Retrieving impulse response function amplitudes from the

submitted to Geophys. J. Int. 1 Retrieving impulse response function amplitudes from the ambient seismic field 3 Loïc Viens 1, Marine Denolle 1, Hiroe Miyake,3, Shin ichi Sakai and Shigeki Nakagawa 1 Earth and Planetary Sciences, Harvard University, Cambridge, MA, USA E-mail: loicviens@fas.harvard.edu Earthquake Research Institute, University of Tokyo, Tokyo, Japan. 3 Center for Integrated Disaster Information Research, Interfaculty Initiative in Information Studies, University of Tokyo, Tokyo, Japan 4 Received...; in original form... 5 6 Key words: Seismic interferometry; Seismic noise; Surface waves and free oscillations; Wave propagation; Body waves; Earthquake ground motions

L. Viens et al. 7 SUMMARY 8 9 1 11 1 13 14 15 16 17 18 19 1 3 4 5 6 7 8 9 3 31 3 Seismic interferometry is now widely used in passive seismology to retrieve the impulse response of the Earth between two distant seismometers. The phase information has been the focus of most studies, as conventional seismic tomography uses travel-time measurements. The amplitude information, however, is harder to interpret because it has been argued to strongly depend on the distribution of ambient seismic field sources and on the multitude of processing methods. Our study focuses on the latter by comparing the amplitudes of the impulse responses calculated between seismic stations in the Kanto sedimentary basin, Japan, using several processing techniques. This region provides a unique natural laboratory to test the reliability of the amplitudes with dense instrumentation, notably the Metropolitan Seismic Observation network (MeSO-net), and complex wave propagation with strong attenuation and basin amplification. We compute the impulse response functions using the cross correlation, coherency and deconvolution techniques of the raw ambient seismic field and the cross correlation of 1-bit normalized data. To validate the amplitude of the impulse response functions, we use a shallow M w 5.8 earthquake which occurred on the eastern edge of Kanto Basin close to a station that is used as a virtual source. Both S and surface waves are retrieved in the causal part of the impulse responses computed with the different techniques, but their amplitudes agree better with those of the earthquake with the deconvolution method. The amplification related to the structure of the Kanto Basin, which overcomes the attenuation, is clearly retrieved from the ambient seismic field. To test whether or not the anticausal part of the impulse response from deconvolution also contains reliable amplitude information, we use a virtual source on the western edge of the basin and show that their surface-wave amplitudes agree well with those of a nearby shallow M w 4.7 event. This study demonstrates that the deconvolution technique is the best strategy to retrieve reliable relative amplitudes from the ambient seismic field in the Kanto Basin and can be used to simulate earthquake ground motions.

Retrieval of impulse response function amplitudes 3 33 34 35 36 37 38 39 4 41 4 43 44 45 46 47 48 49 5 51 5 53 54 55 56 57 58 59 1 INTRODUCTION Over the past decade, new opportunities have emerged in seismology through ambient seismic field seismic interferometry. Shapiro & Campillo (4) empirically showed that the impulse response function (IRF) of the Earth can be retrieved by cross correlating ambient seismic field time series recorded by two distant seismometers. Under certain distribution of ambient seismic field sources, the IRF of the medium retrieved by cross correlation yields the true Green s function (Snieder 4; Wapenaar 4). The ambient seismic field on Earth is, however, mainly excited by the interaction of oceanic waves with the seafloor and the shores (Longuet-Higgins 195), which leads to an uneven distribution of the ambient seismic field sources that potentially biases both phase and amplitude information of the IRFs. The travel-time information of the IRF has been, up to now, the primary focus of passive seismology. To reduce the biases caused by the non-uniform distribution of ambient seismic field sources, pre-processing of the raw ambient seismic field (1-bit normalisation, pre-whitening) is routinely performed before computing the cross correlations (Bensen et al. 7). The travel-time measurements of the pre-processed IRFs have been used to image the Earth structure at local (Lin et al. 13; Mordret et al. 14; Roux et al. 16), regional (Shapiro et al. 5; Lin et al. 8; Nishida et al. 8), and global (Boué et al. 13) scales, to estimate seismic anisotropy (Mordret et al. 13; Takeo et al. 13), monitor velocity changes in volcanoes (Brenguier et al. 8b), and study the response of the crust after a large earthquake (Brenguier et al. 8a, 14). The amplitude information, in contrast, has attracted less attention because it appears to be more affected by the intensity and directionality of the ambient seismic field. Numerical (Cupillard & Capdeville 1; Lawrence et al. 13) and theoretical (Weaver 11; Tsai 11) studies predict a sensitivity of the amplitudes to the distribution of ambient seismic field sources as well as to the data processing. Despite this, several empirical studies demonstrated that the amplitude information seems to be preserved and can be used to simulate the long-period ground motions of moderate M w 4 5 (Prieto & Beroza 8; Denolle et al. 13; Viens et al. 15) and large M w > 6.5 (Denolle et al. 14a; Viens et al. 16b) earthquakes, map site amplification (Denolle

4 L. Viens et al. 6 61 6 63 64 65 66 67 68 69 7 71 7 73 74 75 76 77 78 79 8 81 8 83 84 85 86 87 et al. 14b; Bowden et al. 15) and infer seismic attenuation (Prieto et al. 9; Lawrence & Prieto 11). The amplitude of seismic waves can be affected by several effects: the elastic effects, which are the geometrical spreading, multipathing (focusing and defocusing) and scattering effects, and the anelastic effects, which are also called intrinsic attenuation. These processes are particularly efficient in complex shallow crustal structures, such as sedimentary basins. The low seismic-wave velocity of the soft sediments that compose basin and the shape of the basement both contribute to the trapping of seismic waves and thus their amplification. The Kanto Basin, Japan, is a sedimentary basin that is locally deeper than 4 km and is located beneath the Tokyo Metropolitan area. The Japan Integrated Velocity Structure Model (JIVSM) (Koketsu et al. 8, 1) shows that the basin is constituted of sediments that have S-wave velocities ranging between.5 and 1.5 km/s and that lie over a stiff bedrock of S-wave velocity equal to 3. km/s. The contours of the basement are shown in Figure 1. This complex and deep structure has a resonance period of 6 1 s (Kudo 1978, 198; Furumura & Hayakawa 7; Denolle et al. 14b) and the seismic waves amplified by the basin are a potential threat to the large scale urban structures, such as high-rise buildings or long-span bridges, of the Tokyo Metropolitan area. The Tokyo Metropolitan area is extremely well instrumented. The dense Metropolitan Seismic Observation network (MeSO-net), which is composed of 96 accelerometer stations, was deployed in shallow -m deep boreholes (Kasahara et al. 9; Sakai & Hirata 9) to assess the seismic hazard in the region. There are also dozens of instruments of the Hi-net of the National Research Institute for Earth Science and Disaster Resilience (NIED) (Okada et al. 4; Obara et al. 5), University of Tokyo, and Japan Meteorological Agency (JMA) networks (Figure 1). All stations record continuous signals that contain the waveforms of several moderate M w 4 5 earthquakes that occurred close to seismic stations (epicentral distances < 1 km). The ambient seismic field recorded by the stations has been used in several seismic interferometry studies to infer the complexity of the wave propagation and the seismic amplification in the basin (Denolle et al. 14b; Viens et al. 16a; Boué et al. 16). Therefore, the combination of the large number of stations, the complexity of wave propagation, and the numerous shallow earthquakes makes the

Retrieval of impulse response function amplitudes 5 88 89 9 91 9 93 94 95 96 97 area the ideal natural laboratory to investigate the recovery of reliable amplitudes from the ambient seismic field. In this study, we aim to determine the best processing strategy to retrieve reliable IRF amplitudes from the ambient seismic field. After introducing the different processing techniques, we compare the waveforms of the vertical-to-vertical IRFs computed using one virtual source station located on the eastern edge of the basin. To validate the surface-wave amplitude of the IRFs, we compare their long-period peak ground velocities (PGVs) with the ones of a shallow earthquake that occurred in the vicinity of the virtual source. Finally, we discuss the effect of seasonal variations, the retrieval of realistic S-wave amplitudes, and the possibility of using the anticausal part of the IRFs using one virtual source located on the western edge of the basin. 98 99 1 11 1 13 14 15 16 17 18 19 11 METHODS: CROSS CORRELATION, COHERENCY, AND DECONVOLUTION We use the ambient seismic field data recorded in October 14 by the seismic stations located close to the surface of the Kanto Basin. After instrumental response correction, the acceleration records of the MeSO-net stations are integrated once in time to retrieve the corresponding velocity waveforms and the data-set is divided into 1-hour time windows. Waveforms are band-pass filtered between.5 and Hz (.5 s) and down-sampled to 4 Hz to speed up the computation process. To reduce the bias that might be caused by earthquakes (Bensen et al. 7), we remove the windows that have spikes larger than 1 times the standard deviation of each time window. We finally compute the Fourier transform of each 1-hour non-overlapping time series after using a zero-padding of 1 times the length of the window to increase the resolution when performing the computation in the frequency domain. For each pair of virtual source-receiver stations, we compute the IRFs using three different techniques. The first method is the cross correlation and can be written as C ZZ (x r, x s, t) = F 1 (ˆv Z (x r, ω)ˆv Z(x s, ω)), (1) 111 where ˆv Z (x r, ω) and ˆv Z (x s, ω) are the Fourier transformed time series recorded by the vertical

6 L. Viens et al. 11 113 114 115 116 117 118 119 1 11 1 13 14 component Z at the receiver station x r and the virtual source x s. The symbol is the complex conjugate and ω is the frequency. The inverse Fourier transform, denoted by F 1, of the cross correlation is computed for each 1-hour time window to retrieve the waveforms in the time domain t. We finally stack the cross correlations over 1 month, represented by the brackets, to increase the signal to noise ratio (i.e., equivalent to spatially averaging the effect of the ambient seismic field sources). For the cross correlation, we use both raw and 1-bit normalized ambient field data. The 1-bit normalization is a widely used technique (Campillo & Paul 3; Shapiro & Campillo 4; Bensen et al. 7) that only retains the sign of the data, setting the positive values to 1 and the negative ones to 1. The second technique is the coherency. It is similar to pre-whitening in the frequency domain (Bensen et al. 7), and consists of using the amplitude spectrum of the raw data from both stations as a denominator term when performing the cross correlation. This process can be summarized as 15 16 17 18 19 ( Co ZZ (x r, x s, t) = F 1 ˆv Z (x r, ω)ˆv Z (x s, ω) { ˆv Z (x s, ω) }{ ˆv Z (x r, ω) } ), () where represents the absolute value and {} denotes a smoothing of the spectra using a moving average over points to stabilize the denominator terms. All the other notations are the same as in Equation 1. The third method is the deconvolution, where only the amplitude spectrum of the data recorded by the virtual source is used in the denominator, and can be written as 13 131 13 133 D ZZ (x r, x s, t) = where all the notations are the same as in Equations 1 and. ( F 1 ˆvZ (x r, ω)ˆv Z (x ) s, ω), (3) { ˆv Z (x s, ω) } The travel-time (or phase) information is preserved through all three techniques as the denom- inator term in Equations and 3 only affects the amplitude information. The regularization of the amplitude with the denominator term, however, prevents us from directly comparing the ampli-

Retrieval of impulse response function amplitudes 7 134 135 tudes from these three techniques without any scaling. In the following, we either normalize the amplitudes or calibrate them with earthquake records before comparing the waveforms. 136 137 138 139 14 141 14 143 144 145 146 147 148 149 15 151 15 153 154 155 156 157 158 159 16 3 EFFECTS OF THE PROCESSING ON THE IMPULSE RESPONSE FUNCTIONS We use the techniques described in Section to retrieve IRFs between the TENNOD station, which is the virtual source, and receivers in the basin. The virtual source station has been chosen because of its location close to the epicentre of a shallow M w 5.8 earthquake, which occurred in 14 March 1 at a depth of approximately 11 km (F-net/NIED catalog), that is used to validate the amplitude of the IRFs in Section 4. In the Kanto Basin, the primary source of the ambient seismic field is the Pacific Ocean. Such distribution of ambient seismic field sources and the location of the virtual source and receiver stations both lead to a strong asymmetry between the causal and anticausal parts of the IRFs. As the signal of the anticausal part is very weak, we only focus on the causal part of the IRFs for the TENNOD virtual source. Figure shows the four waveforms, which are normalized to their respective peak absolute value, computed between the TENNOD station and the E.SRTM and E.YMMM receivers (locations shown in Figure 1). In the 1 1 s period range, several groups of waves, which can be explained by the seismic wave propagation in the layered Kanto Basin (Boué et al. 16; Viens et al. 16a), can be observed. The earliest group of waves arriving at 15 and 5 s for the E.SRTM and E.YMMM stations, respectively, has been identified as S waves by Viens et al. (16a) and is seen in the four waveforms. However, differences in the amplitudes are observed among the waveforms, with smaller amplitudes retrieved with the deconvolution method. Nevertheless, the recovery of clear body waves from seismic interferometry without any additional computation remains unusual and has only been observed in a few studies (Roux et al. 5; Poli et al. 1; Boué et al. 13). The second and third wave packets in Figure are likely surface waves. The first group is well retrieved by all the methods, but its duration is shorter for the IRFs retrieved with the raw cross correlation. The second group is very weak for the waveforms obtained from raw and 1-bit cross correlations compared to the two other techniques. To explain this weak signal, we compute the

8 L. Viens et al. 161 16 163 164 165 166 167 168 169 17 171 17 173 174 175 176 177 178 179 18 181 18 183 184 185 186 187 188 Fourier spectra of the IRFs retrieved with the cross correlation and deconvolution techniques of raw data for 8 stations in Figure 3. These receivers are located within the azimuth range of 74 ± 4, between 15 and 1 km from the virtual source. The IRFs obtained by cross correlation have a narrower frequency content (.18 to.3 Hz), which corresponds to the frequency range of the secondary microseism peak, compared to that of the deconvolution (.1 to 1 Hz). Vasconcelos & Snieder (8) demonstrated that this discrepancy between the two techniques is expected because the dependence on the ambient seismic field sources is stronger for the cross correlation than for the deconvolution. Therefore, the last group of surface-wave arrivals, which has a dominant period content of 1 to 3 s (Viens et al. 16a), can only be retrieved by both the coherency and deconvolution methods that generate a broader frequency content. To study the effect of the processing on the reliability of the amplitudes, we assume that the dominant amplitude in the waveforms in sedimentary basins comes from the surface wave. We band-pass filter the IRFs at the same stations as in Figure 3 between 3 and 1 s. The two main reasons of the narrower band-pass filter are the following: first, the cross correlation can only retrieve waveforms at periods longer than 3 s; and second, Viens et al. (16a) demonstrated that both phases and amplitudes of the Z Z (vertical-to-vertical) IRFs between 3 and 1 s are highly similar to those of the M w 5.8 earthquake. Then, we correct their relative amplitude for the surfacewave geometrical spreading (1/ x s, where x s is the virtual source receiver distance) and compute the envelope of the signals using the Hilbert transform. Finally, the waves travelling faster than 5 km/s are probably non-physical and are tapered out. Figure 4 shows the envelopes, which are normalized by a single calibration factor taken as the peak amplitude at the station the closest to the virtual source, against the distance from the virtual source TENNOD. Despite the geometrical spreading correction, the amplitudes of the first surface-wave group generally decays with the increasing distance, a likely signature of the attenuation in Kanto Basin. However, remarkable local amplifications can be observed at some stations, as for example, at the two stations located between 6 and 7 km from the virtual source. We can also note that the amplitude of S waves retrieved with the cross correlation of raw and 1-bit data is higher than that of the two other techniques for most of the stations. Despite the surface-wave geometrical spreading correction,

Retrieval of impulse response function amplitudes 9 189 19 the amplitude of S waves decreases faster than that of the surface waves, which validates that the long-period surface waves are dominant in the Kanto Basin. 191 19 193 194 195 196 197 198 199 1 3 4 5 6 7 8 9 1 11 1 13 14 15 4 VALIDATION AGAINST EARTHQUAKE RECORDS: ATTENUATION AND AMPLIFICATION We showed in Section 3 that the dominant signal is contained by the first group of surface-wave arrivals. To validate the amplitude of this group of waves, we compare their long-period PGVs with those of the M w 5.8 earthquake. However, only the relative amplitude is preserved by seismic interferometry techniques and the IRFs must be calibrated against the earthquake velocity records. To scale up the amplitude of the IRFs to that of the earthquake, we calculate the ratio of earthquake to IRFs long-period PGV at each selected station, compute the mean of the ratio, and correct the IRFs by this factor. This correction is the same for the selected stations but is different for the cross correlation, coherency and deconvolution techniques. We also account for the difference between the epicentre and virtual source locations, which leads to a difference in surface-wave geometrical spreading. We effectively shift the virtual source to the earthquake epicentre by correcting the amplitudes with the ratio of the geometrical spreading terms x s / x, where x s is the virtual source receiver distance and x is the epicentre receiver distance. This correction is relatively minor (mean value of.96) given the proximity of the virtual source to the real source epicentre (8.3 km), the period range of interest (3 1 s), and the fact that the virtual source and the earthquake are located outside of the Kanto Basin (higher seismic wave velocity and therefore longer wavelengths). To reduce the azimuthal effects related to the non-uniform distribution of the ambient seismic field sources and to the surface-wave radiation pattern at the earthquake source (Denolle et al. 14a; Viens et al. 16b), we only calibrate the IRFs within narrow azimuth ranges of 8. Finally, we select the stations located at distances greater than 3 km from the epicentre to ensure a similar path effect for the earthquake and IRF waveforms. The two corrections applied to the amplitudes and the station selection allow us to compare the simulated IRF PGVs with the observed, ground truth, earthquake PGVs.

1 L. Viens et al. 16 17 18 19 1 3 4 5 6 7 8 9 3 For the stations located within the 64±4 azimuth angle from the epicentre, we plot the natural logarithm of the long-period PGVs as a function of the distance from the epicentre in Figure 5. We also show the 1/ x and 1/ x e αx theoretical curves, where x is the epicentre receiver distance and α is an effective attenuation coefficient. We choose a constant value of α = 14 1 3 km 1, which is close to the values found by Prieto et al. (11) in the Los Angeles sedimentary basin (e.g., α = 5 1 3 km 1 in the 5 to 1 s period range). In Figure 5, we can observe that the amplitude decay of the IRF and earthquake PGVs follows the 1/ x e αx theoretical curve relatively well for distances smaller than 8 km and larger than 14 km from the epicentre. However, between 8 and 14 km, there is a large amplification for both predicted and observed values. This amplification correlates well with the deepest part of basin (Koketsu et al. 8, 1), which is also shown in Figure 5. Such amplification at large distance demonstrates that elastic 3-D effects of wave focusing overcome the attenuation in Kanto Basin. To further quantify the match between the observed and predicted amplitudes, we compute the root mean square error (RMS error) between the natural logarithm (ln) of the PGVs, which can be written as RMS error = N n=1 (ln(p GV n eq) ln(p GV n N IRF )), (4) 31 3 33 34 35 36 37 38 39 4 41 where P GV n GF and P GV n eq are the IRF and earthquake PGVs, respectively, and n is the nth sta- tion of a total number of stations N located within an azimuth range. For the 67 stations located within the 64±4 azimuth range, the RMS errors are equal to.39,.457, and.51 for the de- convolution, coherency, and cross correlation, respectively. The minimum RMS error is obtained for the IRFs retrieved with the deconvolution method. The RMS error computed from the PGVs retrieved with the cross correlation technique is comparable to that from the deconvolution and much smaller than the one from the coherency technique. To study the azimuthal dependence of the RMS error, we compute the RMS error for stations located within 8 azimuth ranges, every between 54 and 9 from the epicentre. Results are shown for the raw and 1-bit cross correlation in Figure 6a and for the coherency and deconvolution

Retrieval of impulse response function amplitudes 11 4 43 44 45 46 47 48 49 in Figure 6b. The largest RMS error is obtained for the coherency technique at almost all azimuth angles and the smallest RMS errors are found with the raw cross correlation and deconvolution methods. We also find that the RMS error is higher for the azimuth angles larger than 84. To evaluate the consistency of the PGVs in the RMS estimates, we bootstrap Equation 4 by randomly resampling 1 times the original PGV values and evaluating the 95% confidence interval of the RMS error of the new set of PGV values (Figure 6). As expected, fewer stations in the azimuth angles larger than 84 lead to a greater uncertainty in the RMS value, but the overall mean RMS value may arise from biases due to non-uniform source distribution. 5 51 5 53 54 55 56 57 58 59 6 61 6 63 64 65 66 67 68 5 DISCUSSION 5.1 Seasonal variations The IRFs studied in the previous sections are computed using 1 month of data recorded in October 14. To investigate the effect of possible seasonal variations, we compute the deconvolutions using Equation 3 for the months of April, June, August, and December 14. The waveforms between the TENNOD virtual source and the E.SRTM and E.YMMM receivers, which are normalized with the maximum value of month of April, are shown in Figures 7a and 7b, respectively. The shape of the waveform slightly changes over the year, but the different wave arrivals are observed for each month. Moreover, the maximum amplitude is almost constant over the year and no clear seasonal pattern can be deduced for these two stations. We compute the maximum values of the waveforms normalized with the month of April for all the stations located in the 5 94 azimuth range from the epicentre, and summarize their mean and standard deviation values in Table 1. The amplitudes are the lowest in April, but weakly vary with the seasons (less than 1%) and the standard deviation is around. for each month. This shows that the peak value of the waveforms is stable throughout the year in the Kanto Basin. This contrasts with the study of Stehly et al. (6) that noticed dramatic seasonal variations in the amplitudes with the seismic network in southern California. To verify whether or not the small amplitude variations observed over the year impact the retrieval of earthquake PGVs, we calibrate the IRF amplitudes for each month following the same

1 L. Viens et al. 69 7 71 7 73 74 75 76 77 78 79 8 81 procedure as in Section 4. Figure 8 shows the RMS errors computed using Equation 4 for each month against the azimuth angle from the epicentre. Small variations can be observed over the different months, but the general trend remains the same throughout the year. One interesting feature is that the RMS error for the month of August is the highest for azimuth angles smaller than 6, but the smallest for azimuth angles greater than 8. This can be interpreted that August experienced a more localized, or nearer noise source to influence the amplitude with the somewhat narrow azimuth coverage. December experiences the opposite trend, likely for a similar reason. The month of October allows to retrieve minimum RMS errors in the central part of the basin where strong and complex 3-D effects are observed. One possible explanation for the minimum RMS error for the data recorded in October 14 is that two typhoons passed over the Kanto Basin during this month and might have excited the ambient seismic field more efficiently. However, further work is needed to understand the potential effect of strong meteorological events on our results. 8 83 84 85 86 87 88 89 9 91 9 93 94 95 5. S-wave amplitudes Along the 74±4 azimuth angle, clear S waves can be retrieved. To investigate the reliability of their amplitudes, we perform the same kind of analysis as done for the surface waves. We first band-pass filter the data between 4 and 1 s and we select the phases traveling between 1.7 and 5 km/s. We calibrate the amplitude of the S waves following the same procedure as in Section 4, but with the ratio of the virtual source receiver and hypocentre receiver distances to account for the geometrical spreading of body waves (x n /x h, where x n is the virtual source receiver distance and x h is the hypocentre receiver distance). The S-wave long-period PGVs of the earthquake and IRF are shown in Figure 9. The amplitude of the S waves are reliable with the coherency and deconvolution methods for distances larger than 6 km from the hypocentre. Similarly to surface waves, S waves are clearly amplified in the deepest part of the basin. The overestimation of the IRF PGVs for distances smaller than 6 km from the hypocentre might be explained by the fact that body waves travel directly from the hypocentre to the stations through the basement of the Kanto Basin. Therefore, body waves from the surface-to-surface instruments likely undertake a different

Retrieval of impulse response function amplitudes 13 96 97 98 ray path than from the deep source to the surface instrument. Nevertheless, reliable amplitudes of body waves can be extracted from the ambient seismic field at sufficient distance from the hypocentre using the deconvolution technique. 99 3 31 3 33 34 35 36 37 38 39 31 311 31 313 314 315 316 317 318 5.3 Can the anticausal part of the deconvolution be used? So far, we have only studied the amplitude information of the causal part of the IRFs for seismic waves propagating westward, away from the coast. For earthquakes located on the west of the basin, however, seismic waves will propagate toward the East and most of the energy of IRFs will be contained in the anticausal part. Such configuration is, for example, similar to Southern California (Stehly et al. 6) where earthquakes are expected along the San Andreas Fault and their seismic waves will radiate towards the coast where the Los Angeles Metropolitan area is located. Therefore, evaluating the reliability of the amplitude information contained in the anticausal part of IRFs is critical to predicting shaking from those earthquakes using the ambient seismic field. We retrieved the IRFs with the deconvolution method for the data recorded in October 14 by regarding the E.ZKUM station as the virtual source. This station is located close to a M w 4.7 earthquake (Figure 1), which occurred in 8 January 1 at a depth of km (F-net/NIED catalog). We also use the same calibration procedure as in Section 4 for the surface waves propagating at velocities between.5 and 3 km/s, and show the results for two azimuth angles in Figure 1. We choose the 7±4 angle because of the large number of stations and the 9±4 to sample the deepest part of the Kanto Basin. For these two azimuths, the RMS errors (e.g.,.41 and.476) are comparable to those of the causal part. Observed and simulated PGVs for the stations located above the deepest part of the basin, which reaches a depth of 4.1 km, are clearly amplified compared to the stations located above a basin depth of approximately 3 km. This demonstrates that the amplitude of the anticausal part of IRFs can also be trusted. 319 3 31 6 CONCLUSIONS We retrieved IRFs from the ambient seismic field recorded in the Kanto Basin using three seismic interferometry techniques. We first showed that the waveforms retrieved with the cross correla-

14 L. Viens et al. 3 33 34 35 36 37 38 39 33 331 33 333 334 335 336 337 338 tion technique have a narrower frequency content than the IRFs extracted with the coherency and deconvolution methods. To validate the surface-wave amplitudes of the amplitude calibrated IRFs, we compared their long-period PGVs to those of a shallow M w 5.8 earthquake that occurred nearby the virtual source station. The long-period PGVs of the waveforms retrieved with the cross correlation and deconvolution techniques agree well with the ones of the earthquake and complex 3-D effects, likely caused by the basin structure, are well captured by the ambient seismic field. We also investigated the sensitivity of the amplitudes to seasonal variations and showed that despite small variations, they remain relatively constant throughout the year for the deconvolution method. We also showed that the amplitudes of S waves are preserved for distances greater than 6 km from the hypocentre with the deconvolution and coherency techniques. Finally, we conducted the same analysis on the surface-wave amplitude of the anticausal part of the IRFs from the deconvolution using an earthquake that occurred on the western part of the basin. The large amplification caused by the deepest part of the Kanto Basin is also well retrieved. This analysis demonstrates that the deconvolution technique produces broadband IRFs that contain both surface- and S-wave amplitudes that reproduce those of earthquakes in the complex Kanto Basin. Finally, IRFs obtained from deconvolution can be used to predict accurate seismic amplitudes of future earthquakes. 339 34 341 34 343 344 ACKNOWLEDGMENTS We acknowledge Hi-net/NIED and JMA for providing the continuous data and F-net/NIED for the information about the earthquakes used in this study. We thank Naoshi Hirata and all the MeSOnet project members for the MeSO-net data. The MeSO-net project is supported by the Special Project for Reducing Vulnerability for Urban Mega Earthquake Disasters from the Ministry of Education, Culture, Sports, Science, and Technology (MEXT) of Japan. 345 346 347 REFERENCES Bensen, G. D., Ritzwoller, M. H., Barmin, M. P., Levshin, A. L., Lin, F., Moschetti, M. P., Shapiro, N. M. & Yang, Y., 7. Processing seismic ambient noise data to obtain reliable broad-band surface wave

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Retrieval of impulse response function amplitudes 19 Table 1. Mean and standard deviation of the peak values of the waveform for the months of April, June, August, October, December 14, normalized to peak value of the month of April 14. For each month, we use the deconvolution method between the TENNOD virtual source and 39 receiver stations located within the 5 94 angle from the epicentre. Normalized peak value April June August October December Mean 1. 1.6 1.6 1.4 1.11 Standard deviation..19...

L. Viens et al. 36.5 N 9 Philippine Sea Plate Pacific Plate 36. N 5 km Mw 5.8 E.SRTM 35.5 N Mw 4.7 E.ZKUM 54 E.YMMM TENNOD MeSO net Hi net JMA Univ. Tokyo Earthquakes 35. N 4 Basin depth (km) 139. E 139.5 E 14. E 14.5 E 141. E Figure 1. Map of the Kanto Basin, Japan, including stations of the MeSO-net (purple triangles), Hi-net (black triangles), JMA (blue triangles), and University of Tokyo (green triangles) networks. Coastlines are represented by the black lines and five hundred meter spaced basin depth contours derived from the JIVSM (Koketsu et al. 8, 1) are shown by the coloured lines. The names of the TENNOD and E.ZKUM virtual sources and the two receivers for which the waveforms are shown in Figures and 7 are also showed. The epicentre of the M w 5.8 and 4.7 earthquakes are represented by the red stars and their focal mechanisms are plotted. The two azimuth angles of 54 and 9 that are used in the following are represented by the two black lines departing from the M w 5.8 earthquake epicentre. The upper right insert shows the Japanese Islands (black lines), plate boundaries (grey lines), and the zoomed region (red square).

Retrieval of impulse response function amplitudes 1 Normalized amplitude (a) 8 S wave 7 6 5 4 3 1 TENNOD - E.SRTM (44 km), BP: 1-1 s Vertical component Surface waves 1st arrivals nd arrivals Raw cross correlation 1-bit cross correlation Coherency Deconvolution Normalized amplitude 8 7 6 5 4 3 1 (b) S wave TENNOD - E.YMMM (67 km), BP: 1-1 s Vertical component Surface waves 1st arrivals nd arrivals Raw cross correlation 1-bit cross correlation Coherency Deconvolution -1 5 1 15 5 Time (s) -1 5 1 15 5 Time (s) Figure. Impulse response functions retrieved from the raw cross correlation (red), 1-bit cross correlation (orange), coherency (green), and deconvolution (blue) techniques between the virtual source (TENNOD) and the (a) E.SRTM and (b) E.YMMM stations, which are located at 44 and 67 km from the virtual source, respectively. The location of these two stations is shown in Figure 1. All the waveforms are shown for the Z Z component and are bandpass filtered between 1 and 1 s. The name of each group of arrivals is also indicated.

L. Viens et al. 1 Fourier spectra Vertical component Normalized amplitude 1 1 - Deconvolution Raw cross correlation 1-4.1..3.4.5.6.8 1. Frequency (Hz) Figure 3. Fourier spectra of the impulse response functions extracted using the deconvolution (black) and the cross correlation (red) techniques between the TENNOD virtual source and 8 receiver stations. The thick lines represent the geometric mean of the 8 Fourier spectra. The waveforms are normalized with the peak value of the closest station to the virtual source (18 km) before being Fourier transformed.

11 S wave Retrieval of impulse response function amplitudes 3 Band-pass filter 3-1 s Vertical component 1st arrival of surface wave 1 9 Distance from the TENNOD station 8 7 6 5 4 3 Raw cross correlation 1-bit cross correlation Coherency Deconvolution 5 1 15 5 3 35 Time (s) Figure 4. Envelope of the Z Z impulse response functions retrieved from the raw cross correlation (red), 1-bit cross correlation (orange), coherency (green), and deconvolution (black) techniques as a function of the distance from the virtual source. All the impulse response functions are normalized with the maximum value of the waveform at the closest station from the virtual source, corrected for the geometrical spreading of surface waves (1/ x s, where x s is the virtual source receiver distance), and band-pass filtered in the period range of 3 to 1 s.

4 L. Viens et al. 36 N Mw 5.8 64 ± 4 TENNOD 5 km 4 Basin depth (km) 35 N 139 E 14 E 141 E Deconvolution RMS error:.39 Coherency RMS error:.457 Raw cross correlation RMS error:.51 Vertical component ln of long-period PGV (ln(cm/s)) -1 - -3-4 Earthquake IRF -1 - -3-4 -1-1 -1 Basin depth (km) 1.5.9 1.5 1.5.9 1.5.5.9 1.5 1 3 Vs = 3. km/s 3 Vs = 3. km/s Vs = 3. km/s 3 5 1 15 Distance from epicentre (km) 5 1 15 Distance from epicentre (km) 5 1 15 Distance from epicentre (km) Figure 5. (Upper panel) Map of the Kanto Basin including the basin depth contours from the JIVSM and all the seismic stations. The receiver stations included in the 64±4 azimuth range, which is represented by the two black lines, are used in this figure. (Middle panels) Natural logarithm of the long-period PGVs of the earthquake (red) and impulse response functions (IRFs) after amplitude calibration (blue) waveforms for the three different techniques. The black curves are the theoretical curves 1/ x and 1/ xe αx, where x is the epicentre receiver distance and α is an attenuation coefficient taken as 14 1 3 km 1. For each panel, the RMS error computed using Equation 4 is also shown. (Bottom panels) Velocity profile extracted from the JIVSM (Koketsu et al. 8, 1) for an azimuth angle of 64 from the epicentre. The S-wave velocity of each layer is indicated and the thick line represents the basin depth.

Retrieval of impulse response function amplitudes 5 (a).7.65 Raw cross correlation 1-bit cross correlation (b).7.65 Coherency Deconvolution.6.6.55.55 RMS error.5.45.4 RMS error.5.45.4.35.35.3.3.5.5. 5 56 6 64 68 7 76 8 84 88 9 Azimuth angle ( ). 5 56 6 64 68 7 76 8 84 88 9 Azimuth angle ( ) Figure 6. (a) Mean of the RMS error computed from the long-period PGVs of the earthquake and the impulse response functions retrieved with the raw cross correlation (red squares) and 1-bit cross correlation (orange squares) techniques as a function of the azimuth angle from the epicentre. For each azimuth angle, the 95% confidence interval of the bootstrap is indicated by the error bars. (b) Same as Figure 6a for the RMS errors computed from the long-period PGVs of the earthquake and the impulse response functions computed with the coherency (green) and deconvolution (black) methods.

6 L. Viens et al. (a) TENNOD E.SRTM (44 km), BP: 3 1 s Vertical component (b) TENNOD E.YMMM (67 km), BP: 3 1 s Vertical component 9 8 December (1.19) 9 8 December (1.3) Normalized amplitude 7 6 5 4 3 October (1.9) August (.99) June (1.18) Normalized amplitude 7 6 5 4 3 October (.93) August (.88) June (.87) 1 April (1) 1 April (1) 1 5 1 15 Time (s) 1 5 1 15 Time (s) Figure 7. Impulse response functions retrieved with the deconvolution method between the virtual source (TENNOD) and the (a) E.SRTM and (b) E.YMMM stations from the raw data recorded in April (black), June (blue), August (orange), October (red) and December (green) 14. The waveforms are normalized with the peak amplitude of the impulse response retrieved for the month of April and the maximum value of each waveform is indicated between parenthesis. All the waveforms are shown for the Z Z component and are bandpass filtered between 3 and 1 s.

Retrieval of impulse response function amplitudes 7.6 RMS error.55.5.45.4.35 April June August October December.3.5. 5 56 6 64 68 7 76 8 84 88 9 Azimuth angle ( ) Figure 8. Mean of the RMS error computed from the long-period PGVs of the earthquake and impulse response functions extracted with the deconvolution technique using the data recorded in April (black), June (blue), August (orange), October (red), and December (green) 14 as a function of the azimuth angle from the epicentre.

8 L. Viens et al. 36 N 74 ± 4 Mw 5.8 TENNOD 5 km 4 Basin depth (km) 35 N 139 E 14 E 141 E Vertical component ln of Long-period PGV (ln(cm/s)) -1-1.5 - -.5-3 -3.5-4 -4.5 - Deconvolution RMS error:.39 - Coherency RMS error:.41 Earthquake IRF Raw cross correlation RMS error:.464-1 -1.5 - -.5-3 -3.5-4 -4.5 - -1-1 -1 Basin depth (km) 1 3.5.9 1.5 Vs = 3. km/s 1 3.5.9 1.5 Vs = 3. km/s.5.9 1.5 Vs = 3. km/s 1 3 5 1 15 Distance from hypocentre (km) 5 1 15 Distance from hypocentre (km) 5 1 15 Distance from hypocentre (km) Figure 9. (Upper panel) Map of the Kanto Basin including the basin depth contours from the JIVSM and all the seismic stations. The receiver stations included in the 74±4 azimuth range, which is represented by the two black lines, are used in this figure. (Middle panels) Natural logarithm of the S-wave long-period PGVs of the earthquake (red) and impulse response functions (IRFs) after amplitude calibration (blue) waveforms for the three different techniques as a function of the distance from the hypocentre. For each panel, the RMS error computed using Equation 4 is also shown. (Bottom panels) Velocity profile extracted from the JIVSM (Koketsu et al. 8, 1) for an azimuth angle of 74 from the hypocentre. The S-wave velocity of each layer is indicated and the thick line represents the basin depth.