Coseismic velocity change in and around the focal region of the 2008 Iwate-Miyagi Nairiku earthquake

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 117,, doi: /2012jb009252, 2012 Coseismic velocity change in and around the focal region of the 2008 Iwate-Miyagi Nairiku earthquake Ryota Takagi, 1 Tomomi Okada, 1 Hisashi Nakahara, 2 Norihito Umino, 1 and Akira Hasegawa 1 Received 22 February 2012; revised 12 May 2012; accepted 15 May 2012; published 29 June [1] The 2008 M7.2 Iwate-Miyagi Nairiku earthquake occurred in NE Japan where dense seismic networks exist. Using the data from these networks, we determined the coseismic seismic velocity change associated with this earthquake by two different methods: ambient noise interferometry and vertical array interferometry of coda wave. The purpose of this article is to reveal the spatial distribution and the cause of the velocity change by integrating these two approaches. Ambient noise interferometry revealed a coseismic velocity decrease of Rayleigh wave by % at Hz. We also estimated the spatial distribution of the velocity change by a tomographic inversion. The velocity decrease was distributed in and around the focal area. In the second method, we applied cross-correlation analysis to coda waves observed by the KiK-net vertical array. We detected a shear velocity decrease of approximately 5% in shallow layers up to a few hundred meters depth. Quantitative comparison of the two results reveals that the 5% shear velocity decrease in shallow layers can explain the % decrease of Rayleigh wave velocity. The distribution of the velocity decrease is similar to that of the strong ground motion and the static stress change. However, a significant velocity increase is not observed in the compression area, where a velocity increase is expected. Based on the observations, we consider that the primary factor affecting the velocity change is damage in shallow layers due to strong motion. The effect of the static stress change might be masked by the larger effect of the strong motion. Citation: Takagi, R., T. Okada, H. Nakahara, N. Umino, and A. Hasegawa (2012), Coseismic velocity change in and around the focal region of the 2008 Iwate-Miyagi Nairiku earthquake, J. Geophys. Res., 117,, doi: /2012jb Introduction [2] Monitoring the seismic velocity in the Earth s crust is one of primary targets of seismological studies. The seismic velocity is affected by stress accumulation and pore pressure change, which could directly relate to the occurrence of earthquakes. In addition, estimating site effects after large earthquakes in shallow layers is important in order to accurately predict strong ground motion. [3] Temporal velocity changes associated with large earthquakes and volcanic activity have been observed in several previous studies. Poupinet et al. [1984] observed a velocity decrease after the Coyote Lake earthquake in 1979 using moving window cross-spectral analysis for seismograms of an 1 Research Center for Prediction of Earthquakes and Volcanic Eruptions, Graduate School of Science, Tohoku University, Sendai, Japan. 2 Department of Geophysics, Graduate School of Science, Tohoku University, Sendai, Japan. Corresponding author: R. Takagi, Research Center for Prediction of Earthquakes and Volcanic Eruptions, Graduate School of Science, Tohoku University, 6-6 Aza-Aoba, Aramaki, Aoba-ku, Sendai , Japan. (r-takagi@aob.gp.tohoku.ac.jp) American Geophysical Union. All Rights Reserved /12/2012JB earthquake doublet observed at the same station. Nishimura et al. [2000] applied a similar method to repeated active experiments near Mt. Iwate and detected a velocity decrease of %. Nakamura et al. [2002] revealed a P wave velocity change of at least 1% in shallow regions associated with the 1998 M6.1 Shizukuishi earthquake in NE Japan, using earthquake doublets and active experiments. Based on observations of the delay of the coda wave, they also reported that crustal heterogeneity at greater depths should be changed. Earthquake doublets and/or active experiments with the same hypocenters repeatedly excite similar seismic waves, such that reliable temporal velocity changes are detected without errors in earthquake location or origin time. [4] Recently, ambient noise interferometry has been developed and used to monitor seismic velocity near fault zones and volcanoes. Ambient noise interferometry is an application of seismic interferometry. Seismic interferometry can be used to extract the seismic wave propagation between two seismic stations by computing the cross correlation of random wavefields, such as the ambient seismic noise or the seismic coda wave, recorded at two stations [Weaver and Lobkis, 2001; Campillo and Paul, 2003]. Ambient noise is primarily excited by ocean waves. Surface waves extracted using the cross-correlation function of the 1of19

2 ambient noise are sufficiently accurate for estimating the velocity structure by tomographic inversion [Shapiro et al., 2005]. Ambient noise interferometry is also suitable for detecting the temporal change of subsurface structure at high temporal-spatial resolution because ambient noise is recorded at all times and places. By applying this method to the seismic network in Parkfield, Brenguier et al. [2008] observed a coseismic decrease and post seismic recovery in the seismic velocity associated with the 2004 Mw6.0 Parkfield earthquake. A coseismic velocity change was also detected after the 2004 Mw6.4 Mid-Niigata earthquake [Wegler et al., 2009]. Moreover, Wegler et al. [2009] revealed a sudden drop in seismic velocity upon the occurrence of the main shock using not only the cross-correlation function but also the auto-correlation function of ambient noise. [5] The coda wave is another random wavefield generated by multiple scattering due to heterogeneous structure. Seismic interferometry applied to the coda wave is also useful for exploring the subsurface structure and detecting temporal changes. Sawazaki et al. [2006, 2009] reported a shear velocity decrease within a shallow layer 100 m from the surface associated with the 2000 Mw6.0 Western Tottori earthquake. They used an interferometric method on the coda wave observed at the KiK-net vertical array in Japan. [6] These previous studies revealed that large earthquakes cause temporal velocity changes. However, a number of problems remain to be solved. For example, where does the velocity change occur? Few studies have determined the spatial distribution of the velocity change, although this could be a clue to understanding its cause. Several different factors are likely to affect a seismic velocity change, such as strong ground motion and a static stress change. However, the question remains as to what the primary factor affecting the velocity change is. [7] One difficulty in addressing this question in previous studies may have been the absence of a dense seismic network near the locations where large earthquakes occurred. However, in Japan, nationwide dense seismic networks, such as Hi-net and KiK-net, are operated by the National Research Institute for Earth Science and Disaster Prevention (NIED). The 2008 M7.2 Iwate-Miyagi Nairiku earthquake occurred on 14 June 2008 in the central part of the Tohoku region in northeast Japan. The fault zone of the earthquake is located in the Ou Backbone Range strain concentration zone [Miura et al., 2004]. The depth of the hypocenter was approximately 5 km and the aftershocks alignment was westward dipping [Okada et al., 2010]. The mechanism of the main shock was a reverse fault type. An accelerometer located near the hypocenter recorded a strong motion of approximately 4,000 Gal [Aoi et al., 2008]. An advantage to focusing on this earthquake is that the hypocenter is located among dense seismic networks. [8] Moreover, in the present study, we investigated the coseismic velocity change associated with the 2008 Iwate- Miyagi Nairiku earthquake by integrating two approaches: ambient noise interferometry and vertical array analysis of the coda wave. First, we performed ambient noise cross-correlation analysis to detect the temporal velocity change in the Rayleigh wave using continuous Hi-net records and the records of the Japan Meteorological Agency (JMA) and Tohoku University. We also estimated the spatial distribution of the velocity change using a tomographic inversion. Second, we analyzed the earthquake coda observed at the KiK-net vertical array in order to estimate the shear velocity change in the superficial layer. Finally, by comparing the two sets of results, we considered the cause of the velocity change. 2. Coseismic Change in Rayleigh Wave Velocity Inferred From Ambient Noise Analysis 2.1. Data [9] The data are the vertical components of continuous records observed at 104 seismic stations in the central part of the Tohoku region (Figure 1). The seismic network consists of 86 short-period sensors (43 sensors of Hi-net, 33 sensors of Tohoku University, and 10 short-period sensors of the JMA) and 18 broadband sensors (three sensors of F-net and 15 sensors of Tohoku University). The natural periods of the short-period sensors are 1 or 0.5 s, and the natural periods of the broadband sensors are 20, 120, or 360 s. Hi-net and F-net are operated by the NIED. The sampling frequency of each sensor is 100 Hz. We analyzed seven months of data during the period from 1 March 2008 to 30 September 2008, which is 105 days before and 108 days after the 2008 Iwate-Miyagi Nairiku earthquake. In the ambient noise study, we did not use the station N.ICWH because of the lack of data after the earthquake and the possibility of change in instrument response due to the main shock. [10] In the present study, we analyzed signals below 1 Hz. Data of broadband sensor are more suitable for analysis below 1 Hz because the gain of short-period sensor decays below 1 Hz. The Hi-net tiltmeter also can be used as a broadband sensor [Nishida et al., 2008]. However, the wide dynamic range of short-period sensors enables us to use low frequency signals regardless of low amplitude due to instrument response. Figure 2 shows an example of crosscorrelation functions both for a station pair of Hi-net shortperiod sensors and for a pair of broadband sensors of Tohoku University that are computed by the method described in next section. These station pairs have similar geometry as shown in Figure 1. The cross-correlation function of Hi-net data is comparable to that of broadband data approximately up to 0.1 Hz. Therefore, in this study, we consider that crosscorrelation functions of data observed by short-period sensors are available for detection of the seismic velocity change below 1 Hz Cross-Correlation Method [11] Monitoring the seismic velocity with ambient noise is conducted in two steps. The first step involves extracting the Green s function between two stations by computing the cross-correlation function (CCF) of the ambient noise observed at these stations. The second step involves measuring the time delay and the velocity change by comparing two CCFs for different time periods. [12] In the first step, we calculated the daily CCF from one day-long data set. We divided this into several segments with a length of 360 s and an overlap of 180 s. For each segment, we removed the data offset, resampled the data at intervals of 0.05 s, and corrected for the instrumental response. [13] In order to diminish contamination due to outliers such as earthquake signals and instrumental noise due to 2of19

3 Figure 1. Map of seismic stations and aftershock distribution. White star indicates the epicenter of the main shock. The focal depth is approximately 5 km. Gray circles indicate aftershocks determined by Okada et al. [2012]. The aftershocks between 14 June and 30 September 2008 are shown in this figure. data transfer errors, we removed large amplitude outliers. The daily average level of ambient noise at a seismic station is assumed to be the median of the root-mean square (RMS) amplitudes of all 360-s segments within the day. A segment for which the RMS amplitude was larger than twice that of the median was discarded from the analysis. In this procedure, the average level of ambient noise differs for different days and different stations. [14] Then, we normalized the data amplitude of the 360-slong records in both the frequency and the time domains [Bensen et al., 2007]. In order to normalize the record in the frequency domain, we applied a fast Fourier transform and divided a spectrum by its absolute amplitude at all frequency points, which is referred to as spectral whitening. Then, after performing an inverse Fourier transform, positive amplitudes are assigned a value of +1 and negative amplitudes a value of 1, which is referred to as one-bit normalization. Spectral whitening enhances the temporal change in the CCFs because the source spectrum is canceled out. The onebit normalization reduces the contamination of the deterministic phase that has a large amplitude, such as earthquake signals and instrumental noise. We performed the one-bit normalization in order to reduce the effect of deterministic phases that are not discarded in the previous procedure using the RMS amplitude. [15] After this preprocessing, we computed the CCF of each segment. The CCF is computed in the frequency domain using the fast Fourier transform and is then computed back into the time domain. The daily CCF is the average of the CCFs of all segments within the day. We applied the two-way fourth-order Butterworth filter for the CCFs and examined the velocity change in three frequency bands of Hz, Hz, and Hz Cross-Correlation Function [16] Figure 3b depicts the daily CCFs between stations N.OGCH and N.ICEH in the frequency range of Hz. The CCFs have clear peaks at around 20 s. The largest peak in negative lag corresponds to the wave that propagates from the Pacific coast. The apparent velocity is approximately 2.2 km/s and consistent with the fundamental mode of the Rayleigh wave. Although it exhibits fluctuations in amplitude due to changes in the noise source, the phase of CCFs seems to be stable over time. [17] The amplitude of CCFs can be simply used for estimation of azimuthal distribution of the noise source [Stehly et al., 2006]. In order to estimate temporal change in the noise source, we averaged daily CCFs for 10-day windows with an overlap of 5 days. Then, the peak envelope amplitudes for both causal and acausal parts of CCFs are averaged every 5 of azimuth of station pairs. The causal and acausal parts mean positive lag and negative lag, respectively. Before the averaging, the geometrical spreading is corrected by multiplying the amplitude by square root of separation distance. Figure 3c shows the azimuthal dependence of CCF amplitude in the frequency range of Hz. The large amplitude from 15 to 210 indicate that the noise sources are mainly distributed in the Pacific Ocean. The azimuthal 3of19

4 Figure 2. Example of cross-correlation functions for a pair of Hi-net (N.HMNH-N.KMIH) and for a pair of broadband sensors (TU.SWU-TU.KMB). (a, b) Raw CCFs for N.HMNH-N.KMIH and TU.SWU-TU. KMB. (c, d) Band-path filtered CCFs with the frequency band specified in upper right of each panel. distribution is stable before and after the earthquake without a contamination of aftershocks. In addition, in this time period, long-term variation and seasonal variation of the noise source is not obvious Measurement of the Velocity Change [18] In the second step, we estimated the temporal velocity change using these CCFs as Green s functions of Rayleigh wave between two stations. In order to estimate the velocity change, we measured the time-shift of CCFs relative to a reference CCF. The reference CCF is computed by averaging daily CCFs over 105 days before the earthquake. The velocity change was determined by measuring the time delay between the reference CCF and a moving average of daily CCFs. [19] In the present study, we used the direct part of the CCFs to measure the time-shift, although recent studies have used the coda part. The reason for using the coda wave in other studies is that it consists of multiple scattering waves, and thus small velocity changes are enhanced since the wave passes through the region of velocity change several times [Snieder et al., 2002]. However, using the coda wave makes it difficult to estimate the spatial distribution of the velocity change without using a stochastic approach [Pacheco and Snieder, 2005, 2006]. In contrast, using the direct part, we can estimate the spatial distribution of the velocity change through a simple approach. Therefore, we did not use the coda part of the CCFs, but only the direct part. We chose a time window centered at a peak time of the reference CCF, including four cycles of the wave at a lower limit of a frequency range. [20] The cross-spectral method can accurately determine small differences in travel time between two records. Figure 4 shows an example of a procedure of the crossspectral method. After applying a 5% cosine taper to both the reference trace and the moving average trace, we performed the fast Fourier transform and calculated the cross spectra according to the following equation: S RX ðf Þ ¼ hc R * ðf Þ C X ðf Þi; ð1þ where C R ( f ) represents the spectrum of the reference CCF, C X ( f ) is the spectrum of the moving windowed CCF centered at day X, and S RX ( f ) is the cross spectrum of the reference and the moving windowed CCF at a frequency f. Here, * denotes the complex conjugate. Brackets indicate spectra smoothed by three times the Hanning window in the frequency domain. 4of19

5 Figure 3. Daily cross-correlation functions between N.ICEH and N.OGCH in the frequency range of Hz and azimuthal dependence of amplitude of CCFs. (a) Gray line indicates CCFs averaged over 105 days before the earthquake. Black line indicates CCFs averaged over 108 days after the earthquake. (b) Temporal variation of daily CCFs over seven months. Red and blue indicate the amplitudes of the CCFs. (c) Azimuthal dependence of amplitude of CCFs. The amplitude is normalized by the maximum value. The vertical axis is identical to that of Figure 3b. [21] The coherence Coh( f ) and phase difference f( f ) between the two traces are defined as j Cohðf Þ ¼ S RX ðf Þj 2 S RR ðf ÞS XX ðf Þ ; fðf Þ ¼ ImðS RX ðf ÞÞ tan 1 : ð2þ ReðS RX ðf ÞÞ If the two waveforms are similar, the phase difference is expected to be linear according to fðf Þ ¼ 2pf Dt; where Dt is the time difference between the two traces and the sign is chosen so that the time delay is positive. Therefore, the travel time difference between the two traces is estimated by the slope of the phase difference. The relative velocity change averaged over a path between the two stations is computed as Dv/v = Dt/t. [22] For fitting a slope to the phase difference, we used the coherence as a weighting factor w( f ) according to ð3þ 1 1 wðfþ ¼ Cohðf Þ 1 ð4þ and applied the weighted linear regression within the frequency band. The weighting factor is based on the variance of the phase difference. According to Jenkins and Watts [1968], the variance of phase difference, var(f( f )), is expressed by varðfðf ÞÞ ¼ 1 1 2B e T Cohðf Þ 1 : ð5þ Here, B e is the effective bandwidth of the smoothing filter and T is the length of data. The weighting scheme also have been used in previous studies [e.g., Ito, 1990]. The standard error of the travel time difference s Dt is evaluated by using the residuals from best fitted line according to the following equations: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi X N u ux s t ¼ s f =2pt N f i2 w i ;s f ¼ t ðf i þ 2pf i DtÞ 2 w i = ðn 1Þ; i¼1 where f i, w i and f i are the frequency, the weighting factor and the phase difference at the i-th frequency point, i¼1 ð6þ 5of19

6 Figure 4. Cross-spectral method used to measure the time shift between a reference CCF and a CCF for another time period. (a) Black line indicates a reference CCF computed by averaging CCFs over 105 days before the earthquake for the pair of N.ICEH and N.OGCH at Hz. Red line indicates CCFs averaged over 108 days after the earthquake. White area indicates a time window used to compute the crossspectra in the present study. (b) Enlargement of the time window. (c) Coherence between the two CCFs. White area indicates the frequency range used to estimate time-shift. (d) Phase difference between the two CCFs. Vertical bars with plots mean errors of the phase difference. Solid red line shows the best fitted slope to the phase difference. Dashed red lines indicate the 95% confidence interval of the estimated slope. respectively. Dt is the best fit of the time-shift. N is the number of frequency points within the frequency range and s f represents the residual sum of square divided by the degree of freedom. In the case of Figure 4, the degree of freedom is 5. We chose the 95% confidence intervals as the uncertainties and the error bars. The 95% confidence interval is computed by multiplying the estimated standard error by 2.57 that is referred from t-distribution for five degrees of freedom. Note that the uncertainty defined here is the measurement error of the cross-spectral method. We think that the amplitude of fluctuations of seismic velocity before the earthquake could indicate the systematic error due to the data such as the bias of change in the noise source. [23] Information of time-shits for both the causal and acausal parts of CCFs improves the reliability of the measurement of the velocity change [Stehly et al., 2007]. However, in the present study, stabilities of the causal and acausal parts of CCFs are not comparable as shown in Figure 3b. For an example of the pair of N.OGCH and N.ICEH, the acausal part including the maximum amplitude seems to be more stable. Therefore, we used either one of the causal or acausal part that includes the maximum amplitude. Figure 5 depicts the temporal variations measured from the causal and acausal parts. The measurement from the acausal part including the maximum amplitude is more stable than that from the causal part Temporal Velocity Change [24] Figure 5 depicts the temporal variation of the Rayleigh wave velocity along a path between N.ICEH and N. OGCH in the frequency range Hz. We examined five moving windows with lengths of 1 day, 5 days, 10 days, 20 days, and 30 days. In Figure 5, the velocity change is measured both from the causal and acausal parts of CCFs. However, because the fluctuation of measurement from causal part is too large, we only discuss temporal change estimated from the acausal part. Based on the results for the one-day average, the coseismic velocity change is not clear because of large fluctuations, which means that one day is not sufficient to converge the Green s function to detect velocity change stably. With the exception of the results from the moving window with a length of one day, we can 6of19

7 Figure 5. Temporal variation of seismic velocity estimated both from causal and acausal parts of CCFs for N.ICEH-N.OGCH at Hz. The separation distance is 43.9 km. The lengths of the moving windows are different in the five figures, as specified at the bottom right of each plot. Black dots indicate reliable measurements, where an averaged coherence of within Hz is larger than 0.9, whereas white dots indicate less reliable measurements with an averaged coherence smaller than 0.9. Vertical bars behind the dots indicate the 95% confidence interval evaluated using the standard error. see a clear velocity change at the time of the 2008 Iwate- Miyagi Nairiku earthquake, which is the coseismic velocity change. The Rayleigh wave velocity sudden dropped by about 0.4% after the earthquake, which is similar to the result observed after the 2004 Mw6.6 Mid-Niigata earthquake [Wegler et al., 2009]. [25] The fluctuations of the seismic velocity in the fiveday average correspond to the amplitude variation of daily CCFs shown in Figure 3. For example, the velocity change has offsets around 100 days, 70 days, and 35 days before the earthquake, in which the CCFs have a large amplitude at positive lag and the amplitude at negative lag get smaller. The amplitude variation can be interpreted based on the effect of temporal variation of the noise source, which can be recognized in Figure 3c. Therefore, the offsets are the apparent velocity change due to the change in the distribution of the noise source. The average over a longer time period diminishes the bias and results in stable velocity variation. The temporal variation of the noise source having a period that is longer than the length of the moving average cannot be removed from the velocity variation. Stehly et al. [2006] found a seasonal variation of noise source using ambient noise cross-correlation functions. In this case, the long-term variation such as seasonal variation of the noise source dose not seem to be obvious at Hz as shown in Figure 3c. Therefore, we consider that the bias to the velocity change from the seasonal variation of the noise source might not be significant. The seasonal variations of real velocity also have been observed by previous studies [Sens-Schönfelder and Wegler, 2006; Meier et al., 2010]. However, in Figure 5, we could not recognize the clear seasonal signals such as annual or semiannual variation. Therefore, the seasonal variation of real seismic velocity is not primary factor of the observed velocity change. [26] The temporal variations for different station pairs at the different frequency bands are shown in Figure 6. We used the 20-day moving window of daily CCFs to compute the temporal variations. The frequency dependence of the coseismic velocity change is observed along a path of N.ICEH and N.KGSH. The velocity drop in the range Hz is 0.4% and that in the range Hz is 0.2%. The latter is more stably estimated and also shows spatial variation. The velocity drop along the path through the south of the main shock is larger, such as the decrease by 0.5% along the pair of N.ICEH and N.NRKH. These results show 7of19

8 Figure 6. Temporal variation of seismic velocity for four paths and for three frequency ranges of Hz, Hz, and Hz. The seismic stations used in this figure are shown in Figure 1. The length of the moving window is 20 days. The meanings of black and white dots are similar to those in Figure 4. an existence of clear coseismic change in seismic velocity near the focal area. [27] At the station pair of N.TZWH and TU.MR3, longterm trends and non-coseismic variations are observed rather than coseimic signals. Because of different occurrence times between these variations and the earthquake, these variations are not results of the earthquake. The variations around 30 days before and after the earthquake and long-term trends seem to be characteristic at the station N.TZWH, which could be due to some kind of localized cause or error of the clock. [28] In the present study, clear post-seismic recovery of the seismic velocity is not observed. Previous studies have found post-seismic recoveries of seismic velocity with recovery times of more than one year [Brenguier et al., 2008]. However, the length of the time period of the present analysis is insufficient to discuss such long-period recovery. [29] The characteristics of the background fluctuation depend on the frequency ranges. The background fluctuation at Hz tends to be smaller than that at Hz and Hz. In the high-frequency range of Hz, surface wave reconstruction from ambient noise may not be sufficient due to high attenuation. In the low-frequency range of Hz, the effect of temporal change of the noise source might be larger than the higher-frequency ranges. This is because the frequency range of Hz corresponds approximately to the second spectral peak of the microseism. 8of19

9 Weaver et al. [2009] derived an estimation of the bias of the travel time due to the inhomogeneous distribution of the noise source using a higher order stationary phase approximation. According to their results, an inhomogeneous distribution of the noise source, B(q), gives the bias of the travel time, dt, expressed by dt ¼ B ð0þ 2tw 02 Bð0Þ ; where t is the travel time and w 0 is the central frequency. Here, q is the angle made to the line through the two stations. This equation indicates that the bias becomes larger at low frequency and small separation distance. Accordingly, the large fluctuation of velocity change at low frequency may be caused by a temporal change in the noise source Spatial Distribution of the Velocity Change [30] In order to estimate the spatial distribution of the velocity change, we performed a two-dimensional tomographic inversion. We analyzed only the frequency range of Hz because the temporal velocity change in this frequency range is stable for numerous station pairs. [31] Since we used the direct part of the CCFs, the observed travel time shift of the Rayleigh wave can be expressed as the difference between the integrals of slowness along the raypath before and after the earthquake: Dt ij ¼ T after ij T before ij Z ¼ ray Z s after ðxþdx ray s before ðxþdx; where T before ij and T after ij are the travel times before and after the earthquake between the ith station and the jth station, Dt ij is the travel time shift, and s after ðxþand s before ðxþare the slowness before and after the earthquake, respectively, as a function of location x. The slowness after the earthquake can be written as a slowness change, DsðxÞ, as follows: s after ðxþ ¼ s before ðxþþdsðxþ: Assuming the slowness change is so small that the raypath does not change, we have Dt ij ¼ T after ij T before ij ¼ Z xj x i DsðxÞdx; ð7þ ð8þ ð9þ ð10þ which means that the travel time shift before and after the earthquake is equal to the integral of the slowness change along the raypath. [32] The slowness change in two-dimensional space is expressed using a grid with a grid spacing of 0.15 along the longitude direction and 0.13 along the latitude direction. The slowness change at any location is linearly interpolated by the slowness changes at four neighboring grid points. We assumed that the raypath is along a great circle through the two stations. Under the assumptions, we can rewrite equation (10) in the following simple vector form: d ¼ Am; ð11þ where d is a data vector that consists of Dt ij, A is a forward operator, and m is a model vector. The model is estimated by the damped least squares method with a damping factor of l to minimize the following penalty function: kd Amk 2 þ lkmk 2 : ð12þ Time shifts are computed by the cross-spectral method using the CCFs summed over 105 days before the earthquake and the CCFs summed over 108 days after the earthquake. We selected good-quality data with criteria such that the signalto-noise ratio of a CCF is larger than 5, the coherence between the CCFs and the reference is larger than 0.9, the apparent velocity is in a typical range of Rayleigh wave of from 0.5 km/s to 3.5 km/s, and the separation distance is larger than 12 km, which corresponds to approximately two wavelengths. We considered that the data whose average velocity changes are greater than 1.0% are less reliable and removed those data from the data set. After estimating the slowness perturbations, we convert the slowness changes to relative velocity changes using a phase velocity map at a period of Hz estimated from the three-dimensional velocity model by Nishida et al. [2008]. The data used by Nishida et al. [2008] are similar to data of this study except for data of JMA and Tohoku University. Figure 7b shows the phase velocity map. The relationship between the slowness change and the velocity change is as follows: Ds ¼ 1 Dv : ð13þ v v We chose a damping factor of l = 150 based on the tradeoff curve shown in Figure 8 such that both the data variance and the model variance are small. The diagonal part of the resolution matrix is an indicator of the resolution at each grid point. The resolution matrix R is computed as R ¼ A T A þ l 2 1A I T A. [33] Figure 7a is the result of the tomographic inversion. By this inversion, the mean square of residuals decreased from s 2 to s 2 and the variance reduction is 31%. In Figure 7a, we only show the estimated model at grid points where the resolution is larger than by 0.1. The resolution is shown in Figure 7d. In and around the focal area of the 2008 Iwate-Miyagi Nairiku earthquake, velocity decrease is estimated and significant velocity increase is not observed. The large velocity decrease is distributed in a region from the central part to the southern part of the fault zone. The maximum velocity decrease is % at the south of the hypocenter of the main shock. We consider that the velocity increase in the southwest of study area is an apparent coseismic change as shown in Figure Coseismic Change in Shear Velocity in a Superficial Layer Inferred From Vertical Array Analysis 3.1. Data [34] Vertical array analysis is suitable for estimating the shear velocity change in the near-surface layer [e.g., Sawazaki et al., 2009]. In Japan, a nationwide network named KiK-net is managed by the NIED. Each KiK-net station has two accelerometers on the surface and at the bottom of the borehole in order to observe strong motion 9of19

10 Figure 7. (a) Spatial distribution of the velocity change in the range of Hz. Data having a resolution smaller than 0.1 are masked. (b) Phase velocity map of the Rayleigh wave at a frequency of Hz computed using the three-dimensional model of Nishida et al. [2008]. (c) Data used to estimate the spatial distribution of the velocity change. Color represents the average velocity changes along the raypaths. (d) Diagonal components of the resolution matrix. both on the ground and below ground. The two sensors have the same frequency response with a flat gain from DC to approximately 20 Hz. We can use the two sensors as a vertical array. Since the KiK-net collects only event data triggered by large motion intensity, we analyzed the earthquake record observed at KiK-net stations. From the point of view of the reconstruction of the body wave propagating in the vertical direction between the two sensors, the event data including the body wave is more effective than the ambient noise, which consists primarily of the surface wave. Figure 9 shows a map of the stations and the hypocenter distribution used in the present analysis. The depths of the boreholes used in the present study are from approximately 100 m to 300 m, except for MYGH01 the depth of which is 1,000 m. The IWTH25 station is located approximately 3 km from the epicenter of the 2008 Iwate-Miyagi Nairiku earthquake. The time period of the events is from January 2005 to June The sampling frequency is 200 Hz before 2007 and 100 Hz after We selected earthquake records for which the epicentral distance is smaller than 300 km and signal-tonoise ratio in a time window described below is larger than 2. The signal-to-noise ratio is defined using a RMS amplitude of a pre-trigger portion (before the onset of P wave) as a noise level Cross-Correlation Function [35] We can reconstruct the Green s function between the surface and the bottom of the borehole by calculating the 10 of 19

11 Figure 8. Tradeoff curve between data variance and model variance. The data variance is the mean square of residuals. The model variance is the smoothness of the estimated model. The value of the damping factor is specified near the circles. CCF between two records observed at these locations. In the present study, we only used horizontal components to extract S wave velocity change. This is because, considering comparison with ambient noise result, Rayleigh wave velocity is more sensitive to S wave velocity than P wave velocity. Another reason is that uncertainty of measurement of P wave velocity change is larger than that of S wave because of the small travel time. Since the horizontal components of the borehole sensor were not necessarily oriented to the north and the east, we first rotated the two horizontal components to the north and the east according to estimations by Shiomi et al. [2003]. After removing the offsets of the seismograms, we applied a band-pass filter with a frequency band of 4 16 Hz to both records. The filter is a second-order Butterworth type without a phase shift. We analyzed the S coda part within a time window starting from 20 s after the direct S wave with the maximum amplitude. The length of the time window was s. We then performed a fast Fourier transform of both waveforms and multiplied the spectrum of the surface data by the complex conjugate of the spectrum of the borehole data. The CCF is obtained by returning the cross spectrum to the time domain and normalized by the norms of the surface and the borehole data. [36] Figure 10 shows the EW component of the seismograms observed at the surface sensor and the bottom sensor of IWTH25. The amplitude of the surface is approximately four times larger than that of the bottom, which is caused by site amplification. The CCF computed within the time window has a clear peak at 0.26 s in positive lag. Since the travel Figure 9. Map of the KiK-net stations and the epicenters of the event data used in the present study. White squares indicate the locations of the KiK-net stations. Circles and stars indicate the epicenters of the events before and after the 2008 Iwate-Miyagi Nairiku earthquake, respectively. Figure 10. Seismograms observed by KiK-net and crosscorrelation function of these seismograms. (a) EW components of event data observed at the surface sensor and the bottom sensor of IWTH25. Each waveforms is filtered at 4 16 Hz. The event is an M3.5 aftershock that occurred at 14:22 in June The epicenter distance is 9 km. The scale of the borehole data is four times greater than that of the surface. (b) Cross-correlation function between the two seismograms computed within the time window shown in Figure 10a. 11 of 19

12 Figure 11. Cross-correlation functions of EW components at IWTH25 and IWTH26. (a) Stacked crosscorrelation functions. Gray line indicates the CCFs averaged over a time period before the 2008 Iwate- Miyagi Nairiku earthquake. Black line indicates the CCFs averaged over a time period after the earthquake from 15 June 2008 to 30 September A CCF of the main shock is not included in the average CCF. (b) Cross-correlation functions of individual events from 2005 to 2009 at IWTH25. Black arrow indicates the main shock. Red waveform indicates the CCF of the main shock. (c, d) Similar plots as Figures 11a and 11b, but at IWTH26. time of the shear wave computed using logging data is estimated to be s, the large amplitude at the positive lag corresponds to an upgoing shear wave propagating from the bottom to the surface. As shown in Figure 10, we can extract the Green s function from a random coda wave Measurement of the Velocity Change [37] Figure 11 depicts the individual cross-correlation functions computed from data of one event arranged by the occurrence time. The delay of the peak time is obvious at IWTH25 and IWTH26. A maximum delay of 0.04 s is observed with the data of the main shock at IWTH25. The peak delay remains after the 2008 Iwate-Miyagi Nairiku earthquake and gradually recovers over more than one year. Since we used a coda wave with a small amplitude, this peak delay is not the result of a nonlinear site effect due to the instantaneous increase in the dynamic strain [Chin and Aki, 1991]. Therefore, this peak time delay can be considered as a static velocity decrease due to the damage caused by the strong ground motion at the main shock. [38] Since the time shift that we want to estimate is smaller than the sampling frequency, e.g., 100 Hz, we measured the time shift using the cross-spectral method mentioned in the ambient noise analysis. A time window is centered by the peak time with a length of 0.5 s. In order to stabilize an estimation of temporal variation, we used a moving average over 10 events with an overlap of nine events. A reference CCF is computed by stacking the CCFs before the 2008 Iwate-Miyagi Nairiku earthquake Results [39] Figure 12 shows the temporal velocity change of the EW components at six stations. The results for the NS components are similar to those for the EW components. The shear velocity suddenly dropped by approximately 5% at the time of the Iwate-Miyagi Nairiku earthquake at the two stations near the epicenter of the main shock, IWTH25 12 of 19

13 Figure 12. Temporal variation of shear velocity within a shallow layer at six stations. The relative velocity change is computed from a reference CCF and the 10-event moving window of the CCFs. EW components are used in this figure. Black dots are relative velocity change estimated using all data. Gray areas indicate the time period that includes both data before and after the Iwate-Miyagi Nairiku earthquake due to the moving window of 10 events. Red dots are relative velocity change estimated using data without aftershocks. Error bars represent the 95% confidence intervals. and IWTH26. After the earthquake, some fluctuations of seismic velocity are observed. We consider that the fluctuations are caused by the change of wavefield due to aftershocks. Therefore, we removed the CCFs of aftershocks data from the data set and estimated the temporal variation again. Because almost all aftershocks were distributed in depth shallower than 15 km, we removed the event data where hypocenters were shallower than 30 km. Although the temporal resolution is reduced, measurement without aftershocks data gives similar results at IWTH25 and IWTH26. Therefore, the coseismic velocity decreases at IWTH25 and IWTH26 are robust. At other stations, the fluctuations after the earthquake seem to be suppressed. [40] A shear velocity reduction of a few percent is reasonable because similar velocity reductions have been estimated in shallow layers [Sawazaki et al., 2009; Yamada et al., 2010; Nakata and Snieder, 2011]. One important observation is that the 5% shear velocity reduction in a shallow layer is much larger than the velocity reduction of % of the Rayleigh wave obtained from the ambient noise analysis. We discuss the relationship between the two results in the next section. [41] At IWTH26, the data period is long enough to discuss the recovery. The shear velocity that dropped at the 2008 Iwate-Miyagi Nairiku earthquake gradually recovered over approximately two years and almost returned to its value before the earthquake. The long-term recovery over a few years is similar to the results of previous studies, such as those of Brenguier et al. [2008] and Sawazaki et al. [2009]. In contrast, at IWTH25, the shear velocity did not fully recover after one year. However, a lack of data unfortunately makes it difficult to discuss the long-term recovery at IWTH25. [42] In order to compare the velocity change of the Rayleigh wave estimated from the ambient noise in the previous section, we estimate the velocity change according to the difference in travel time between the average CCFs of the time periods from 2005 to 13 June 2008 and from 15 June 2008 to 30 September In this estimation, we did not use the CCFs of aftershock data. Figure 13b shows the spatial distribution of the shear velocity change. The large velocity decreases are observed near the main shock, which are caused by the Iwate-Miyagi Nairku earthquake as shown in Figure 12. Although a few velocity changes with large amplitude are also observed far from the focal area, we don t think that these velocity changes are caused by the Iwate- Miyagi Nairiku earthquake because the effect of the earthquake should primary depend on the distance from the source. One possible interpretation of velocity decrease in the northeast could be a result of strong ground motion the M6.8 Northern-Iwate earthquake on 24 July 2008 that is a deep intraslab earthquake. The coseismic decrease at 13 of 19

14 Figure 13. Spatial distributions of velocity change, peak ground acceleration, and static strain change. (a) Coseismic change of Rayleigh wave velocity in the range of Hz as estimated by ambient noise analysis, as described for Figure 7a. Yellow star indicates the epicenter of the main shock. Blue contours are drawn every 1 m of coseismic slip as estimated from geodetic data [Iinuma et al., 2009]. The outermost contour represents the coseismic slip of 1 m. Green circles indicate the epicenters of aftershocks that occurred from 14 June to 30 September of 2008 [Okada et al., 2012]. Gray contour indicates a hinge line between the compression and dilatation of the volumetric strain change shown in Figure 13d. (b) Shear wave velocity change in the shallow layer estimated by vertical array analysis of the earthquake coda. Averages between results of NS and EW components are shown. Small circles are for the data where the average between the EW and NS components is smaller than a half of difference between the EW and NS components. Background colors represent elevation. Small star in northeast is epicenter of the M6.8 event on 24 July (c) Peak ground acceleration observed at KiK-net and K-NET that are shown as gray squares. The PGA is the maximum amplitude of the three-component vector. (d) Volumetric strain change caused by the coseismic slip at 2.5 km. Two black rectangles indicate fault planes used to compute the strain change [Ohta et al., 2008]. Red areas indicate dilatation, and blue areas indicate compression. 14 of 19

15 Figure 14. Phase velocity change of the Rayleigh wave due to the shear velocity decrease in the shallow layer at IWTH25 (Figures 14a 14c) and IWTH26 (Figures 14d 14f). (a) Phase velocity change as a function of frequency under four different conditions that are shown in Figures 14b and 14c. Black dot is observed phase velocity change based on the ambient noise analysis. The phase velocity change at the point estimated by the tomographic inversion is plotted. (b) Shear velocity models assumed in order to compute the phase velocity change of the Rayleigh wave. Dashed line is the direct connection of the logging-data and the model by Nishida et al. [2008] (Model 1). Solid line is a smoothed version of the dashed line (Model 2). Green is the model of J-SHIS. (c) Reduced velocity models. Black line indicates the logging-data that represents the shear velocity before the earthquake. Red line indicates the data for the model with a velocity reduced by 5.0% in all layers above the bottom of the borehole, and gray line indicates the data for the model with a velocity reduced by 16.1% in two shallow layers. (d f) are similar plots to Figures 14a 14c. IWTH25 is 5.2% in the NS component and 4.6% in the EW component. At IWTH26, the decrease in the NS component is 7.1%, and the decrease in the EW component is 6.3%. The coseismic velocity decreases are located in the area in which Rayleigh wave velocity decrease is large. 4. Discussions 4.1. Quantitative Comparison of the Two Results [43] We performed two different analyses and obtained two primary results. The first result is a Rayleigh wave velocity change of 0.1% to 0.5% in the range of Hz, which is estimated from the ambient noise analysis. The second result is a shear velocity change of approximately 5% in the superficial layer, the depth of which is shallower than 260 m at IWTH25 and 108 m at IWTH26, as estimated by vertical array analysis of the earthquake coda. In this section, we compare these two results quantitatively. In order to evaluate the quantitative relationship between them, we compute the phase velocity change of the Rayleigh wave by associated with a shear velocity change in the superficial layer. We then compare the theoretical estimation with the observations performed using the ambient noise method. 15 of 19

16 Figure 15. Sensitivity kernels of Rayleigh wave at Hz for the structure models (Model 1 and Model 2) shown in Figure 14. (a) Blue and red lines indicate the sensitivity kernels for Model 1 and Model 2 at the station IWTH25, respectively. (b) The sensitivity kernels for Model 1 and Model 2 at the station IWTH26. [44] When we computed the Rayleigh wave velocity, we assumed one-dimensional models based on the logging data and the three-dimensional model by Nishida et al. [2008]. Because the depth sensitivity of Rayleigh wave depends on subsurface structure below the bottom of the borehole, we made the two types of models shown in Figures 14b and 14e as two end-members. For the first model, we directly connected the logging data with Nishida s model at the bottom of the borehole. The second model is the smoothed version of the first model. The density (in g/cm 3 ) is scaled by the P wave velocity (in m/s) according to the relation r = 0.31 V P 0.25 [Gardner et al., 1974]. Meanwhile, the shear velocity changes obtained in the present study are the average changes between the surface and the depth of the bottom of the boreholes. Therefore, we also made two different assumptions concerning the layers in which the shear velocity decreased: the shear velocity changes are homogenous between the two sensors or the shear velocity changes are localized in the shallowest part of the superficial layer (Figures 14c and 14f). Specifically, at IWTH25, we assumed that the shear velocity decreased homogeneously by 5.0% in all layers above the bottom of the borehole or by 16.1% in shallow layers of up to 34 m. We made both models based on the velocity structure of logging data so that travel time shift is identical to observed travel time-shift estimated from the cross-correlation function. Similarly, at IWTH26, we assumed that shear velocity decreased homogeneously by 5.7% in all layers or by 11.6% in shallow layers of up to 36 m. [45] Using these two velocity models and these two assumptions of changing layers, we then computed the phase velocity change of the Rayleigh wave. The phase velocity was computed by the matrix method [Dunkin, 1965]. Figure 14 shows the computed phase velocity change as a function of frequency. In general, the phase velocity change at high frequency is larger than that at low frequency. This is because the sensitivity of the Rayleigh wave at higher frequency is larger for shallower structures. The magnitude of the phase velocity change strongly depends on the velocity model and the depth limit of the changed layers. Figure 15 depicts the partial derivative (i.e., sensitivity) of the Rayleigh wave phase velocity with respect to the shear velocity computed by a method by Saito [1988]. The sensitivity at Hz has two peaks near the surface and at a depth of 2.5 to 3.0 km. Because the amplitude of the near surface sensitivity strongly depends on the velocity models, the predictions based on the four models are different. [46] One problem of this prediction of phase velocity change is which velocity model fits the reality. In Japan, the Headquarters for Earthquake Research Promotion and the NIED provide an earthquake hazard map named J-SHIS (Japan Seismic Hazard Information Station). For the prediction of the strong ground motion, J-SHIS project integrated several kinds of methods based on geodetic, seismic and geological data to develop a model of subsurface structure [Fujiwara et al., 2009]. According to the structure model used in J-SHIS (available from bosai.go.jp/), in the area around IWTH25 and IWTH26, the base-rock depth at which the shear velocity is larger than 3 km/s is relatively deep as shown in Figure 14. This data may supports that the second model is more realistic. [47] The important consideration is that if we assumed the smoothed model and homogeneous change in all layers, the phase velocity change is 0.1% to 0.3% at IWTH25 and 0.1% to 0.6% at IWTH26, which is comparable to the observed velocity change by % estimated by the ambient noise method. In other words, the large shear velocity drop in shallow layers can explain the velocity change of the Rayleigh wave in the range of Hz Possible Mechanism of Velocity Change [48] We estimated the spatial distribution of the Rayleigh wave velocity change and the shear wave velocity change in shallow layers. Since we used the direct parts of the CCFs and performed tomographic inversion, the spatial resolution of the Rayleigh wave velocity change is higher than that in previous studies that used the coda parts of the CCFs. In addition, the shear velocity change estimated from KiK-net data focuses on the near-surface layer. [49] However, the coseismic change in distance between two stations has possibility to appear as a velocity change. The GPS measurement revealed that the coseismic displacement was up to 1.5 m [Ohta et al., 2008]. Since the average separation distance is approximately 15 km, the average change in distance of 15 km is from 0.01 to 0.02%. This value is much smaller than that of the observation. [50] A stress or strain change may cause a seismic velocity change as a result of opening and/or closing cracks, the creation of new cracks, and the redistribution of pore fluid. Stress changes can be divided into two types: static and dynamic. Static stress changes are caused by coseismic slip of the fault and results in opening of cracks in the dilatational region and closing of cracks in the compressional region [Nishimura et al., 2000]. A velocity decrease is expected in the dilatational region, and a velocity increase is expected in the compressional area. Dynamic stress changes are caused by seismic wave, especially those associated with strong motion. Dynamic stress changes are well known to cause nonlinear behavior in the site response for strong motion of more than 100 Gal [e.g., Chin and Aki, 1991]. 16 of 19

17 Figure 16. (a) Expected phase velocity change of Rayleigh wave at Hz due to the static stress change. White rectangles are the faults model used to compute the static strain change [Ohta et al., 2008]. (b) P wave velocity of Granite rock as a function of pressure which is constructed from Birch [1961, Table 9]. (c) Vertical profile of volumetric strain change along the N across the epicenter of the main shock. Horizontal distance is from 140 E. Black line is the northern fault of Ohta et al. [2008]. Dynamic stress changes cause damage to rocks near the site, which might remain after the strong motion passes though the site. Such damage is expected to decrease the seismic velocity. Dynamic effects are dominant in shallow layers where the seismic wave is amplified. In the next sections, we consider whether the static or dynamic effect is dominant in the observations Static Stress Change [51] We computed the static strain change using a computational program by Okada [1992]. We assumed a fault model by Ohta et al. [2008] estimated from GPS data. Figure 13d depicts the volumetric strain change at a depth of 2.5 km in which the Rayleigh wave has large sensitivity as shown in Figure 15. The dilatational area is distributed near the main shock, and the compressional area exists to the south and north of the focal area. In three dimension, the compressional area is distributed in the north and south of the faults, and above the upper edge and below the bottom edges of the faults as shown in Figure 16c. [52] Based on our observations, the velocity decrease of the Rayleigh wave is widely distributed in and around the focal area, as shown in Figure 13a. The spatial distribution of the velocity decrease is correlated with that of the dilatational strain. However, in the compression area, no significant velocity increase is observed. Therefore, the velocity change cannot be interpreted as only a static stress change. [53] On the other hand, a laboratory experiment has shown that the seismic velocity is affected by the confining pressure [Birch, 1961]. We predicted the phase velocity change due to the static stress change. According to Birch [1961, Table 9], the stress sensitivity, 1/V(dV/dP), can be computed at any depth. Here, we assume a density of 2700 kg/m 3 and a 1-D velocity structure by averaging the model by Nishida et al. [2008] in this region. From the table by Birch [1961], we used only the gradient dv/dp. We multiplied the gradient by 1/V P to evaluate the sensitivity for P wave at any depth, where V p is the P wave velocity of the 1-D structure based on Nishida et al. [2008]. Although the experiment by Birch [1961] is for the P wave, we used the same gradient for S wave. [54] Using the computed volumetric strain change and a bulk modulus of Pa, we estimate the P and S wave velocity change at any depth. Then, we calculated the phase velocity change of Rayleigh wave at Hz. Figure 16a depicts the predicted phase velocity change. The velocity decreases around 0.5% are predicted near the faults, which are comparable to the ambient noise results. However, because the amplitude of the predicted velocity change is dependent on the stress sensitivity, the spatial variation should be discussed rather than the amplitude. The predicted velocity decrease seems to correlate with the ambient noise observation. However, the velocity increases are also expected by the static stress change. Considering the observation in the absence of a velocity increase in the area where velocity increase is expected, the static stress change is consider not to be the main factor causing the observed velocity change Damage in Shallow Layers Due to Strong Motion [55] The peak ground acceleration (PGA) is related to the dynamic stress change. Figure 13c is observed at KiK-net and K-NET. K-NET is a network used to observe strong motion on the ground and is managed by the NIED. The 17 of 19