We estimated the changes in seismic velocity in the southern Tohoku district of Japan during the six-month period centered on the 11 March 2011 Tohoku-oki earthquake, using scattered waves retrieved by autocorrelation of ambient seismic noise. The estimated velocity decrease after the earthquake, and after two large aftershocks in the study area, was as great as 1.5% in the area nearest to the mainshock. The velocity changes displayed gradual healing. The spatial distribution of the velocity change showed a correlation with both the changes in static strain, derived from GPS records, and the peak particle velocity experienced during the three earthquakes, derived from strong-motion records. Therefore, our results show that velocity changes possibly contain information from deep in the crust bearing on coseismic stress release, in addition to shallower effects due to strong ground motion.
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 GPS network observations of the giant Tohoku-oki earthquake of 11 March 2011 (Mw 9.0) revealed that the coseismic displacement included eastward movement of up to 5.3 m and subsidence of up to 1.2 m in the eastern Japanese island arc [Ozawa et al., 2011]. This large displacement caused enormous strain change in the Tohoku region [Takahashi, 2011; Yoshida et al., 2012]. The earthquake also caused widespread strong ground motion. Therefore, we sought to monitor velocity changes in the southern Tohoku region and assess their causes using ambient seismic records from the Japanese Hi-net system.
 Autocorrelation of ambient noise records yields the seismic response for a coincident source and receiver position [e.g., Wapenaar and Fokkema, 2006]. The method assumes that the noise source is mutually uncorrelated for different source positions [e.g., Weaver and Lobkis, 2004; Roux et al., 2005; Wapenaar and Fokkema, 2006]; therefore, the phase of the noise source should be random, and earthquakes, with their deterministic phases, are regarded as anomalies. We applied running absolute amplitude normalization [Bensen et al., 2007] to suppress earthquakes. The window size used for the normalization affects the weighting range to suppress strong amplitudes. We found that the size of the window significantly affected the traveltime of coherent events in the ACF, and after careful investigation we selected a window length of 25 s. We also applied zero-phase amplitude whitening to balance the frequency component [Bensen et al., 2007; Meier et al., 2010]. We used a moving average of the amplitude and a damping factor of 5% of the maximum amplitude to stabilize the whitening.
 To estimate the velocity perturbation due to earthquakes, we applied the stretching interpolation technique [e.g., Sens-Schönfelder and Wegler, 2006; Hadziioannou et al., 2009]. The resulting ACF represents the zero-offset seismic response and contains the scattered wave with the traveltime perturbation evolving each day. The method elongates the time axis, interpolates the amplitudes of the calculated trace, and searches for the parameter value that produces a waveform most similar to the reference trace:
where ϵ is a stretching parameter, fref represents the reference trace, fcur represents the current trace, and C(ϵ) is the correlation coefficient between the reference and elongated traces. We searched for the value of ϵ yielding the maximum value of C in equation (2) by adopting a grid search algorithm. Since a part of data showed multiple local maxima, we manually picked the local maxima that yielded the smoothest transitions from day to day. The stretch parameter ϵcorresponds to a relative time-shift (Δt/t) of the dominant event, and we assumed that it relates to a relative velocity change (Δv/v) as [Hadziioannou et al., 2009],
 Note that in this analysis we assume that (1) the autocorrelated trace is dominated by the scattered wave generated from the subsurface and (2) the traveltime perturbation directly corresponds to the velocity perturbation, which indicates that the velocity perturbation is homogeneous in the medium, or at least in the region where the scattered waves propagate within the specified time window.
3. Data and Result
3.1. Survey Area
 The survey area includes Fukushima and Ibaraki prefectures in the southern Tohoku district (Figure 1). Although the maximum depth of the Hi-net stations is 3500 m, most stations are 100 m to 200 m deep (Figure 1). We used the vertical component of the records from 58 Hi-net stations from 9 January to 30 June 2011, a total of 173 days. During that time, the survey area experienced at least two aftershocks causing a large surface deformation that was detected in satellite observations (interferometric synthetic aperture radar or InSAR) of the Geospatial Information Authority of Japan (GSI). These were the North Ibaraki event of 19 March (Mw 5.8, 10 km deep) and the South Fukushima event of 11 April (Mw 6.7, 10 km deep) (Figure 1). The fault traces on the ground estimated from InSAR are approximately 7 km in the North Ibaraki event and 14 km in the South Fukushima event (Geospatial Information Authority of Japan (GSI), 2011, http://www.gsi.go.jp).
3.2. ACF and Temporal Variation of the Velocity Perturbation
 We autocorrelated each day of seismic data and obtained 173 ACFs for each of the 58 Hi-net stations. A typical ACF record is that of station N.YBKH (Figure 2a), which shows data for the 2–10 s traveltime interval after bandpass filtering between 2 and 5 Hz. Data for the period 13–14 March were not available. A coherent event is apparent in the ACF, and its characteristics changed after 11 March. We show the temporal change in the velocity (traveltime) perturbation (ϵ) at station N.YBKH in Figure 2b for the 2–10 s period. We stacked all ACFs to obtain the reference trace for equation (2)and as a calculated trace we used each 1-day ACF after the application of a 5-day moving average window. We calculatedC(ϵ) for a range of −10% ≤ ϵ ≤ 10% with Δϵ = 0.1% and picked maximum values after spline interpolation. Because the averaged waveform was defined as the zero percentage perturbation, ϵ starts from around −0.5%. A positive value of ϵ indicates that traveltime was longer (velocity was slower) in the current trace than in the reference trace. The sudden change of ϵon 11 March corresponds to the Tohoku-oki mainshock, when the velocity dropped 2%. A gradual recovery of the velocity [e.g.,Peng and Ben-Zion, 2006; Vidale and Li, 2003; Schaff and Beroza, 2004; Rubinstein and Beroza, 2004] was observed after the Tohoku-oki earthquake. This observation matches that of another study focusing on near-surface velocity change due to the Tohoku-oki earthquake [Nakata and Snieder, 2011]. We fit this healing curve with the logarithmic line ϵ(d) = alog10(d) + b, where d is the elapsed day, b corresponds to the maximum ϵ and obtained the coefficient (a) as −0.53 (white line in Figure 2b). This relation indicates that the velocity recovered to 99% of its preseismic value a month after the mainshock. This time-scale of the recovery is consistent with a decrease of the shear modulus due to strong ground motion, as suggested bySawazaki et al. . The coseismic velocity perturbation remained around 0.5% 100 days after the earthquake.
 Station N.THGH (Figure 2c) is near the fault that ruptured in the North Ibaraki aftershock of 19 March (Figure 1). It is apparent that the maximum change in velocity was later than in Figure 2b and that the velocity changed in two steps, caused by two earthquakes: the 11 March event caused a 0.8% perturbation and the 19 March event caused a further 1% perturbation.
 Station N.IWWH (Figure 2d) is near the fault that ruptured in the South Fukushima aftershock of 11 April (Figure 1). As the waveforms before and after 11 March are very different, the correlation coefficient in the stretch analysis has low values in the pre-mainshock period (Figure 2d). Furthermore the velocity perturbation did not show a discontinuity on 11 March (black line in Figure 2d). This lack of discontinuity might be due to the effects of strong near-surface deformation, the change in seismicity that was not fully removed before autocorrelation, or the change in the source characteristics of the ambient noise. We focused on the dominant events appearing at 2.0–2.8 s and calculatedϵ using that small time window (blue line in Figure 2d). We could track these events from 20 February to 30 June. The resulting curve shows less stability than the curve generated with the longer time window; however, it shows a strong velocity drop on 11 March and closely tracks the other curve in the post-earthquake period (Figure 2d). The results clearly show velocity reductions caused by the two earthquakes of 11 March and 11 April.
 The stretching interpolation technique (equations (1) and (2)) assumes a homogeneous velocity change within the time window. However, the scattering events at different traveltimes (lag times in ACF) may propagate through different regions of the subsurface, and consequently they may contain information about different depths. Therefore, we investigated the use of equations (1) and (2) with different lag times. Figure 2e shows the calculated velocity perturbations at station N.YBKH for lag times of 2–10 s, 2–6 s, and 6–10 s. The coseismic jump at 11 March with the lag time of 2–6 s (approximately 3%) is larger than that with the lag time of 6–10 s (approximately 0.5%). This may indicate that coherent events with longer traveltime propagate through deeper structures, and the shallower subsurface experienced larger velocity reductions than the deeper subsurface. The result with the lag time of 2–10 s represents an average of values in the other two lag times.
3.3. Spatial Variation of the Velocity Change
 Observations at some stations were interrupted by strong shaking and the velocity perturbation gradually healed, as shown in Figure 2b. In analyzing the spatial distribution of the velocity change, we therefore attempted to minimize these factors by calculating the difference between the averaged velocity change between the preseismic (9 January-10 March) and postseismic (11 March-30 June) periods (Figure 3a).
Figure 3a, produced using a kriging interpolation, shows that the eastern part of the study area near the coast had larger velocity reductions than the western part. The maximum velocity change was approximately 1.5% in the eastern area. Nearly the entire region showed a velocity decrease; we believe that the small velocity increases in a few places are within the uncertainties of our method.
4. Discussion and Conclusion
 We detected notable velocity changes during the six-month period encompassing the Tohoku-oki earthquake using scattered waves retrieved by autocorrelation of ambient noise. In this section we evaluate two likely reasons for these velocity changes. First, earthquakes produce changes in the regional stress field, and rock physics modeling predicts velocity changes arising from the change in effective pressure due to the opening or closing of cracks [e.g.,Toksöz et al., 1976]. Second, coseismic strong motions may cause nonlinear behavior of elastic properties of the lithosphere [e.g., Vidale and Li, 2003; Schaff and Beroza, 2004; Peng and Ben-Zion, 2006]. In this study, we try to use a static strain change and a peak particle velocity as the indicators of stress change and strong motions respectively because these can be estimated from observable quantities in the field.
 Static strain change can be derived from GPS records from the GEONET network operated by the GSI. We used horizontal displacements from GPS GEONET F3 daily coordinate records over the survey period to calculate static area strain (summation of normal strain for two horizontal axes) change, derived by using the constant strain triangle element method [e.g., Terada and Miyabe, 1929]. Figure 3bshows the estimated static area strain change between 1 January and 29 June 2011. The Tohoku-oki earthquake caused almost the whole survey region to experience dilatation (positive area strain change). The largest amounts of dilatation were near the coastline, corresponding to the large velocity change we estimated by passive image interferometry (Figure 3a). The polygon of unusually large dilatation in Figure 3b is a consequence of the two aftershocks at North Ibaraki (19 March) and South Fukushima (11 April).
 We also compared the estimated velocity changes to the spatial distribution of peak particle velocity from the Kik-net strong-motion network, during the three earthquakes in the study period (Figure 3c). Kik-net stations are collocated with almost all Hi-net stations at the same depth (Figure 3c) and recording acceleration. Foregoing research consider a peak acceleration as a measure of damaging due to strong ground motion [e.g., Schaff and Beroza, 2004]. Beresnev and Wen pointed out that a peak acceleration is a frequency-dependent measure of maximum strain assuming the sinusoidal displacement input of a one-dimensional transverse wave propagating toz-direction (u = u0sin(ωt − kz)) as,
where γ is a strain, a0 is a peak acceleration, v0 is a peak particle velocity, and V is a propagating velocity [Beresnev and Wen, 1996]. In order to obtain frequency-independent measure of maximum strain as a relative damaging, we estimate a peak particle velocity (equation (4)). We obtained the distribution of peak particle velocity from Kik-net data after bandpass filtering from 0.1 to 10 Hz. The cumulative values of peak particle velocity recorded during the three earthquakes (Figure 3c) show a trend similar to those of the velocity change (Figure 3a) and the area strain change (Figure 3b), with the largest particle velocities distributed near the coastline.
Figure 4ashows the average velocity change against the estimated area strain change for each of the Hi-net stations. Similarly,Figure 4bplots the velocity change against the observed cumulative peak particle velocities for the Kik-net stations. Because velocity healing is nonlinear, some stations showed unstable values ofϵ shortly after earthquakes, and the crossplot of Figure 4bshows much scatter. To reduce scatter, we plotted only the stations that showed clear and stable velocity decreases from the Tohoku-oki earthquake (red dots inFigure 4). Both Figures 4a and 4b show a clear positive correlation of the velocity decrease (positive ϵ). The anomalous station N.THGH showed a velocity decrease even though the area experienced compression (arrow in Figure 4a). The compression was the result of fault activity associated with the two aftershocks (Figure 3b). However, station N.THGH did not experience anomalous particle velocities (arrow in Figure 4b).
 This observation suggests that the velocity change estimated in this study is affected by the near-surface strong motion and may correspond to damage to near-surface rocks around 200 m depth. However, the velocity change we measured is smaller than that reported byNakata and Snieder , who estimated a shear velocity decrease of ∼5% at a depth of a few hundred meters by cross-correlating earthquakes observed by the Kik-net vertical array. Furthermore, we showed that later arriving events show a smaller velocity change (Figure 2e) and that strain change correlated with velocity change (Figure 4a). The fact that our results are based on scattered waves with traveltimes of 2 to 10 s indicates that the scattered waves are generated at a maximum 25 km depth, considering an average P-wave velocity of 5000 m/s. These results, therefore, support our contention that the velocity change we measured contains information on the results of stress release deep underground in addition to shallow effects due to strong ground motion.
 We thank the National Research Institute for Earth Science and Disaster Prevention for providing the Hi-net and Kik-net data used in this study. We obtained GPS GEONET F3 coordinate data from GSI. S. Minato acknowledges support from a Grant-in-Aid (212666) from the Japan Society for the Promotion of Science Fellows. This study was supported by the Global Center for Education and Research on Human Security for Asian Megacities (GCOE). The useful comments of two anonymous reviewers helped to further improve this article.
 The Editor thanks Ulrich Wegler and Roel Snieder for assisting with the evaluation of this paper.