The mantle beneath the Japanese islands is complex because of subduction of the Pacific and Philippine Sea plates and the deformation associated with it. Detection of seismic anisotropy should be useful for understanding the processes occurring in such mantle. Here we resolve seismic anisotropy of the mantle wedge from that of the underlying subducted Pacific slab using a large number of measurements of shear wave splitting for a family of core-reflected shear phases: ScS, sScS, ScS2, and sScS2. The anisotropy of the mantle wedge changes sharply across the volcanic front. On the Pacific side of the volcanic front a vertically propagating shear wave is polarized with the fast direction approximately parallel to the trench, whereas on the back-arc side it is polarized with the fast direction approximately parallel to the plate convergence direction. The Pacific slab is uniformly anisotropic with the NNW fast direction, consistent with the paleospreading direction of the northwestern Pacific seafloor. The preferential alignment of anisotropic crystals frozen in the plate at the time of its formation appears to be preserved down to depths beyond 400 km within the slab.
 The thermomechanical structure and stress-strain state beneath Japan are complex, owing mainly to subduction of two plates, the Pacific and Philippine Sea plates, which are descending westward and northwestward beneath the Japanese islands, respectively. The consequent complex deformation of the crust and mantle should be reflected in seismic anisotropy and may be detected by observing phenomena associated with seismic anisotropy. One of such phenomena is splitting of the polarization of shear waves into two mutually perpendicular directions inherent to the anisotropic structure. The polarization azimuth of the fast component and its time advance to the slow component are often called splitting parameters [e.g., Babuška and Cara, 1991; Savage, 1999]. Observation of shear wave splitting requires records of well-isolated shear waves little contaminated by other phases. Shear waves from nearby deep shocks, such as direct S or ScS phase, or shear waves generated by P-to-S conversion at the core-mantle boundary are often analyzed from this viewpoint. The anisotropy so far estimated from shear wave splitting observations shows complex, sometimes conflicting patterns beneath the Japanese islands [e.g., Ando et al., 1983; Fukao, 1984; Iidaka and Obara, 1994, 1995; Hiramatsu and Ando, 1996; Fouch and Fischer, 1996; Nakajima and Hasegawa, 2004; Long and van der Hilst, 2005, 2006]. As pointed out by Long and van der Hilst , the complex splitting patterns are due in part to the dependence of the measurements on the polarization and propagation direction.
 In order to minimize the associated uncertainty, we analyze multiply core-reflected shear waves, ScS, sScS, ScS2, and sScS2, from only three deep shocks with different focal mechanisms recorded by more than 600 stations in Japan. Table 1 and Figure 1a show the pertinent information about these shocks and the stations. The three events are chosen for high signal-to-noise ratios of the records. Figures 1b–1d show the cross sections of the P wave tomographic model [Fukao et al., 2001] along typical epicenter-to-station paths (shown in Figure 1a) for each of the three events. The typical raypaths of multiple ScS phases are superposed on the tomographic cross sections to illustrate how the multiple ScS paths cross the subducting slab and the overlying mantle wedge. The dashed lines in Figure 1 indicate the surface reflection legs of sScS and ScS2. In each cross section the relative location of the hypocenter with respect to the tomographic image of the subducted slab is not accurate enough. We assume that the hypocenter is located near the top of the subducted slab. This assumption has often been used in tomographic studies to define the upper surface of the subducting slab as a sharp boundary of velocity contrast [e.g., Abdelwahed and Zhao, 2007].
Table 1. Event Information From Preliminary Determination of Epicenters
AZ and SD are average and standard deviation of the polarization azimuths (in degrees clockwise from north) of multiple ScS radiated from each source to the stations used in the analyses.
17 Nov 2002
28 Jun 2002
27 Jul 2003
 With this assumption the first anisotropic layer is the subducted slab right beneath the hypocenter for the ScS and ScS2 phases and is the mantle wedge right above the hypocenter for the sScS and sScS2 phases. The use of multiple ScS for a common source-receiver pair, the use of hundreds of such pairs for an event and the use of several deep shocks with different focal mechanisms are all useful to resolve anisotropic zones vertically overlapped, as will be explained later. In addition, the steep raypaths of multiple ScS phases minimize contaminations of S-to-P converted phases generated at the free surface and crustal discontinuities.
 We use data from the dense Japanese arrays of the high-sensitivity seismograph network (Hi-net) [Obara et al., 2005] and full-range seismograph network (F-net) [Okada et al., 2004] of the National Research Institute for Earth Science and Disaster Prevention (NIED). Figure 1a shows the station distributions and the focal mechanisms for the three events: the Kuril, Vladivostok, and Sakhalin events. The epicentral distances are short, from 2.5 to 23 degrees. Also shown are the surface reflection points of the ScS2 and sScS2 phases from the three events, which are densely distributed in the back-arc regions. The F-net consists of about 70 broadband seismic stations and their data are used as supplement to the Hi-net data. The Hi-net consists of more than 600 stations each of which equips with three-component short-period seismometers and two-component borehole tiltmeters. The tiltmeters are placed at the bottom of boreholes of 100-m depth or more. The tiltmeter is a pendulum-type force-balance accelerometer and serves as both a sensor for crustal movement and a high-sensitivity long-period seismometer [Obara et al., 2005]. The two-component tilt records are converted to two-component horizontal velocity seismograms by integration. We confirm that their response to ground acceleration is flat at frequencies less than about 0.5 Hz. Since our target phases of multiple ScS are dominant in frequency around 40 mHz, the integrated tilt records are band-pass-filtered between 5 and 30 mHz to enhance the target phases often buried in noise. This choice of band-pass filtering has enabled us to analyze the multiple ScS phases up to sScS2.
Figures 2a and 2b show a comparison of the multiple ScS phases from the Kuril event observed at F-net broadband seismic station SBT and Hi-net tiltmeter station AKIH, which are only 45 km apart from each other. The instrumental responses are equalized to each other. The ScS, sScS, ScS2, and sScS2 can be clearly distinguished from the background noise, showing little waveform differences between SBT and AKIH. Figures 2c–2f show the particle orbits of these phases at AKIH. The particle orbits are not linear but elliptical, indicative of shear wave splitting.
3. Method and Obtained Splitting Parameters
 When shear wave travels through an anisotropic medium, its component polarized parallel to the fast direction of the medium begins to lead the orthogonal component. The splitting parameters consist of the polarization azimuth ø (in degrees) of the fast component and its advance dt (in seconds) to the slow component. We use the waveform correlation method [e.g., Fukao, 1984] to determine the splitting parameters. When two horizontal seismograms are rotated clockwise, an appropriate rotation would resolve the shear wave into two orthogonally polarized phases whose waveforms must be similar to each other. To find an appropriate azimuth of rotation a correlation is taken between the two rotated seismograms. Values for the rotation azimuth ø and the time lag dt that yield the maximum correlation are regarded as the splitting parameters. Resolution of measured anisotropy will be discussed in section 4.
3.1. Splitting Parameters for the Multiple ScS Phases
 We obtained the splitting parameters for the Kuril and Vladivostok events at more than 300 stations and for the Sakhalin event at ∼100–300 stations. Figures 3–5 summarize the shear wave splitting parameters of the multiple ScS phases for the Kuril, Vladivostok, and Sakhalin events, respectively. Arrows and their lengths in Figures 3–5 represent the polarization directions of the fast wave (ø) and time lags (dt) between the fast and slow waves. Dots indicate the stations at which the measured dt values are less than 0.5 s and the relevant particle motion shows practically a linear orbit. All of the multiple ScS from the Kuril event split consistently with almost uniform øs around N25°W (Figure 3). The ScS and ScS2 from the Vladivostok event also show the øs around N25°W but with smaller time lags and with some exceptions notably in southern Hokkaido (Figures 4a and 4c). The sScS from this event shows systematically different fast directions of about N60°E (Figure 4b). The ScS from the Sakhalin event shows two distinct fast directions (Figure 5a), while the remaining phases split consistently with the øs around N60°W (Figures 5b–5d).
3.2. Differential Splitting Parameters for the Multiple ScS Phases
 The sScS has a near-source surface reflection leg in addition to the raypath similar to ScS path (Figures 1b–1d). In order to isolate near-source anisotropy, we first remove the ScS path effect from the original sScS waveform using the splitting parameters of the forerunning ScS. We then measure the splitting parameters for the corrected sScS waveform, which we regarded as the differential splitting parameters sScS-ScS. We also take the differential splitting parameters ScS2-ScS to resolve the anisotropy along the surface reflection leg of ScS2, which passes through the whole mantle in addition to the raypath similar to ScS (Figures 1b–1d). Because splitting operator is not in general commutative [Silver and Savage, 1994], this striping method works only in limited cases. As detailed in section 4.3, we are in fact dealing with such unique cases.
Figure 6 plots the measured sScS-ScS splitting parameters by bundled black lines at the epicenters, showing consistency of the measurements for each event. The upper mantle is anisotropic with the ø of N32°W ± 2° and dt of 0.9 s ± 0.4 s (average and standard deviation) above the Kuril source, with N57°E ± 4°, 0.9 s ± 0.3 s above the Vladivostok source, and with N56°W ± 4°, 1.7 s ± 0.7 s above the Sakhalin source. Figure 6 also plots the measured ScS2-ScS and sScS2-sScS splitting parameters for the Sakhalin event by green arrows at the surface reflection points of ScS2 and sScS2, respectively. Because of the relatively low signal-to-noise ratio of the ScS2 from the Sakhalin event, the available differential parameter sets of ScS2-ScS are limited, to which we add the available sets of sScS2-sScS, leading to a total of 127 sets with the well-defined major group (92 sets) showing the fast directions around WNW (ø: N59°W ± 5°, dt: 1.4 s ± 0.7 s). Plotted arrows in Figure 6 are the differential splitting parameters of this group. We here also plot the splitting parameters of the ScS from the Sakhalin event at the corresponding stations, where WNW polarizations are marked by blue arrows and NNE polarizations are marked by red arrows. The 150-km isodepth contours of the Wadati-Benioff zone (Figure 6, thick gray lines) delineate the volcanic fronts along the southern Kuril to Honshu arcs and along the Ryukyu arc. The blue arrows are dominated on the Japan Sea side of the volcanic front and smoothly continue to the green arrows distributing on the Japan Sea. The red arrows are, on the other hand, dominated on the Pacific side of the volcanic front.
Figure 7 shows the measured ScS2-ScS parameters, which are on average (N27W° ± 2.9°, 1.6 s ± 0.6 s) for the Kuril event and (N27°W ± 4.5°, 1.1 s ± 0.4 s) for the Vladivostok event. The individual parameters are plotted by green arrows at the ScS2 surface reflection points. The splitting parameters plotted at stations (black arrows) are those for the ScS from the Kuril event, which show uniformly the NNW fast directions with time lags of 1–1.5 s in agreement with the results of Fukao , who analyzed the shorter-period ScS from a deep Kuril islands earthquake.
4. Discussion of Resolutions of Estimated Splitting Parameters
4.1. Comparison of Splitting Parameters From Long-Period and Broadband Seismograms
 Low-pass filtering of the original records affects our estimates of splitting parameters. We evaluate this effect using the F-net broadband records, which are band-pass-filtered between 5 and 30 mHz to obtain long-period seismograms and between 5 and 100 mHz to obtain broadband seismograms. We compare the splitting parameters determined from long-period seismograms to those determined from broadband seismograms. Such a comparison is not always easy because a uniform treatment can be made for all the long-period seismograms while a different treatment is required for each broadband seismogram after a careful visual inspection of waveform to avoid noise contamination. This difficulty limits the number of the F-net stations available for the comparison, only 24, 7, and 7 for the Kuril, Vladivostok, and Sakhalin events, respectively. Figure 8 plots the values of ScS splitting parameters from the long-period seismograms against those from the broadband seismograms. The splitting parameters obtained from the long-period and broadband seismograms are in fair agreement at almost all the stations, indicating that there is no systematic bias in the splitting parameter determination from long-period seismograms against determination from broadband seismograms. The number of splitting parameters available from the long-period seismograms is far greater than the number available from the broadband seismograms. We take a full advantage of this large number of observations for each of the three events.
4.2. Limitations in Splitting Parameter Determination
 The shear wave polarization depends on the focal mechanism [e.g., Aki and Richards, 2002]. If the incident shear wave is polarized in the either fast or slow direction, then no splitting can be observed in the anisotropic system [e.g., Savage, 1999]. We test the limitations in splitting parameter determination in a frequency band of our interest. Figure 9a shows an example of the two horizontal components of the long-period synthetic ScS wave for the Sakhalin event computed by the spectral-element method (SEM) [Komatitsch and Tromp, 2002a, 2002b] for an isotropic, laterally heterogeneous mantle model S20RTS [Ritsema et al., 1999] together with a crust model, CRUST2.0 [Bassin et al., 2000], and a topography and bathymetry model, ETOPO5 (from the National Oceanic and Atmospheric Administration, 1998). The computation is made using the Earth Simulator, Japan Agency for Marine-Earth Science and Technology (JAMSTEC). Figure 9b shows the corresponding particle motion in the N70°E direction (polarization direction at N20°W) which is defined by the focal mechanism. Starting from this ScS seismogram, we generate a series of seismograms distorted by the anisotropy specified by the first direction ø and time lag dt. More specifically, the original NS and EW components are rotated by ø, then relatively time-shifted by dt, and finally rotated back to the NS and EW components. We found in the synthetic test that if dt is taken to be less than 0.5 s, the wave splitting with this dt cannot be resolved by our method. If time lag is determined to be less than 0.5 s from an observed seismogram, we consider this to be the case where anisotropy cannot be resolved. Figures 9c–9e show the particle motion diagrams of synthetic split seismograms for a time lag of 2 s and for fast directions at N20°W, N40°W, and N65°W, respectively, where the particle motion changes from a linear orbit to elliptical orbit. The orbit remains to be almost linear if the fast direction is within 10° around N20°W (or N70°E). In this azimuthal range it should be difficult to detect any anisotropic effect. The greatest off-linear elliptic motion occurs when the fast direction lies at about 45° away from N20°W (or N70°E), where it should be able to determine the splitting parameters most accurately. This situation is examined more closely by carrying out the following test.
 Our test is to recover the splitting parameters using the correlation method from the synthetic seismograms calculated for a fixed dt of 2 s with various values of ø. Figure 9f shows the result of this recovery test. It is practically impossible to recover the splitting parameters if the fast direction is within 10° around N20°W (or N70°E). If, on the other hand, the fast direction is about 45° away from N20°W (or N70°E), we can make approximately correct estimates of ø and dt. If the fast direction deviates from this azimuth of N65°W (or N25°E), dt tends to be underestimated and the estimate of ø tends to be biased to N65°E (or N25°E). In general, the measured fast direction tends to be biased to an azimuth of 45° away from the polarization direction (or the orbit direction) of the ScS (or its family) incident to the anisotropic layer, and the measured time lag tends to be smaller than the real one. This nature of uncertainty is inherent to any splitting parameter determination based on waveform correlation, although the degree of uncertainty depends on how different the dominant period of the target phase is from the split time difference. Usually, shear wave splitting study is made using many earthquakes with a limited number of stations without full awareness of this uncertainty associated with each event. This situation is likely to be one of the main reasons for why shear wave splitting measurements tend to scatter.
 In the above experiment we correct the seismograms for the effect of splitting using the measured splitting parameters. The particle motion of the anisotropy-corrected wave is superposed on the original particle motion diagram in each of the three cases (Figures 9c–9e). In each case the particle motion shows a linear orbit, demonstrating that the linear orbit after correction for splitting using the measured splitting parameters does not prove reliability of the measured values. We repeat the similar test by changing the value of dt. In general, more accurate estimates of ø and dt can be made for a greater value of dt. Regardless of any value of dt in a reasonable range, however, it is practically impossible to detect the splitting effect if the fast direction lies within 10° around the direction of the incident wave motion. Accordingly, when the particle diagram shows a linear orbit, it is difficult, in general, to distinguish whether this is due to the isotropy in the mantle or due to the approximate coincidence of either of the two split directions with the incident ScS polarization azimuth. Use of the multiple ScS phases from three different deep events to hundreds of stations is essential to overcome such difficulty.
4.3. Assessment of Uncertainties Associated With Differential Splitting Parameters
 We examine how the concept of differential splitting parameter works, by taking the simplest case of sScS-ScS, where the ScS ray passes an anisotropic layer specified by ø2 and dt2 and the sScS ray passes additionally another anisotropic layer specified by ø1 and dt1 prier to the incidence to the second anisotropic layer. Let the measured splitting parameters for the ScS wave from the observed ScS record be ø′2 and dt'2. The differential splitting parameters of sScS-ScS are meant to be the splitting parameters of the sScS wave after the correction for its passage through the second anisotropic layer using the measured parameters ø′2 and dt′2. Our question is whether or not the measured differential splitting parameters ø′1 and dt′1 can approximate the true splitting parameters ø1 and dt1. This question is examined using the synthetic ScS and sScS seismograms at station HONH for the Vladivostok event, where ScS and sScS waves are polarized in the N20°E direction at the source. The split ScS waveform is synthesized by applying a splitting operator (ø2, dt2) to the original split-free ScS seismogram. We consider three cases for ø2, N20°E, N45°E, and N65°E, while dt2 is taken to be commonly 1 s. In the first case the fast direction ø2 coincides with the ScS (or sScS) polarization direction at the source, where the ScS record should have no resolving power to detect anisotropic signature. In the third case, ø2 deviates by 45° away from the polarization direction so that the ScS record should have the highest resolving power. The second is an intermediate case. In each of these three cases, the split sScS waveform is synthesized first by applying a splitting operator (ø1, dt1) and next by applying the splitting operator (ø2, dt2). While dt1 is fixed to 2 s, ø1 is successively changed from 0° to 180°. Figures 10a–10c show the results of our measurements of differential splitting parameters in the three cases. In either of the three cases, it is practically impossible to recover the differential splitting parameters (ø1, dt1) if ø1 is within 10° around N20°E (or N70°W). If, on the other hand, ø1 is about 45° away from N20°E (or N70°W), we can make approximately correct estimates of ø1 and dt1. If ø1 deviates more from this azimuth of N65°E (or N25°W), the estimate of dt1 tends to be less than 2 s and the estimate of ø1 tends to be more strongly biased to N65°E (or N25°W). In the first and second cases the estimate of dt2 is strongly asymmetric with respect to N20°E (or N70°W). Besides this asymmetric nature, the limitations involved in the determination of differential splitting parameters of sScS-ScS are similar to those involved in determination of splitting parameters of ScS. The measured fast direction ø′1 tends to be biased to an azimuth 45° away from the polarized direction (or the orbital direction) of the incident ScS (as well as sScS), and the measured time lag dt′1 tends to be smaller than the real one. Note that if ø1 is in certain ranges relative to the polarized direction of the incident ScS (and sScS), the splitting parameters (ø1, dt1) can be recovered approximately even if the values of (ø2, dt2) are poorly estimated. This result demonstrates usefulness of the concept of differential splitting parameters to discriminate two different anisotropic layers although we have to be careful about the associated limitations.
5. Modeling of Anisotropy From Differential Splitting Parameters
5.1. Seismic Anisotropy in the Mantle Wedge
Figures 6 and 7 suggest the coexistence of two anisotropic systems beneath the Japanese islands. The anisotropic system suggested in Figure 6 is based mainly on the data from the Sakhalin event, while the system suggested in Figure 7 is based mainly on the data from the other two events. As discussed in section 4.2, multiple ScS phases from the Sakhalin event are originally polarized around N20°W, and accordingly they should be little split by the NNW fast anisotropic system as indicated in Figure 7. They should be sensitively split by the NNE fast (or WNW fast) anisotropic system as indicated in Figure 6. On the other hand, multiple ScS phases from the Kuril and Vladivostok events are polarized around N15°E at their sources, and accordingly they should be little split by the NNE fast (or WNW fast) anisotropic system as indicated in Figure 6. A splitting pattern change from the trench-parallel fast direction to convergence-parallel fast direction across the volcanic front has been pointed out by Nakajima and Hasegawa  and Long and van der Hilst [2005, 2006] and interpreted in terms of the transition of olivine fabric in the mantle wedge from the B-type to other types across the volcanic front [Jung and Karato, 2001; Kneller et al., 2005].
5.2. Seismic Anisotropy in the Pacific Slab
 The NNW anisotropic system suggested in Figure 7 develops extensively below the mantle wedge. It is difficult to identify the exact depths of this anisotropic system from the present data alone. Most work, however, suggests a largely isotropic lower mantle [e.g., Kaneshima and Silver, 1995; Meade et al., 1995] and a transversely isotropic D″ layer with little evidence for azimuthal anisotropy [Garnero et al., 2004; Kustowski et al., 2008]. The results of Kaneshima and Silver  using S and SKS waves indicate that the lower mantle can be considered as isotropic at least for nearly vertically propagating shear waves. Our preferred model is the one having anisotropy in the subducting slab which is the most anomalous zone along the multiple ScS paths in terms of seismic velocity. We note in Figure 7 that the observed NNW fast directions connect smoothly to the fastest directions of the azimuthal anisotropy of Pn velocity [Shimamura et al., 1983] and 25-s-Rayleigh wave group velocity [Smith et al., 2004] parallel to the Mesozoic fracture zones on the northwestern Pacific seafloor [Nakanishi, 1993]. The azimuthal anisotropy of the Pacific plate is well known and has been interpreted by the preferred orientation of the plate-constituent minerals, primarily olivine [e.g., Maggi et al., 2006]. The a axis of olivine tends to be preferably oriented parallel to the spreading direction within the plate at its infancy [Nicolas and Poirier, 1976]. If the plate anisotropy is symmetric about the horizontal axis of the olivine preferred orientation, Pn and short-period Rayleigh waves propagate with the fastest direction parallel to this axis, and vertically incident S wave is split with the fast direction parallel to it [Crampin and Taylor, 1971]. Upon subduction of this plate, the vertically incident S wave to the subducted slab is polarized in the fast direction coinciding with the horizontal projection of the inclined axis of the olivine preferred orientation. The associated time lag becomes maximum when this inclined axis dips at 45° [Crampin, 1976]. The observations shown in Figure 7 imply that the preferred orientation of olivine minerals is preserved in the lithospheric plate from its surface part down to the subducted part.
5.3. Modeling of Two Anisotropic Systems
 We construct an anisotropic mantle wedge model based on Figure 6 and an anisotropic slab model based on Figure 7, assuming that the Wadati-Benioff zone delineates the upper surface of the slab. The model slab is uniformly anisotropic with the fast direction of N25°W (in horizontal projection) and one-way time lag of 0.5 s, an average feature of the observed splitting parameters shown by green and black arrows in Figure 7. The only exception is in the presumably oldest slab portion directly below the Vladivostok source at 566-km depth, where the anisotropic system is assumed to be the same as that directly above it. The mantle wedge beneath the Japan Sea is modeled to be uniformly anisotropic with the fast direction of N60°W and one-way time lag of 0.5 s, an average feature of the observed splitting parameters shown by green arrows in Figure 6. The mantle wedge beneath each station is anisotropic with the fast direction and time lag characterized by either a blue, red, or orange arrow in Figure 6. Orange arrows in southern Hokkaido represent the splitting parameters of ScS from the Vladivostok event, where the effect of slab anisotropy beneath the source and that beneath the station are approximately canceled out. Our model includes the anisotropy of the upper mantle above each of the three foci, which is based on the averages of the splitting parameters shown by black arrows at the epicenter of each event.
5.4. Model Consistency
 In order to examine the consistency of our anisotropic model with the observations, we synthesize the split seismograms by appropriately rotating and time shifting the synthetic seismograms. We first calculate the synthetic seismograms for the isotropic Earth model for the three earthquakes. We next rotated and shift in time two horizontal components of the synthetic multiple ScS phases. For example, a split sScS2 seismogram is synthesized by rotating and time shifting the original synthetic seismogram first according to the model of the upper mantle anisotropy just above the source, second according to the model of the subducted slab anisotropy, third according to the model of the mantle wedge anisotropy beneath the Japan Sea, forth according again to the model of the subducted slab anisotropy and finally according to the model of the mantle wedge anisotropy just beneath the station. We measure the splitting parameters for the resultant split sScS2 by the waveform correlation method. The measured values are shown by arrows in Figures 3–5 in comparison with the observed splitting parameters for the Kuril, Vladivostok, and Sakhalin events, respectively. The agreement is in general remarkable, demonstrating the overall consistency of our model with the observations.
 The agreement between the observed and predicted splitting parameters is evaluated by calculating the variance reduction. Denoting Aobs and Asyn as the splitting parameter vectors determined from the observed and synthetic seismograms, we define the variance reduction as
 If ∣Asyn∣ = 0, we redefine ∣Asyn∣ = ɛ and ∣Aobs − Asyn∣ = ∣Aobs∣, where ɛ is a minimum unit in dt measurement (=0.5 s). The summation is taken over all the available data. The variance reduction reaches 60% or more for each phase from each event, except for the cases of the ScS2 from the Sakhalin event and the sScS2 from the Vladivostok event where the variance reductions are less than 50%.
 We for the first time resolved the slab anisotropy from the mantle wedge anisotropy by a differential splitting parameter technique. This technique is different from the multiple ScS technique of Vinnik and Farra , which assumes the presence of only one anisotropic layer so that the splitting effects of multiple ScS are cumulative. The effectiveness and limitations of our technique were discussed. The use of multiple ScS phases from several deep shocks with different mechanisms and availability of such records at hundreds of closely spaced stations were essential to resolve two mutually overlapped anisotropic layers.
 The observed time lags on the order of a second cannot be attributed entirely to the crustal anisotropy, because the crustal anisotropy is considered to produce dt of less than 0.3 s [e.g., Kaneshima et al., 1988]. Contribution from the mantle anisotropy has to be taken into account to explain the observed dt. We have shown that the mantle anisotropy consists of two anisotropic layers and that two layers are suffice to explain the observations. If there is some additional layer whose anisotropic system is different from those we found, its effect should be sensed by the waves from at least one of the two events with the ScS polarization angles mutually different by 45°. There is little indication for the effect of the third anisotropic system on the observed multiple ScS seismograms.
 In the mantle wedge, we have identified two types of anisotropy all along the Southern Kuril, northern Honshu, and Ryukyu arcs. These two types of anisotropy are clearly separated by the volcanic front, on the Pacific side of which the trench-parallel polarization is dominant. On the Japan Sea side, the convergence-parallel polarization is dominant. The convergence-parallel polarization appears to extend far away from the volcanic front to the northeastern margin of the Asian continent across the Japan Sea.
 The anisotropy with the NNW fast direction prevails almost uniformly in the deeper mantle beneath the Japanese islands. Although it is difficult to identify the depths of this anisotropic system from the present data alone, we have argued, on the basis of the available evidence, that the anisotropy is associated with the subducting slab of the Pacific plate. The anisotropic slab can be regarded simply as the subducted part of the anisotropic Pacific plate. The slab anisotropy extends over depths down to the 410-km discontinuity or even beyond that, where a-olivine may persist in a metastable state within the cold core of the descending slab [Kaneshima et al., 2007] (but see Hiramatsu et al. ). We need more studies to locate accurately the NNW anisotropic layer in the mantle.
 We thank H. Kawakatsu for his valuable comments at the early stage of this study. We thank M. Obayashi for the tomographic model and M. Nakanishi for the map of Mesozoic fracture zones on the Pacific seafloor. The SEM synthetics in this work were calculated by the SPECFEM3D program package. The Generic Mapping Tools [Wessel and Smith, 1991] and Seismic Analysis Code [Goldstein et al., 1998] were used in this study. This research was supported by the Ministry of Education, Culture, Sports, Science, and Technology of Japan through the Deep Slab Project (16075208). One of us (Y.T.) was supported by Grant-in-Aid for JSPS Fellows 19–45142.