomponent C3s are more symmetric than Cs. Seismograms of C3 ZΣZ, the summation of C3 ZNNZ,C3 ZEEZ, and C3 ZNNZ. The SNR of C3 ZΣZ is improved for both the acausal artifacts and coda. (c) Relative amplitudes of C ZZ and C3 ZΣZ. The stations are arranged with increasing distance from the earthquake virtual source. The general decreasing amplitude from left to right is associated with geometric spreading. Local amplifications are captured by both C and C3 GFs, showing that relative amplitudes are preserved through C and multicomponent C3 method. The color version of this figure is available only in the electronic edition. methods. Figure 3a shows that, though noisier, the GFs for C3 ZZZZ t are more symmetric than those for C ZZ t. To quantify the symmetry of the GFs, we calculate the correlation coefficients between the causal and flipped anticausal parts of each C ZZ t and C3 ZZZZ t. More symmetric GFs would have higher correlation coefficient values. The distributions of the coefficients are shown in Figure 4. Because C3 ZNNZ t and C3 ZEEZ t also contain highly coherent signals, they contribute to a more stable overall C3 result. Following Liu et al. (26), we define the SNR as the ratio of peak amplitude of the wave-packet envelope, which is calculated with the Hilbert transform, over the root mean square of the coda noise. The 3-s-long noise window starts at s after the arrival of the peak amplitude. For each station pair, we compute the SNR both on the causal (SNR ) and anticausal parts (SNR ) and take the ratio of SNRs for C3 ZΣZ t to those for

5 EQ-TARGET;temp:intralink-;df;33;236 EQ-TARGET;temp:intralink-;df6;33;63 Multicomponent C3 Green s Functions for Improved Long-Period Ground-Motion Prediction Counts CC of C ZZ + and C ZZ- CC of C3 ZZZZ + and C3 ZZZZ- zero (Aki and Richards, 22). That is, we assume the P SV and SH fields are excited separately. The clear signals given by C3 TZZT t result from the complex 3D crustal structure of the study area that couples P SV into SH motion and vice versa. We observe perceptible improvements on T T GFs by incorporating horizontal source components in C3. To maximize SNRs and to retain relative amplitude relationships among components of a Green s tensor, it is necessary to use all three source components. Counts Correlation coefficient (CC) Figure 4. Histogram of correlation coefficients of the causal and flipped anticausal part of C ZZ GFs. Horizontal axis indicates the coefficient value, varying from to. We divide the coefficients into 2 bins and each bin has equal width of.. The vertical axis gives the number of the GFs in each coefficient bin. Same as but for C3 ZZZZ GFs. C3 ZZZZ GFs have consistently and systematically much higher correlation coefficients between the causal and anticausal waveforms, indicating they are more symmetric than C ZZ GFs. The color version of this figure is available only in the electronic edition. C3 ZZZZ t, thatis,snr C3 ZΣZ t =SNR C3 ZZZZ t and SNR C3 ZΣZ t =SNR C3 ZZZZ t. The average ratios over all station pairs are.29 for the causal part and.3 for the anticausal part (Fig. c), demonstrating the improvement in SNR for C3 ZΣZ t. Improvements in SNR can also be observed visually by comparing C3 ZΣZ t in Figure 3b with C ZZZZ t in Figure 3a. We repeat the same procedure to obtain all the components of the Green s tensors and rotate the coordinate system from north east vertical (vertical positive downward) to radial transverse vertical. Figure 6 shows examples of comparisons between horizontal horizontal (e.g., radial radial [R R] and transverse transverse [T T]) GFs extracted from C3 with vertical impulse source and those with multicomponent sources. Horizontal components particularly benefit from the multicomponent C3 estimation (Fig. a,b). The average of C3s from different source components strengthens coherent signals and suppresses incoherent ones, improving the reliability of the estimated GFs. It is interesting to note that C3 TZZT t, constructed from C ZT t, depends on P=SV to SH coupling. In layered media, the coupling between Rayleigh and Love waves does not exist, and therefore the ZT component of the Green s tensor is in theory Virtual Earthquake Seismograms We exploit the symmetry of the GFs and average the causal and flipped anticausal time series. We make the approximation that a Green s tensor s cross terms ZT, TZ, RT, and TR are zero and only use ZZ, RR, RZ, ZR, and TT components in the excitation of the virtual earthquake seismograms. The time-domain GFs, taken as the time derivatives of the C3s, are Fourier transformed into the frequency domain, noted as G RR ω ; G RZ ω ; G ZR ω, G ZZ ω, and G TT ω. We apply equations (4) (6) to correct surface-impulse responses to displacements radiated from a buried double-couple point source (Denolle et al., 23). We choose a Fourier transform convention such that an outward propagating wave (in the x direction) can be written proportional to exp iωt ikx. To simplify the notation, we suppress explicit ω dependence while retaining the source-depth dependence h. For the Love-wave component: EQ-TARGET;temp:intralink-;df4;33;293u T l ik LM TR l h M TZ l h GTT ; and for Rayleigh-wave components: u Z r ik RM RR r h M RZ r h GZR r 2 ik RM ZR r 2 h M ZZ r 2 h GZZ ; u R r 2 ik RM ZR r 2 h M ZZ r 2 h GRZ r ik RM RR r h M RZ r h GRR : 4 6 l h is the fundamental Love-wave displacement eigenfunction at depth h, whereas r h and r 2 h are the horizontal

6 6 Y. Sheng, M. A. Denolle, and G. C. Beroza (c) SNR - (C3 RΣR )/SNR - (C3 RZZR ) SNR - (C3 TΣT )/SNR - (C3 TZZT ) SNR - (C3 ZΣZ )/SNR - (C3 ZZZZ ) SNR ratio Mean :.28 Mean :.38 Mean : and vertical displacement eigenfunctions for fundamentalmode Rayleigh waves. h is the earthquake source depth, which is taken to be 2.3 km for the Borrego Springs event (from U.S. Geological Survey catalog; see Data and Resources). M is the earthquake moment spectrum tensor, whereas k L and k R are the Love and Rayleigh wavenumbers. The correction terms at different frequencies for each component are shown in Figure 7a. The corner frequency f c used in our study is.2 Hz, estimated based on the model proposed in Hanks and Thatcher (972), with an assumed stress drop Δσ 3 MPa, the observed seismic moment M, and an averaged shear velocity β 3 km=s. We use an omegasquared source model as the moment rate function, shifted by the source duration: SNR + (C3 RΣR )/SNR + (C3 RZZR ) SNR + (C3 TΣT )/SNR + (C3 TZZT ) Mean :.3 Mean : SNR + (C3 ZΣZ )/SNR + (C3 ZZZZ ) Mean : SNR ratio Figure. Histograms of the ratio of the multicomponent C3 signal-to-noise ratios (SNRs) and single-component C3 SNRs, for all three components (from a to c: RR, TT, ZZ) on both (right) causal and (left) anticausal parts. Multicomponent C3 GFs generally have higher SNR than original C3 GFs, particularly for TT components. The color version of this figure is available only in the electronic edition. for Rayleigh and Love waves to calibrate the virtual earthquake seismograms to real earthquake displacement amplitudes. The factors are determined by comparing the observed and synthetic seismograms of another earthquake that occurred near the virtual source. We take the transverse amplitude ratio as the Love-wave normalization factor, whereas the average of the vertical and radial amplitude ratios is the Rayleigh-wave normalization factor. We compare the waveforms in Figure 7b. The seismograms we construct match the observations reasonably well. They capture the amplitude difference among different components (e.g., the small amplitudes of Rayleigh and large amplitudes of Love waves on stations CI.MTG and CI.EML), which highlights the importance of making source depth and mechanism corrections in the VEA. To highlight the accuracy of the VEA-predicted amplitudes with multicomponent C3, we show in Figure 8 peak amplitudes for the virtual and real earthquake waveforms for the Borrego Spring earthquake. To make a better comparison, we also show the results of using the C Green s tensor for constructing virtual earthquake seismograms. There is a good match between the observed and predicted amplitudes, both for the C and multicomponent C3 results. We estimate the best-fitting linear trend, with L-norm minimization between the predicted and observed peak amplitudes on a log scale. The corresponding slopes, shown in Figure 8, are close to one for the two cases. Multicomponent C3, however, yields a smaller sum squared residual, indicating its higher reliability in predicting strong ground motions. We also plot several velocity amplitude spectra in E Figure S (available in the electronic supplement to this article). Both multicomponent C3 and C virtual seismograms match well with the observed strong motions in the 4 s period band with similar spectral amplitudes. Conclusions EQ-TARGET;temp:intralink-;df7;;9S ω e iω 2πfc ω 2πf c 2 : 7 Even though relative amplitudes among different components at different stations are preserved, the retrieved GFs are dimensionless. Because of the different and unknown input source energy for Rayleigh and Love waves in the ambient wavefield, we use separate normalization factors Because coda waves are more diffuse than the raw ambient seismic field, we use the coda of the first-order correlations (C) to improve our estimate of GFs, thereby improving the symmetry and amplitude stability. As suggested by Froment et al. (2), we use widely distributed background stations as secondary sources and enhance the source distribution, therefore reducing the bias caused by uneven noise source excitation in the first-order correlation. We show that it is possible to reconstruct an improved Green s tensor with this approach if we use all three components of

7 Multicomponent C3 Green s Functions for Improved Long-Period Ground-Motion Prediction C3 TZZT 2 2 C3 RZZR 2-2 C3 RZZR C3 TZZT C3 RΣR SNR - = 6.88 SNR + = 8. SNR - =. SNR + = 9.93 C3 TΣT SNR - = 7.74 SNR + =.27 SNR - = 2.4 SNR + = 6.4 C3 RΣR SNR - =. SNR + =.7 SNR - = 7.7 SNR + = 2.43 C3 TΣT SNR - = 6.93 SNR + =.8 SNR - = 2.7 SNR + = Figure 6. Horizontal horizontal C3s for a vertical impulse source and multicomponent sources for station pair YN.TR2-CI.RAG and YN.TR2-CI.GMR. The waveforms are band-pass filtered at 4 s and normalized to their peak amplitude for comparison. Multicomponent C3s have better SNR, especially for TT components. SNRs of the causal part (SNR+) and anticausal part (SNR ) are shown in the plots. the wavefield. Multicomponent C3 GFs have more reliable amplitudes than C GFs and higher SNR than the original C3 GFs. When combined with VEA, we find an improved accuracy in ground-motion predictions. We compare synthetic seismograms with recorded waveforms from the 26 M w.2 Borrego Springs earthquake. The virtual earthquake seismograms match well with the real displacement records both in phase and amplitude, which verifies that VEA provides reliable prediction of long-period ground motions (4 s) for the SJFZ earthquake. In this study, we neglect possible coupling between P SV and SH waves, which are expressed in the cross terms ZT,TZ,RT,andTRoftheGreen s tensors. We observe energy coupling across these components in the 4 s period range. Such wave conversions have been predicted at the edge of sedimentary basins in numerical simulation of wave propagation (Day et al., 22). Essentially, considering this basin edge effect would yield more reliable groundmotion predictions; in constructing C3, we use all available stations from the CI network, other than the virtual source R and the receiver station R2, as the secondary sources. For different pairs of (R, R2), the distributions of the secondary sources are different. We ignore the possible influence on C3s from such changes in the secondary source distributions. Incorporating these effects into VEA is a possible future research direction. Constructing multicomponent C3 is computationally somewhat more expensive than the first-order correlation, especially with a large number of background stations. With C already computed, however, the increase of the computation time is modest. Assume that T is the unit time to compute a single cross correlation. With N time windows of seismic noise, a number of stations (Nsta), the total computational cost to calculate the nine-component C between each nonredundant station pairs is Nsta Nsta =2 9 N T.Considering that we use both causal and anticausal parts of C GFs and all three components of the secondary source, and that there are Nsta-2 secondary sources per station pair, the additional cost to construct multicomponent C3 Green s tensor between all station pairs is 2 3 Nsta 2 Nsta Nsta =2 9 T. The ratio of the additional cost to calculate the C3s from the Cs is 6 Nsta 2 =N, and taking the practical example that Nsta 2 and N (48 windows of 3 min per day for year) with Nsta N, the increase is only about 7% the computation time of the Cs. With growing seismic networks and duration of continuous records, high-performance computing is becoming necessary to process ambient noise cross correlation. Prieto et al. (29) and Lawrence and Prieto (2) showed that spatial coherency of the ambient seismic field can be used for attenuation tomography. Stehly and Boué (27) suggested that there could be a strong trade-off between the noise source distribution and the attenuation extracted from the amplitude decay of the noise correlations, even for a linear array. On the other hand, Zhang and Yang (23) demonstrated that C3 yields more reliable attenuation estimates for linear arrays, which could result from the enhanced source distribution with the C3 method. Our study shows considerable improvement in the estimates of the GFs at all components of the Green s tensorand in particular for the Love waves. With our multicomponent C3 technique, it would be straightforward to generalize the

8 8 Y. Sheng, M. A. Denolle, and G. C. Beroza Radial Trans Vertical Radial Trans Vertical s 8 s s Radial correction MTG POB2 3 GMR JEM WWC 8 2 JEM EML MTG POB2 33 PLM KYV 24 PLM 27 3 Transverse correction 9 MGE DGR 2 6 IDO EML 3 8 JEM GMR BLA2 PER 2 EML MTG 24 PLM POB MUR MCT 27 Vertical correction 9 BBS SVD HAY GOR GMR 8 2 JEM EML MTG 24 PLM 27 POB GMR RAG Virtual seismogram Real seismogram Figure 7. Correction terms for all components varying with azimuth and the relative locations of some stations. For station CI.EML, for example, the transverse correction is large, whereas the vertical and radial corrections are close to zero (nodes of the focal mechanism), corresponding to large amplitude for the synthesized Love wave but small amplitudes for synthesized Rayleigh waves, matching well with observed records shown in. Comparison between virtual earthquake seismograms and observed earthquake waveforms for the 26 M w.2 Borrego Springs earthquake. The waveforms are band-pass filtered between 4 and s. The color version of this figure is available only in the electronic edition. above attenuation studies from only using ZZ GFs to all nine components. Finally, we note that although our application has been for ground-motion prediction, improved estimates of GFs resulting from multicomponent C3 should provide improved results for any application of ambientfield GFs. Data and Resources Data used in this study were obtained from the Southern California Seismic Network CI (doi:.794/sn/ci) and from the San Jacinto Fault Zone Experiment YN (doi:.794/sn/yn_2). U.S. Geological Survey (USGS)

9 Multicomponent C3 Green s Functions for Improved Long-Period Ground-Motion Prediction 9 3 R T Z 3 R T Z Observed PGD (m) 4 Observed PGD (m) 4 Slope =.23 Total residual =.2 C Slope =.994 Total residual =.92 C3 4 3 Predicted PGD (m) 4 3 Predicted PGD (m) Figure 8. Observed and predicted peak displacement amplitudes, band-pass filtered at 4 s. We compare the radial (circle), transverse (square), and vertical (triangle) observed peak ground displacements (PGDs) with the virtual earthquake approach waveforms constructed from C Green s tensor and multicomponent C3 Green s tensor. The black line in each panel represents the L-linear regression, with each slope and total residual to ideal fit. The total residual from is smaller than that from, indicating that the multicomponent C3 Green s tensor yields more reliable amplitude prediction in constructing virtual earthquake seismograms. catalog was searched using (last accessed January 27). Acknowledgments The authors thank Fabian Bonilla and Luis A. Dalguer for their valuable comments, which helped improve and clarify this article. This work was supported by the Southern California Earthquake Center (SCEC; Contribution Number 736). SCEC is funded by National Science Foundation (NSF) Cooperative Agreement EAR and U.S. Geological Survey (USGS) Cooperative Agreement G2AC238. This work was also supported through NSF Awards EAR-2867, titled Ground Motion Prediction Using Virtual Earthquakes. References Aki, K., and P. G. Richards (22). Quantitative Seismology, Second Ed., University Science Books, Sausalito, California. Boore, D. M., and G. M. Atkinson (28). Ground-motion prediction equations for the average horizontal component of PGA, PGV, and %- damped PSA at spectral periods between. s and. s, Earthq. Spectra 24, no., Campillo, M., and A. Paul (23). Long-range correlations in the diffuse seismic coda, Science 299, no. 66, 47, doi:.26/science.78. Cui, Y., E. Poyraz, K. B. Olsen, J. Zhou, K. Withers, S. Callaghan, J. Larkin, C. Guest, D. Choi, A. Chourasia, et al. (23). Physics-based seismic hazard analysis on petascale heterogeneous supercomputers, Proc. SC '3: Proc. of the International Conf. on High Performance Computing, Networking, Storage and Analysis, Denver, Colorado, 8 2 November 23. Day, S. M., D. Roten, and K. B. Olsen (22). Adjoint analysis of the source and path sensitivities of basin-guided waves, Geophys. J. Int. 89, 324, doi:./j x x. Denolle, M., E. M. Dunham, G. A. Prieto, and G. C. Beroza (23). Ground motion prediction of realistic earthquake sources using the ambient seismic field, J. Geophys. Res. 8, 22 28, doi:.29/ 22JB963. Denolle, M., E. M. Dunham, G. A. Prieto, and G. C. Beroza (24). Strong ground motion prediction using virtual earthquakes, Science 343, , doi:.26/science Denolle, M., H. Miyake, S. Nakagawa, N. Hirata, and G. C. Beroza (24). Long-period seismic amplification in the Kanto basin using the ambient seismic field, Geophys. Res. Lett. 4, , doi:.2/ 24GL942. Froment, B., M. Campillo, and P. Roux (2). Reconstructing the Green s function through iteration of correlations, C. R. Geosci. 343, no. 8, Graves, R., T. H. Jordan, S. Callaghan, E. Deelman, E. Field, G. Juve, C. Kesselman, P. Maechling, G. Mehta, K. Milner, et al. (2). CyberShake: A physics-based probabilistic hazard model for southern California, Pure Appl. Geophys. 68, , doi:.7/s Hanks, T., and W. Thatcher (972). A graphical representation of seismic source parameters, J. Geophys. Res. 77, no. 23, , doi:.29/jb77i23p4393. Lawrence, J. F., and G. A. Prieto (2). Attenuation tomography in the western United States from ambient seismic noise, J. Geophys. Res. 6, no. B632, doi:.29/2jb7836. Liu, X., Y. Ben-Zion, and D. Zigone (26). Frequency domain analysis of errors in cross-correlations of ambient seismic noise, Geophys. J. Int. 27, 6362, doi:.93/gji/ggw36. Longuet-Higgins, M. S. (9). A theory of the origin of microseisms, Phil. Trans. Roy. Soc. Lond. A 243, 3. Lozos, J. (26). A case for historic joint rupture of the San Andreas and San Jacinto faults, Sci. Adv. 2, no. 3, E62. Ma, S., and G. C. Beroza (22). Ambient-field Green s functions from asynchronous seismic observations, Geophys. Res. Lett. 39, L63, doi:.29/2gl7. Olsen, K. B., S. M. Day, J. B. Minster, Y. Cui, A. Chourasia, M. Faerman, R. Moore, P. Maechling, and T. Jordan (26). Strong shaking in Los Angeles expected from southern San Andreas earthquake, Geophys. Res. Lett. 33, L73, doi:.29/2gl2472. Paul, A., M. Campillo, L. Margerin, E. Larose, and A. Derode (2). Empirical synthesis of time-asymmetrical Green function from the correlation of coda waves, J. Geophys. Res., no. B832, doi:.29/24jb32.

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