A temporal change of shear wave anisotropy within the marine sedimentary layer associated with the 2011 Tohoku-Oki earthquake
Institute for Research on Earth Evolution, Japan Agency for Marine-Earth Science and Technology, Yokohama, Japan
Corresponding author: T. Tonegawa, Institute for Research on Earth Evolution, Japan Agency for Marine-Earth Science and Technology, Postal address: IFREE, JAMSTEC, 3173-25, Syowa-machi, Kanazawa-ku, Yokohama, 236-0001, Japan. Tel: +81-45-778-5965.
 We found persistent reflections of S waves from the bottom of a ∼350 m thick marine sedimentary layer on the outer rise of the Japan Trench, just to the east of the source area of the 2011 great Tohoku-Oki earthquake (Mw9.0), by auto-correlating ambient seismic noise recorded on 1 year continuous records of broadband ocean bottom seismometers. The two-way travel times of reflected S waves, which vary as a function of the polarization direction, indicate a velocity anisotropy of ~1.7% in the sedimentary layer. The fast direction is estimated to be trench parallel, possibly due to cracks or normal faults formed by bending of the plate in the outer rise. The travel time also shows a coseismic velocity reduction of ~2%, with slightly reduced anisotropy, within the layer. The change gradually recovered to pre-earthquake conditions through 4 months after the earthquake, although recovery was not complete during the period of the observation. We also detected a similar anisotropic structure and magnitude of coseismic velocity reduction in this layer based on S coda of earthquakes with magnitudes greater than 5.0. Such coseismic changes can be explained either by increases of crack density and crack sphericity within the suddenly stressed sedimentary layer or by channeling and networking of water flow in the strongly shaken sedimentary layer.
 Detection of temporal variations of subsurface seismic structure provides information on time-dependent processes occurring within the Earth. Using auto-correlation functions (ACFs) derived from seismic ambient noise observed at a single station, Wegler and Sens-Schönfelder  detected a velocity reduction of 0.6% associated with the 2004 Mid-Niigata (Chuetsu) earthquake (Mw6.6). On the other hand, using cross-correlation functions of ambient noise, Brenguier et al. [2008a] reported velocity reductions of 0.04% for the San Siemon earthquake (M6.5) and 0.08% for the Parkfield earthquake (M6.0) along the San Andreas fault zone and their relaxations. Brenguier et al. [2008b] reported a velocity reduction of 0.05% caused by pre-eruptive inflation of the volcanic edifice of the Piton de la Fournaise. Subsequent to these relatively earlier studies, several papers employing auto- or cross-correlation functions of ambient noise have reported temporal variations of seismic velocities associated with, e.g., the 2007 Noto Hanto earthquake (Mw6.6) [Ohmi et al., 2008] and small earthquake swarms observed in 2007 in Kyusyu, southwestern Japan [Maeda and Obara, 2009]. Nagaoka et al.  also reported a velocity decrease and its relaxation prior to the volcanic eruption at Mt. Asama in 2008. These findings of temporal variations of seismic structure are based on travel time measurement of surface waves or scattered waves.
 On the other hand, if temporal variations in travel times of vertically reflected body waves can be obtained using reflections extracted from continuous noise records, it should be possible to obtain information on the depth extent and time history of the velocity change. In other words, the depth extent of the change is estimated by determining the reflection depth, and the time history of the change is elucidated by continuously measuring two-way travel time of the reflected wave with a relatively high sampling rate, e.g., 1 day. Claerbout  suggested that reflection responses can be obtained by auto-correlating transmission responses, assuming a 1-D acoustic medium. Wapenaar  confirmed that the suggestion could be applied to the case of a 3-D inhomogeneous medium; wave propagations of direct turning waves, body wave reflections, and surface waves between two locations could be retrieved by cross-correlating records of ambient noise. Indeed, previous studies have retrieved body wave reflections by cross-correlating ambient noise wavefields [e.g., Draganov et al., 2007, 2009; Zhan et al., 2010; Ryberg, 2011; Poli et al., 2012]. Tibuleac and von Seggern , using ACFs of ambient noise, detected P and S waves reflected from the Moho to investigate temporal variations of seismic structures in the crust.
 In this study, we calculated ACFs for ambient noise observed by the three broadband ocean bottom seismometers (BBOBSs) deployed on the surface of the marine sedimentary layer (i.e., seafloor) at locations ~100–400 km east of the Japan Trench in the outer-rise region (Figure 1a) and attempted to retrieve persistent reflections from subsurface structures below each of the BBOBS sites. The time period of the observation was from July 2010 to July 2011, which included the occurrence time of the Tohoku-Oki earthquake (Mw9.0) on 11 March 2011 (Figure 1a). The seismic P wave velocity (Vp) of the marine sedimentary layer in this region is 1.6 km/s [Shinohara et al., 2008], and S wave velocity (Vs) can be estimated to be ~200 m/s by using the P wave velocity and Vp/Vs of ~8.0 [Table 1; Fujie et al., 2013]. The thickness has been reported as 270–300 m [Fujiwara et al., 2007] and 400 m [Shinohara et al., 2008]. The Vs of the basaltic basement near its top is ~2.7 km/s [Shinohara et al., 2008]. Densities of the sediments and the basalts in the northwest Pacific Ocean reported by Ocean Drilling Program Leg 191 [Kanazawa et al., 2001] are 1.265 to 1.450 g/cm3 and 2.745 g/cm3, respectively. Thus, the absolute value of S wave reflection coefficient at the interface between the sedimentary layer and the basaltic basement is 0.91 when the ray path impinges with an incidence angle of 90°; the largest impedance contrast below the BBOBSs is therefore likely to be at the base of the sedimentary layer.
Table 1. Seismic Velocity Within the Marine Sedimentary Layer
 Most previous studies detected velocity changes by implicitly assuming a seismically isotropic structure below the employed receivers/network. However, if anisotropic structures are present beneath the receiver, and velocity changes are related to those anisotropies, then that information can potentially help interpreting the causes of the induced velocity change. By rotating two horizontal components of ambient seismic noise, Miyazawa et al.  successfully estimated the anisotropic seismic structure along a downhole well by extracting direct S waves for different polarization directions. Measuring the travel times of direct S waves propagating between the surface and borehole sensors, Nakata and Snieder [2012a] detected changes in velocity and anisotropic structures over a period of 10 years (2000–2010). Our attempt was to extract the reflected S waves polarized to a fixed azimuth and to estimate the anisotropic structure between the seafloor and the underlying seismic discontinuity. We also investigated whether an anisotropic velocity change, if any, was induced by the 2011 Tohoku-Oki earthquake and how the observed changes could be explained in relation to the anisotropic structures beneath the BBOBS sites.
2 Data Processing
2.1 Calculation of the ACF
 The BBOBSs consist of a three-component CMG-3T broadband seismometer (Guralp Systems Ltd.) with a flat velocity response over the period of 0.02–360 s [Sugioka et al., 2012] and a sampling rate of 100 Hz. We applied a bandpass filter of 2.0–5.0 Hz to the two horizontal components. The directions of horizontal component of the three BBOBSs were determined by using waveforms of direct P waves both from events occurring close to the source region of the 2011 Tohoku-Oki earthquake and from 12–20 teleseismic events. The magnitudes of the used events were greater than 5.7. The frequency band was chosen to be 0.07–0.1 Hz. The directions determined were consistent between those from the near earthquakes and from the teleseismic events, and the 1σ uncertainties of the directions were estimated to be less than ±7°.
 Two approaches were taken to extract ambient noise from the records by excluding other energetic signals. In the first approach, based on the typical noise level in the frequency band (~1.0 µm/s) at the three BBOBS sites, the absolute values of velocities greater than 2.0 µm/s were reset to zero to avoid the contamination of energetic signals, such as earthquakes. In the second approach, as in previous studies [Wegler and Sens-Schönfelder, 2007; Ohmi et al., 2008], we set a threshold value of 10 times the standard deviation of the seafloor velocity; the velocity amplitude was set to be zero when it exceeded this value. The threshold value in this case is changed dynamically according to the time series used. Although we attempted two approaches to set values to remove the effects of other energetic signals, the results of the amount of temporal variation were consistent with one another. This notion is important because the noise level increased by at most one order immediately after the earthquake. We next disregarded the amplitude of the records by using a one-bit signal [e.g., Brenguier et al., 2007], to further ensure the exclusion of other energetic signals. We then synthesized the waveform by rotating the two horizontal components at 5° intervals and calculated the ACFs using a time series length of 600 s. The rotation angle (θ) is measured clockwise from north (Figure 1b). The ACF stacked for 1 day was prepared for approximately 370 days. The ACFs of the rotated waveforms for all directions should allow us to extract the reflected S wave polarized into a certain direction.
2.2 Extraction of the Reflected S Wave
 Figures 2a and 2e show ACFs stacked for 1 day as a function of rotated direction for the two BBOBSs at sites A and B, where a strong signal at a lag time of 3.0–4.0 s is observed. No such signal is observed at station C. These signals are most likely related to a vertically propagating S wave reflected from a subsurface structure beneath the stations. The travel time of the signal is slightly perturbed as a function of the rotated angle at station A, and probably at station B.
 The lag time of the signal is considered as two-way travel time between the seafloor and a subsurface discontinuity. Using Vs = 200 m/s and lag times of 3.0 s and 3.5 s at stations A and B, the depths of the discontinuities are calculated as 300 m and 350 m (Table 2). These values are in good agreement with the thickness of the sedimentary layer obtained in the previous studies [e.g., Fujiwara et al., 2007; Shinohara et al., 2008]. Since the velocity increases downward across the bottom of the sedimentary layer, the topside reflections of S waves emerged in the ACF are expected to show negative polarities. The reflected S wave obtained at station B indeed shows a negative peak at a lag time of ~3.5 s, whereas comparable negative and positive peaks are present at station A. For the observation at station A, as will be discussed further in section 4.2, the earlier negative amplitude at a lag time of ~3.0 s should be regarded as a reflection from the bottom of the sedimentary layer. Because no signals at a lag time of 3.0–3.5 s were observed in the ACF using the vertical component, the observed signals detected on the horizontal components are likely to be shear waves.
Table 2. Thickness of the Marine Sedimentary Layer
Two-way travel time
2.3 Daily Variations of the Travel Time of Reflected S Waves
 Temporal variations in travel time of the reflected S waves would be expected at the time of the Tohoku-Oki earthquake, because several conditions, such as the water contents, the form and amount of cracks, and maybe the stress state, within the unconsolidated sedimentary layer underneath the seafloor were possibly affected by the M9.0 earthquake, which potentially contributed to S wave velocity variations. The amplitudes of the reflected S waves were weaker than those before the earthquake, and the amplitudes had not completely recovered by ~3 months after the earthquake, as indicated by the ACFs at both stations A and B (Figures 2b and 2f). As the phase of the reflected S wave is nearly coherent over the observation period (in contrast to the amplitude), we measured the temporal variations in the travel times of the reflected S waves. One might argue that if a seismometer were abruptly displaced relative to the seafloor by the earthquake-associated strong shaking, the orientation and sensitivity of this instrument could be changed stepwise in time so that a quantitative comparison before and after the earthquake would be difficult. However, because a sudden decrease of the reflection amplitude at the time of the earthquake recovered gradually through the subsequent 3 months, our observations likely reflect variations in the seismic velocity structure beneath the station.
 In order to investigate fluctuation in the travel time of the reflected S wave, we first synthesized a reference waveform by stacking all the ACFs in a time window of 2.5–4.0 s of for every 600 s long segment over the whole entire observation period (~370 days) and over the whole rotated directions. The cosine taper with a time length of 0.2 s was applied to both sides of the reference waveform. Then, we cross-correlated the reference waveform with every 1 day stacked ACF trace at every rotated direction in the same time window as for the reference waveform. In order to detect any azimuthal variation in the travel time of the reflected S wave, we also prepared the reference waveform for each rotated direction by stacking the ACFs over 200 days from the beginning of the observations. The cross-correlation with such reference waveforms enables us to see more accurately the temporal variation in travel time of the reflected S wave for each rotated direction.
 The error associated with the travel time measurement is given by the 1σ uncertainty in the travel time measurement, which is estimated by using a bootstrap-resampling technique. First, we prepare 24 ACFs for 1 day, where each ACF is calculated using ambient noise with a time length of 1 h. This choice of time length makes it possible to retrieve the S reflection by auto-correlating ambient noise, although S/N of the retrieved signal is relatively low compared to the one with 1 day stack. Second, we randomly choose 24 ACFs with repetition from the set of the 24 ACFs and stack them. Third, cross-correlating the stacked waveform with the reference waveform, we can obtain a relative travel time of the stacked waveform. Finally, repeating the above processing 1000 times, we estimate the standard deviation by using the 1000 relative travel times.
3 Results of Shear Wave Anisotropy and Its Temporal Variation
 Figures 2c and 2g show daily variations of the travel time of the reflected S wave, which are estimated by using the reference ACF that was obtained by stacking the ACFs over the entire observation period and over the whole rotated azimuths. The color scale indicates the relative time of the reflected S wave to the corresponding reference waveform. For example, at station A, prior to the earthquake, Figure 2c shows an azimuthally sinusoidal pattern (blue and green colors), which indicates faster S waves polarized in the N20°–30°E direction and slower S waves polarized in the N110°–120°E direction. The polarization direction is symmetric in a 180° rotation. Figure 2d shows temporal variations in the relative times of the faster reflected S waves polarized in the N25°E direction, and in those of the slower reflected S waves polarized in the N115°E direction. Error bars are attached to each measurement. The differential travel time between the fast and slow directions is ~0.05 s against the two-way travel time of the reflected S waves of ~3 s (Figure 2a), leading to a velocity anisotropy of 1.7%. Interestingly, the S wave velocity structure beneath station B shows a similar but weaker anisotropy (see Figures 2g and 2h and Table 3). The fast directions at the two stations are nearly parallel to the trench. In view of this consistency with the tectonic feature, the anisotropic structure within the sedimentary layer is likely caused by tensional cracks or/and normal faults formed by bending of the plate in the outer-rise region. This inference is supported by the observation of a stronger anisotropy at station A than at station B. According to the plate flexural theory at an ocean trench [Turcotte and Schubert, 2002], the bending stress of the plate is expected to be higher at A than at B.
Table 3. Pre-seismic Velocity Structure
 After the Tohoku-Oki earthquake, the travel time of the reflected S waves was delayed for all rotated directions at station A (Figures 2c and 2d), but the fast and slow polarization directions were not changed. The delay time in the fast polarization direction was 0.07 s, whereas in the slow polarization direction, the delay time was 0.05 s. These values with the two-way travel time of ~3 s correspond to velocity reductions of 2.3% and 1.7% in the fast and slow polarization directions, respectively. However, as shown in Figure 3, the minimum delay time (minimum velocity reduction) of ~0.04 s (1.3%) is obtained in the rotated direction N135°E, which is different from both the trench-normal slow direction and the trench-parallel fast direction observed before and after the earthquake, implying some complexity in the velocity reduction process. The reductions had not completely recovered within a time period of 4 months after the earthquake. The degree of the anisotropy was changed at the time of the earthquake, and it did not completely recover with the time, as is shown by the orange colored arrows in Figure 2d. In contrast, no velocity variations associated with the Tohoku-Oki earthquake were observed at station B (Figure 2h). Although it seems that the fast and slow directions were shifted at station B as a result of the earthquake (Figure 2g), this could not be conclusively detectable due in part to a limited sampling rate of 100 Hz.
 Temporal variations in seismic velocities associated with the 2011 Tohoku-Oki earthquake have been reported in the Japanese Islands. Velocity reductions of 5–10% and changes in the anisotropic structure associated with the Tohoku-Oki earthquake occurred at depths between the bottom of the borehole and the ground surface [Nakata and Snieder, 2012b; Takagi and Okada, 2012]. Using receivers at the bottom of boreholes only, Minato et al.  reported a velocity reduction of at most 3.0% associated with the 2011 Tohoku-Oki earthquake, when using a lag time of 2–6 s of the ACFs to measure velocity perturbations. This velocity reduction might reflect a structural change at greater depths, judging from the employed lag time of ACFs. Comparing to the results of these studies, we obtained significantly smaller velocity reductions within the deep-sea sedimentary layer than those observed in the land shallower sedimentary layer. However, the difference of velocity reduction would reflect not only the site difference of land and seafloor observations but also the magnitude of earthquake-induced stress and/or intensity of shaking.
 Three earthquakes with magnitudes greater than 6.0 occurred during the observation period prior to the Tohoku-Oki earthquake (Figures 1 and 2). In addition, a large earthquake of magnitude 7.3 occurred on 9 Mar 2011, near the hypocenter of the 2011 Tohoku-Oki earthquake. Small changes in seismic velocity corresponding to these events might have occurred (Figures 2c and 2g); however, they were not large enough to be able to recognize their gradual recoveries.
4.1 Retrieval of Reflected S Waves
 Several researchers have successfully retrieved reflections from subsurface structures by correlating records of ambient noise [e.g., Draganov et al., 2007, 2009; Zhan et al., 2010; Ryberg, 2011; Poli et al., 2012; Tibuleac and von Seggern, 2012]. However, wave propagation characteristics retrieved by correlating ambient noise depend on the wave types contained in the employed record, as well as on the geometries of the stations, sources, and structural discontinuities. Surface wave information has been retrieved by correlating wavefields in which horizontally propagating surface waves are dominant [e.g., Campillo and Paul, 2003; Shapiro and Campillo, 2004]; however, Tonegawa et al.  found that near-vertical reflections can be constructed by correlating wavefields that contain signals with sufficiently small slowness. Indeed, the under-estimation of body waves has been pointed out if both noise sources and stations are distributed at the ground surface [Forghani and Snieder, 2010; Snieder et al., 2010].
 One might therefore suspect that it is difficult to extract upper side reflections by auto-correlating wavefields of ambient noise using data for such a short period as only 1 day and that retrieval of reflection signals will require more sophisticated techniques that enhance weak reflections. However, there are some advantages for the retrieval of reflections in our case. We used a frequency band of 2.0–5.0 Hz; although artificial noise associated with our daily activities is dominant in this frequency band in the case of land observations, such noise should be weak in the case of deep seafloor observations. Another advantage is that, because the S wave velocity is low (~200 m/s), the wavelengths in the frequency band of 2.0–5.0 Hz are less than 100 m, significantly less than the thickness of the sedimentary layer (300–400 m); thus, S wave reverberation can easily occur within the layer. This possibly results in multiply reflected or scattered wavefields inside the marine sedimentary layer. Our successful retrieval of the reflection signal could be contributed by such a diffusive wavefield that is unique to the marine sedimentary layer. On the other hand, P wave reflections from the base of the marine sedimentary layer were not observed in the ACF using the vertical component. This is probably because the velocity contrast of P waves at the base of the sedimentary layer is less than that of S waves, and the wavelength of P waves in the frequency band of 2.0–5.0 Hz, 320–800 m, is greater than the thickness of the sedimentary layer. These facts imply that P wave reverberations are less efficient within the sedimentary layer.
4.2 Temporal Variations Estimated by ACFs Using S Coda
 The continuous seismic records after the 2011 Tohoku-Oki earthquake possibly contain coda-related wavefields generated by the aftershocks, in addition to the ambient noise. These wavefields might have affected our analysis of the ambient noise, because the technique we used, including the zero padding and one-bit signal (see section 2.1), cannot completely remove the effect of deterministic phases. This effect might cause the observed weaker amplitudes of S reflection after the earthquake (Figure 2b and 2f). To ensure our detection of the reflected S wave and its temporal variation at station A, we attempted to extract reflections using the wavefields of S coda generated by earthquakes.
 We used 117 earthquakes with magnitudes greater than 5.0 which occurred during the period of the BBOBS observations. The epicentral distances of the events were between 2° and 10°. We discarded earthquakes occurring during Mar. 2011, to avoid possible misinterpretations of the wavefields excited by multiple earthquakes mutually adjacent in time. Similarly to the above analysis of ambient noise, we applied a bandpass filter of 2.0–5.0 Hz, rotated the two horizontal components at 5° intervals, and calculated ACFs for each rotated direction using a time window of 40–100 s after S wave arrival. However, the one-bit normalization was not performed, so as to enhance the contribution of the energetic signals. Figure 4 shows the reflected S waves retrieved for each earthquake (Figure 4b), where the main lobe of the reflection wavelet shows a negative polarity (Figures 4a–4c). We regard this lobe with a negative polarity as the reflected pulse from the subsurface discontinuity.
 Although, in the case of the ambient noise analysis, it was difficult to identify the main lobe of a wavelet, we can now regard the lobe with a negative polarity as the reflection because of the consistency in its timing and polarity with the corresponding signal retrieved from the S coda. The negative polarity, indicated by arrows in Figures 4a–4c, implies reflection at a discontinuity from a low to high impedance, as expected for the base of the sedimentary layer.
 Figure 4d displays temporal variations in the travel times of reflected S waves, obtained using S coda. Here, the reference waveform was synthesized by stacking the 117 ACFs. The fast/slow polarization directions are the same as those obtained using the ambient noise. A velocity reduction is observed at the instant of the Tohoku-Oki earthquake for all rotated directions. The travel time delays (0.05–0.06 s) are also independent of the rotated direction. Thus, the features recognized by the ambient noise approach and the seismic coda approach are consistent with one another, rendering the reliability of the obtained velocity reduction within the sedimentary layer.
 Although the consistent results are obtained, the use of ambient noise in this study has the following advantages with respect to the use of S coda: (1) S reflection emerged in the ACFs using ambient noise shows a better S/N than that from coda-related wavefields (Figure 4c), (2) as mentioned in section 2.3, S reflection can be retrieved with ACFs using ambient noise with a time length of 1 h. This means that we can achieve a temporal resolution as high as 1 h, (3) we can obtain ACF with a constant temporal interval, and (4) at the frequency band of 2–5 Hz, the amplitude of ambient noise is relatively high at these seafloor stations. Therefore, if we use coda of earthquakes, their magnitudes should be greater than 4.0 to use seismic coda well above the noise level; we used earthquakes with magnitudes greater than 5.0 in this study.
4.3 Interpretations of the Obtained Velocity Characteristics
 We obtained the shear wave anisotropy within the marine sedimentary layer before and after the 2011 Tohoku-Oki earthquake, and the coseismic velocity reduction of a few percent; the magnitude of the coseismic velocity reduction is independent of the polarization direction (Table 4). In land observation, Nakata and Snieder [2012a] reported the observation of velocity reduction and variation of shear wave anisotropy in shallow structure that can be related to several mechanisms, including major earthquakes, precipitation, and plate motion. In our case, coseismic changes in the velocity structure may be attributed, e.g., to changes in the stress environment that bends the plate and produces normal faults or/and cracks in the outer-rise region or to the effects of strong seafloor shaking associated with the M9.0 earthquake. Water-saturated pores in the marine sedimentary layer may be easily channeled to form water flow networks by strong shaking, and these networks would reduce the effective shear modulus. However, it is difficult to evaluate quantitatively how strong shaking causes coseismic anisotropy changes, seismic wave velocity reduction, and post-seismic velocity recovery. Here, we attempt to explain the observed velocity characteristics by a crack model.
Table 4. Post-seismic Velocity Structure
4.3.1 Estimates of Elastic Constants Using a Crack Model
 We examined whether the observed velocity characteristics can be explained by an effective medium containing aligned ellipsoidal inclusions (i.e., cracks) in a homogeneous medium that produces anisotropies in the propagation of elastic waves. The effective elastic constants of such a composite medium could be calculated with variable crack density and aspect ratio (AR) of aligned spheroidal cracks. Since the porosity of marine sediments in the northwest Pacific Ocean is reported to be on the order of 80% [Kanazawa et al., 2001], the solid and fluid phases would be continuous, i.e., biconnected, under the condition of such a high porosity. We therefore used the method [Sheng, 1990; Hornby et al., 1994; Jakobsen et al., 2000] that is based on a combination of self-consistent approximation (SCA) [Willis, 1977] and differential effective medium (DEM) theory [Nishizawa, 1982]. The combined SCA/DEM theory allows us to create a solid-fluid material that is biconnected at all porosities [Jakobsen et al., 2000], and estimate shear wave velocities of the medium as functions of AR and porosity (φ). In this study, we first generated a biconnected material at a porosity of 50% using SCA, and then, estimated effective elastic constants at other porosities using DEM [Hornby et al., 1994; Jakobsen et al., 2000].
 We considered an oblate spheroidal crack with short axis (a3) horizontal and perpendicular to the direction of the Japan Trench, long axes a1 = a2, and AR =a3/a1, which produces a transverse isotropy (where a1, a2, and a3 are the principle axes of the ellipsoidal inclusion). The crack shape is spherical when AR = 1.0, while it is flat and circular when AR << 1.0. In the case that the ray path impinges perpendicularly, i.e., with an incidence angle of 90° measured from a horizontal axis, on the symmetric axis (a3) of the spheroidal crack, the fast and slow shear wave velocities are estimated by calculating the elastic constants C66 and C44. The polarization directions of the shear waves described by the elastic constants are parallel and perpendicular to the Japan Trench, respectively; we refer to these shear waves as S∥ and S⊥ waves, and their velocities as VS∥ and VS⊥, respectively.
 The shear wave anisotropy beneath station A is estimated as 1.7% prior to the earthquake (Table 3). The velocity reduction is estimated to be 2.3% and 1.7% in the fast and slow directions, respectively. Assuming Vs = 200 m/s, shear wave velocities before the earthquake in the fast and slow directions were 201.7 m/s and 198.3 m/s, respectively; these became 197.1 m/s and 194.9 m/s after the earthquake. Our aim is to find a crack model that can explain these velocity characteristics. We assume that the observed isotropic shear wave velocity of 200 m/s represents the value in the case where φ = 0.8 and AR = 1.0. We also assume that the initial values of Vp, Vs, and density ρ in the case of φ = 0 is smaller than the typical clay values (Vp = 3.53 km/s, Vs = 1.67 km/s and ρ = 2.56 g/cm3 [e.g., Mavko et al., 1998; Ruiz and Dvorkin, 2009]) by a constant multiplication factor. The Vp, Vs, and density values of water-saturated spheroidal cracks are set to be 1.5 km/s, 0.0 km/s, and 1 g/cm3.
 After some trial, we found that a multiplication factor of 0.5 can reproduce Vs = 200 m/s at φ = 0.8 and AR = 1.0. We calculated the effective elastic constants at a specific volume fraction of water-saturated spheroidal cracks with a given AR using the initial values of Vp = 1.76 km/s, Vs = 0.84 km/s, and φ = 0.
4.3.2 Variations in the AR and Porosity
 Figures 5a and 5b show VS∥ and VS⊥ as functions of AR and porosity. Figure 5c shows the relative VS∥ and VS⊥ difference in percent: VR = (VS∥ – VS⊥)/VS∥ × 100. All the observations are well inside the white box in Figures 5a and 5b, and this box part is enlarged in Figures 5d and 5e, respectively. The two white lines in Figure 5d indicate VS∥ and VR before the earthquake; their intersection (x) represents the conditions of AR and porosity beneath station A before the earthquake. Similarly, the two yellow lines indicate VS∥ and VR after the earthquake, and their intersection (y) represents the conditions of AR and porosity after the earthquake. Note that the two intersections (x′ and y′) in the case of VS⊥ (Figure 5e) are the same as those in the case of VS∥ (x and y).
 The results show that both AR and porosity increased (x to y and x′ to y′) due to the effects of the 2011 Tohoku-Oki earthquake. The crack shapes became more spherical, and the volume fraction of water within the marine sedimentary layer increased. These processes can be explained by existing cracks further widened by infiltration of water and fresh cracks newly opened by earthquake-induced tensional stresses [Obana et al., 2012]. The water would be supplied mainly by sea water from above. Although we used a porosity value of φ = 0.8, the result remains similar for a range of φ values. This suggests that increases in AR and porosity in marine sediments as a consequence of the earthquake are the robust characteristics of the near-source outer-rise region.
 As shown in Figure 3, the direction of the minimum velocity reduction (N135°E) at the time of the earthquake is not related to either the fast or the slow polarization directions. In terms of the crack model, this may reflect some directional change of tensional stresses due to the earthquake from the plate-bending related stress system. To take into account this, more sophisticated models, which can treat cracks aligned in two directions, may have to be employed.
 We retrieved the S reflections from the base of the marine sedimentary layer by auto-correlating ambient seismic noise. The travel times of the reflected S waves indicate the existence of ~2% anisotropy within the sedimentary layer. The trench-parallel fast direction is probably caused by cracks or normal faults formed by plate-bending stress in the outer-rise region. A velocity reduction of ~2%, with a slightly reduced anisotropy occurred within the layer at the time of the 2011 Tohoku-Oki earthquake; the change was gradually recovered over a time period of 4 months after the earthquake, but was not completely recovered at the end of the observation period. The coseismic velocity and anisotropy changes can be explained semiquantitatively by a stress-sensitive crack model although they may be explainable by other models as well. The velocity reduction and anisotropy change were also confirmed using the S coda of earthquakes rather than ambient noise.
 The comments from N. Nakata, an anonymous reviewer, and the associate editor greatly improved the manuscript. T. T. was funded by a Research Fellowship of the Japan Society for the Promotion of Science for Grants-in-Aid for Young Scientists (B) (24740313). We also thank T. Isse to give us information for direction of horizontal component of BBOBSs.