Corresponding author: Y. Abe, Aso Volcanological Laboratory, Graduate School of Science, Kyoto University, Minamiaso, Aso, Kumamoto 869-1404, Japan. (firstname.lastname@example.org)
 We investigated the seismic velocity discontinuities in the uppermost mantle of Kyushu, a subduction zone in Japan, using receiver function analyses developed especially for discontinuities with high dipping angles. We elucidated the regional variation of discontinuities, as being the continental Moho, oceanic Moho, and upper boundary of the Philippine Sea slab. From the geometry of these discontinuities and contrast in S wave velocities, we discovered that the oceanic crust of the Philippine Sea slab has a low velocity and is possibly hydrated down to 70 km beneath south Kyushu, 80–90 km beneath central Kyushu, and less than 50 km beneath north Kyushu. The fore-arc mantle wedge beneath central Kyushu has a low-velocity zone and possibly contains hydrated materials and free fluid but such a low-velocity zone does not exist in the fore-arc mantle wedge beneath north Kyushu and south Kyushu. Beneath south Kyushu, water dehydrated from the slab could move to the back-arc side and cause arc volcanism. Beneath central Kyushu, water dehydrated from the slab could move to the fore-arc side and cause a gap in volcanism and hydration of fore-arc mantle materials. Beneath north Kyushu, the oceanic crust does not appear to convey water abundantly in the mantle wedge. The low-velocity hydrated fore-arc mantle extends landward beneath the northern part of central Kyushu and could produce volcanic rocks partially contaminated by slab-derived fluid.
 Kyushu island is located on the eastern margin of the Eurasian plate, under which the Philippine Sea (PHS) plate is subducting in a northwest direction at a rate of 50 mm per year (Figure 1) [Seno et al., 1993]. There are several active volcanoes in Kyushu. The area of the PHS plate subducting beneath Kyushu is divided into two parts by the Kyushu-Palau Ridge, a remnant island arc. The northern part is known as the Shikoku Basin, which was formed 26 Ma [Okino et al., 1994], and the southern part is known as the West Philippine Sea Basin, which was formed about 50 Ma [Hilde and Lee, 1984].
 In a subduction zone, volcanic activities are thought to be induced by aqueous fluid conveyed by the subducting slab into the upper mantle [e.g., Tatsumi, 1986]. Tatsumi  indicated that hydrous minerals in the oceanic crust of the slab and at the bottom of the mantle wedge are conveyed by subduction and release aqueous fluid at a depth of about 110 km. The released fluid then moves upward into the mantle wedge, decreasing the solidus temperature and causing partial melting.
 Volcanic rocks in the subduction zones have a lower content rate of high field strength (HFS) elements in all the trace elements (e.g., Nb, Zr, and Ti) than volcanic rocks in ocean islands and mid-ocean ridges [e.g., Tatsumi, 1995]. HFS elements are incompatible and fluid immobile, and this chemical property of volcanic rocks implies that magmas are affected by fluid dehydrated from the subducting slab. Magmas ejected from volcanoes in Kyushu vary in the amount of contamination by slab-derived fluid. Based on trace element analysis, magmas erupted from active volcanoes on the volcanic front in south Kyushu (Kirishima, Sumiyoshi-ike, and Kaimon-dake, shown in Figure 1) have a low content of HFS elements and are interpreted to be influenced by slab-derived fluid [Shinjo et al., 2000]. Howzever, the results of trace element analysis by Kita et al.  indicate that volcanoes in the Beppu-Shimabara graben (Figure 1), a series of depressions described by Matsumoto , eject both magmas which are and are not influenced by slab-derived fluid. According to the study of Kita et al. , magmas erupted from Aso are the most contaminated by slab-derived fluid and those from Yufu and Tsurumi are the least contaminated of magmas erupted from volcanoes in the graben. Miyoshi et al.  estimated the boron content of volcanic rocks in Kyushu. Boron is an incompatible and highly fluid-mobile element exclusively contained in oceanic sediments, and volcanic rock largely contaminated by slab-derived fluid will contain a large amount of boron. The study found that magmas erupted from Kirishima are largely contaminated by slab-derived fluid, while those from Yufu, Tsurumi, Kuju, and Unzen volcanoes are minimally contaminated, and there is a large variety in the degree of contamination in magmas from Aso.
 In an area where volcanic rocks that are not contaminated by slab-derived fluid are distributed, causes of volcanism other than fluid-induced melting are suggested. Based on ground deformation measurements taken with triangulation and trilateration surveys between 1885 and 1985, Tada  estimated that the Beppu-Shimabara graben spreads in north-south direction at 1.4 cm per year and interpreted the graben as being a rift valley. Therefore, mantle upwelling could occur along the graben. Sugimoto et al.  stated that some magmas erupted from the Yufu and Tsurumi volcanoes (Figure 1) are generated by a partial melting of the PHS slab, based on trace element and isotope analyses of volcanic rocks.
 In Kyushu, there is a clear volcanic front lying subparallel to the depth contour of the Wadati-Benioff zone (Figure 1). While there is a distance of less than 50 km between volcanoes on the volcanic front lying south from Kirishima and north from Aso, there is a 110 km gap in volcanism between Aso and Kirishima.
 In order to understand how the slab-derived fluid influences both volcanism and the gap in volcanism in Kyushu, and to gain a deeper understanding of the processes involved in arc volcanism, it is necessary to identify the along-arc variation in the distribution of water within the uppermost mantle.
 Seismic tomography is a useful method for revealing water circulation beneath subduction zones. For example, based on velocity structures of several subduction zones estimated from seismic tomography, Hasegawa and Nakajima  constructed a model to explain how magmas in arc volcanism are generated and how they ascend in the mantle wedge. In the model, melt is generated by fluid that is conveyed to beneath a back-arc region by the process of subduction, and by convection of the mantle wedge, the melt ascends toward the volcanic front in the low-velocity region.
 The structure of the upper mantle beneath Kyushu has been examined using seismic tomography [Zhao et al., 2000; Honda and Nakanishi, 2003; Wang and Zhao, 2006; Nakajima and Hasegawa, 2007; Xia et al., 2008; Hirose et al., 2008; Tahara et al., 2008; Zhao et al., 2011]. These studies show that there is a high-velocity region along the Wadati-Benioff zone which corresponds to the subducted oceanic plate and a low-velocity region in the fore-arc mantle. Peridotite in the mantle changes into serpentinite by the addition of water, and serpentinite has a lower seismic velocity than peridotite [Christensen, 2004]. Therefore, the low velocity is interpreted to be evidence of serpentinization. However, evidence of water distribution detected by the previous studies using seismic tomography is not sufficient to explain the gap in volcanism and the variety within the chemical composition of the volcanic rocks in Kyushu.
 In this study, we attempt to elucidate the distribution and along-arc variation of water, by detecting seismic velocity discontinuities using receiver function (RF) analyses. In other subduction zones, seismic velocity discontinuities in the upper mantle have been detected [e.g., Yuan et al., 2000; Bostock et al., 2002; Sodoudi et al., 2006; Kawakatsu and Watada, 2007; Audet et al., 2009; Sodoudi et al., 2011]. Based on detected seismic velocity discontinuities, these studies revealed hydrated portions of the oceanic crust and the fore-arc mantle. We previously detected discontinuities in the uppermost mantle in the central Kyushu region using RF analyses and obtained evidence of water distribution situated beneath a narrow region [Abe et al., 2011a]. In this paper, we examine the geometry of the discontinuities beneath the entire area of Kyushu.
 An RF is calculated by deconvolving the vertical component of a teleseismic P wave and its coda portion from its corresponding horizontal component [Langston, 1979]. RFs detect the phases in teleseismic coda that are converted to S waves at seismic velocity discontinuities. We used waveform data recorded at 65 stations by Hi-net (established by the National Research Institute for Earth Science and Disaster Prevention (NIED) [Obara et al., 2005]) from June 2001 to May 2010 and at 55 stations of J-array (established by Japan Meteorological Agency (JMA), Kyushu University, Kagoshima University, and Kyoto University [Morita, 1996]) from August 1996 to October 2009. The location of stations is shown in Figure 2. All the data used in this study were obtained using short-period seismometers with a natural period of 1 s. We calculated 19,866 RFs from 529 teleseismic events, with epicentral distances between 30° and 90° and with magnitudes greater than 5.5. The RFs were calculated using the extended-time multitaper method [Helffrich, 2006] that was improved by Shibutani et al.  and by using a 0.3 Hz low-pass Gaussian filter. As an example, Figure 3 shows the RFs obtained from station IZMH (indicated with a yellow square in Figure 2) and the epicentral distribution of teleseismic events from which the RFs were calculated. Both radial and transverse RFs and their ray parameters were averaged with spacing in 10° of back azimuth.
 In this study, we detected seismic velocity discontinuities and estimated their geometry by stacking migrated RFs. The PHS slab beneath Kyushu dips steeply, and Abe et al. [2011b] showed that the geometry of the oceanic Moho cannot be correctly estimated from migrated RFs when assuming a velocity structure that consists of horizontal layers. In order to estimate the geometry correctly, it is necessary to stack RFs by taking the refraction at the dipping discontinuities into account. Therefore, we stacked the RFs using the method developed by Abe et al. [2011b], as shown below.
 In Figure 4, we show the RF sections beneath the box C–C′ (as shown in Figure 2), to explain the process of geometry estimation. The RF peaks that were migrated beneath the box were projected onto the section C–C′. The section consists of 2 km by 2 km cells, and the red and blue cells represent positive and negative RF amplitudes, respectively. When two or more RFs were projected onto the same cell, the amplitudes were averaged.
 We stacked the migrated RFs within the intervals 31°N–34°N and 129°E–132°E. We firstly migrated transverse RFs using the ak135 seismic velocity model [Kennett et al., 1995], assuming that conversion planes were always horizontal. From the hypocentral distribution of the intermediate-depth earthquakes beneath Kyushu, we estimated that the strike direction of the PHS slab is 208° and that the slab dips in a WNW (N62°W) direction (Figure 1). Therefore, transverse RFs with back azimuths in the range of 118°–298° should enable the detection, by positive (negative) peaks, of a discontinuity parallel to the PHS slab that has an upward (downward) decreasing seismic velocity. Because the Wadati-Benioff zone steeply dips, teleseismic P waves from the downdip or strike direction can impinge subparallel to the PHS slab. If discontinuities parallel to the Wadati-Benioff zone exist, it would be difficult to detect and estimate this geometry with the converted phases from such a P wave. Therefore, we decided to use only the transverse RFs with a back azimuth in the range of 118°–178° to detect the upper and lower boundaries of the subducting oceanic crust. The green circles in Figure 3a show the epicenters of teleseismic events for these RFs. We obtained RF sections parallel to the dipping direction of the PHS slab, which were cut at every 0.1° of latitude. The RF sections were generated from the stacked RF peaks below the rectangular areas, with a width of 40 km and a distance of 200 km. Figure 4a illustrates one of these RF sections. From these sections, we obtained the three-dimensional geometry of a dipping discontinuity corresponding to the oceanic Moho, which was indicated by consecutive positive peaks (shown by the green line in Figure 4a).
 The second part of the process was to iteratively migrate and stack the RFs, assuming a horizontal discontinuity at a depth of 35 km (the continental Moho) and an additional dipping discontinuity. The geometry of this additional discontinuity (purple lines shown in Figures 4b–4d) was determined from the geometry of the oceanic Moho, which was estimated from the former stacking (green lines in Figures 4a–4c). Although we assumed a dipping interface, we always migrated the RFs using the one-dimensional velocity distribution of the ak135 model. In the RF sections obtained from the fourth stacking, the RF peaks coincide with the geometry of the dipping discontinuity assumed for the stacking (Figure 4d). Thus, the geometry of the dipping discontinuity obtained from the iteration processes converged with the correct geometry. In Figure 4d, the geometry of the oceanic Moho, detected by positive peaks, is subparallel to the Wadati-Benioff zone.
 Although it is not possible to estimate the geometry of an interface that is not detected by obvious consecutive RF peaks, we assumed the geometry of each interface in the whole analytic area to migrate RFs. The undetectable part of the geometry in the first and second stackings was extrapolated from the detectable part and used for the migration, together with the detectable part for the second and third stackings, respectively. However, in the fourth stacking, we assumed a dipping discontinuity parallel to the upper surface of the Wadati-Benioff zone, instead of an extrapolated portion of the discontinuity. A large portion of the extrapolated discontinuity dips gentler than the Wadati-Benioff zone at the same depth, because shallower dipping discontinuities (up to 90 km in depth) were well obtained, and it dips gentler than the deeper portion of the Wadati-Benioff zone. The steeper the assumed discontinuity, the shallower the depth limit where the RFs are migrated (as shown in Figure 4). Therefore, only when we assume the geometry of a dipping discontinuity parallel to the Wadati-Benioff zone, we can judge whether a discontinuity parallel to it is absent or undetectable. For example, on the purple line in Figure 4d, the discontinuity corresponding to the oceanic Moho exists to a depth of 90 km and does not exist at depths between 90 km and 130 km. Discontinuities parallel to the Wadati-Benioff zone cannot be detected at depths deeper than 130 km.
 In the fourth stacking, we used both radial and transverse RFs, which had back azimuths in the range of 0°–360°. Red and green circles in Figure 3a show the epicenters of these RFs. We stacked the RFs of the horizontal components, which were parallel to the horizontal component of the vibration direction of the S waves converted at the assumed discontinuity. This method of imaging is called “vectorial imaging” [Kawakatsu and Yoshioka, 2011]. With this method, both RF peaks corresponding to subhorizontal discontinuities and those corresponding to dipping discontinuities are enhanced, and using the amplitudes of these peaks, the magnitude of the velocity contrast at a discontinuity becomes easy to be estimated. To accurately estimate the velocity contrast, we stacked only the RF peaks that were generated from phases converted from teleseismic P waves impinging the assumed discontinuities at 20°–40° of incidence angles. These angles correspond to the incidence angles of teleseismic P waves with epicentral distances between 30° and 90° to the horizontal Moho, which exists at a depth of 35 km. If any anisotropic media existed, the RF peaks corresponding to the boundaries of the media would vary with the back azimuth [e.g., Savage, 1998]. To minimize the effect of such anisotropic media, we averaged 12 images of stacked RFs with a spacing of 30° back azimuth.
 Previously, other methods using teleseismic waveforms have been developed to detect discontinuity [e.g., Sheehan et al., 2000; Rondenay et al., 2005; Boyd et al., 2007]. In such methods, each part of a teleseismic waveform, or RF, has an effect on an isochronal surface of a travel time delay between the direct wave and the scattered wave. In our study, we assumed dipping angle and dipping direction of a conversion surface anywhere in the analytic area and plotted each part of an RF on strictly limited points, where the direct wave and the converted wave satisfied Snell's law. The previously developed methods can detect completely unknown discontinuities, but these are difficult to detect with our method. To detect a dipping discontinuity, it is necessary for us to roughly know its dipping direction. However, we are able to roughly estimate the dipping direction of the subducting slab from the geometry of the Wadati-Benioff zone. Because each part of every RF used was plotted only on possible conversion points, our imaging is not biased by the use of waveforms from limited back azimuths observed at a small number of stations.
 In section 3 below, we show the results obtained from the RF sections constructed from the fourth stacking and further discuss these results in section 4.
 The RF peaks stacked beneath each of the four boxes in Figure 2 were projected along a section. In each section, the positive peaks corresponding to the continental Moho appear at depths of 30–40 km (“CM” in Figures 5a, 6a, 7a, and 8a). These depths are comparable to those observed in previous studies using the SP converted waves of intermediate-depth earthquakes [Nakamura et al., 2002] and using a travel time analysis of local earthquakes [Oda and Ushio, 2007]. RF peaks corresponding to the continental Moho are negative beneath the fore-arc region in sections B–B′ and C–C′ (“IM” in Figures 6a and 7a). We obtained positive RF peaks corresponding to the oceanic Moho of the PHS slab below the Wadati-Benioff zone. These peaks extend to a depth of 80 km in section B–B′, 90 km in section C–C′, and 70 km in section D–D′ (“OM” in Figures 6a, 7a, and 8a). Okamoto et al.  observed seismic waves guided by the low-velocity oceanic crust in central and south Kyushu and found that the low-velocity oceanic crust extends to a depth of 60 km. We revealed that the oceanic crust has low velocity down to the deeper portion than that confirmed by Okamoto et al. . In section A–A′, the RF peaks corresponding to the oceanic Moho are obscure (Figure 5a). Negative peaks corresponding to the upper boundary of the PHS slab were also observed over the Wadati-Benioff zone at a depth of 50–80 km in section C–C′ and down to a depth of 60 km in section D–D′ (“ST” in Figures 7a and 8a). The thickness of the subducting oceanic crust is estimated to be about 12 km (see Figures 7a and 8a).
4.1 Water Transportation in the Subducting Oceanic Crust
 According to Hacker et al. [2003a], the subducting oceanic crust of the PHS slab has an S wave velocity reduction of at least 10% in the anhydrous slab mantle until the point where the stable oceanic crustal rock facies changes from lowsonite + amphibole + eclogite (3.0 wt % H2O) to amphibole + eclogite (0.6 wt % H2O) or to zoisite + eclogite (0.3 wt % H2O).
 To understand water transportation in the subducting oceanic crust, we estimated the amplitude of the RF peak produced by an S wave, converted at a discontinuity dipping at an angle of 30°–50° with a velocity contrast of 10%. We assumed three velocity models with dipping discontinuities and calculated the RFs from waveforms synthesized with generalized ray theory [Helmberger, 1974].
 The assumed velocity models have a slab subducting in a WNW direction (N62°W) and are shown in Table 1. The three models differ in the thickness and dipping angles of the layers. Table 1 shows the thickness of each layer measured vertically. The thickness of the dipping oceanic crust of each model measured perpendicularly to its boundaries is 12 km, which is the same as the thickness of the oceanic crust in the sections C–C′ and D–D′ (Figures 7a and 8a). Parameters (S wave velocity, Vp/Vs, and density) of both the mantle wedge and the slab mantle correspond to those of unmetamorphosed harzburgite, as estimated by Hacker et al. [2003a], and parameters of the oceanic crust correspond to those of metamorphosed mid-ocean ridge basalt estimated by Hacker et al. [2003a].
Thickness of the oceanic crust of each model is 12 km when measured perpendicularly to the oceanic Moho.
 We assumed 30 hypocenters with back azimuths of 15°, 45°, 135°, 165°, 195°, 225°, 255°, 285°, 315°, and 345°, and with epicentral distances of 40°, 60°, and 80°. We did not assume hypocenters with back azimuths of 75° and 105° because we analyzed few events that occurred of the eastern side of Kyushu (Figure 3). We then estimated the incidence angle of the teleseismic wave of events toward the assumed slab dipping at 30°, 40°, or 50°, and selected 16 sets of hypocenter and dipping angle where the teleseismic wave had an incidence angle of 20°–40°. The 16 sets of back azimuth, epicentral distance, and dipping angle of the slab are shown in Table 2.
Table 2. Amplitudes of RF Peaks Corresponding to the Oceanic Mohoa
Models 1–3 correspond to those in Table 1. Teleseismic P waves from hypocenters shown in this table arrive at the oceanic Moho of each model at incidence angles between 20° and 40°.
Average and SD
0.062 ± 0.012
 We calculated radial and transverse RFs from the 16 waveforms and rotated each couple of radial and transverse RFs to the horizontal component of the vibration direction of the S wave converted at the oceanic Moho. Figure 9 shows the 16 synthesized RFs. The intervals of negative and positive peaks corresponding to the upper and lower boundaries of the assumed oceanic crust, respectively, were 1.3–1.4 s. In Figure 3b, we can find the peaks of RFs observed at IZMH that correspond to the upper and lower boundaries of the oceanic crust of the PHS slab. We selected the transverse RFs of IZMH that were regarded to have been generated by teleseismic waves with incidence angles on the oceanic Moho of 20°–40° and put green triangles on the peaks which corresponded to the upper and lower boundaries of the oceanic crust in Figure 3b. Near station IZMH, the oceanic Moho dips at 45° (section C–C′ in Figure 7a). When we assessed the incidence angles to be 20°–40°, we assumed the dipping angle and dipping direction of the slab as being 45° and N62°W, respectively, and the P wave velocity of the upper mantle as being 8.4 km/s. The intervals between a peak corresponding to the upper boundary of the oceanic crust and a peak corresponding to the oceanic Moho were 1.15–1.45 s, which corresponded to those of the synthesized RFs (Figure 9). Therefore, the assumed oceanic crust of the models shown in Table 1 has an appropriate thickness for estimating the amplitude of RF peaks corresponding to the oceanic Moho.
 Table 2 shows the amplitudes of RF peaks generated by S waves converted at the oceanic Moho. We calculated the average and standard deviation (SD) of the amplitudes and confirmed that an S wave converted at a discontinuity dipping at 30°–50° and having a velocity contrast of 10% produces an RF peak amplitude of 0.062 ± 0.012 on vectorial imaging sections. In Figures 5c, 6c, 7c, and 8c, we clarify the amount of S wave velocity contrast at the detected discontinuities, by showing cells with positive amplitudes of less than 0.062 in grey and those with amplitudes larger than 0.062 in a warm color (yellow or red). Discontinuities dipping at 30°–50°, indicated by yellow or red cells, have an S wave velocity contrast greater than 10%. In Figures 6c, 7c, and 8c, amplitudes of RF peaks corresponding to the oceanic Moho are larger than 0.062 at depths to 80 km, 90 km, and 70 km beneath B–B′, C–C′, and D–D′, respectively.
 We then measured the accuracy of RF amplitudes on the sections by randomly selecting half of the calculated RFs 10 times and generating the sections. The SD of each cell was calculated from the 10 sets of the RF sections. We show the SD of each cell on the four sections in Figures 5d, 6d, 7d, and 8d.
 We subsequently confirmed which cell had a definite amplitude of over 0.062 and which cell had a definite amplitude smaller than 0.062. In Figures 5e, 6e, 7e, and 8e, the red color indicates cells with an amplitude greater than (0.062 + SD) and the grey color indicates the cells with an amplitude less than (0.062 − SD). Therefore, the red and grey colors indicate cells that definitely have an amplitude greater or smaller than 0.062, respectively, even if the cell has an uncertainty as large as the SD. Most of the peaks corresponding to the oceanic Moho beneath C–C′ and D–D′ and some of those peaks beneath B–B′ definitely have an amplitude larger than 0.062 (Figures 6e, 7e, and 8e).
 Based on the amplitude of peaks corresponding to the oceanic Moho, the oceanic crust is interpreted to contain more than 3.0 wt % of H2O down to a depth of 80 km, 90 km, and 70 km beneath B–B′, C–C′, and D–D′, respectively (Figures 6c, 7c, and 8c). Beneath B–B′, we can neither confirm nor deny whether some of the peaks that correspond to the oceanic Moho, which are not indicated by either red or grey in Figure 6e, have an amplitude of larger than 0.062. However, most of peaks corresponding to the oceanic Moho at depths between 70 km and 80 km are confirmed to have an amplitude of larger than 0.062 in section B–B′ (Figure 6e), and hydrous phases (lowsonite + amphibole + eclogite; 3 wt.% H2O) are interpreted to exist to a depth of 80 km beneath B–B′. Hacker et al. [2003b] and Yamasaki and Seno  hypothesized that dehydration embrittlement is responsible for the occurrence of intermediate-depth earthquakes. Based on this hypothesis, the presence of seismicity above the oceanic Moho (Figures 6a, 7a, and 8a) implies that dehydration reactions occur in the hydrous oceanic crust. Hacker et al. [2003b] indicated that hypocenters of intermediate-depth earthquakes in several subduction zones are correlated to the pressure-temperature space where hydrous phases of the oceanic crust are stable. Therefore, intermediate-depth earthquakes in the oceanic crust would be caused by an equilibrium dehydration reaction. Although it is possible that metastable gabbro exists as a low-velocity layer at the top of the slab [Hacker et al., 2003b; Abers, 2005], the low velocity of the oceanic crust with a high seismicity is, in all likelihood, caused by hydrous materials in the oceanic crust beneath central and south Kyushu.
 Although intermediate-depth earthquakes occur down to 150 km in depth beneath A–A′, RF peaks corresponding to the oceanic Moho are unclear. This result suggests either that the oceanic crust does not have a significantly lower S wave velocity than the slab mantle or that the low-velocity oceanic crust exists but is too thin to be resolved by our RFs. Using analyses of reflection and refraction waves of seismic survey in the area 25°N–31°N and 132°E–138°E, Nishizawa et al.  estimated the thickness of the oceanic crust of PHS plate to be between 5 km and 10 km, except in the area beneath the Kyushu-Palau ridge.
 Therefore, we assumed the minimum thickness of the oceanic crust as being 5 km and confirmed the existence of a thin oceanic crust beneath A–A′. We synthesized RFs in the same manner described above, using velocity models identical to those in Table 1, but incorporating a thin oceanic crust with a thickness of 5 km measured perpendicularly to the boundaries. Amplitudes of peaks corresponding to the upper and lower boundaries of the oceanic crust dipping at 30°–50° were estimated to be −0.039 ± 0.006 and 0.042 ± 0.010, respectively. In Figure 5f, the red color indicates cells with an amplitude larger than a result of (SD + 0.042). The yellow color indicates cells with an amplitude between results of (−SD + 0.042) and (SD + 0.042), and larger than a result of (SD − 0.039). The light blue color indicates cells with an amplitude between the results of (SD − 0.039) and (−SD − 0.039), and smaller than (−SD + 0.042). The blue color indicates cells with an amplitude smaller than a result of (−0.039 − SD). The grey color indicates cells with an amplitude larger than a result of (SD − 0.039) and smaller than a result of (−SD + 0.042). Cells with an amplitude larger than a result of (−SD + 0.042), and smaller than a result of (SD − 0.039), are not colored. Therefore, a red color indicates cells which are confirmed to have an amplitude larger than 0.042, the yellow color indicates cells that definitely have an amplitude larger than −0.039, the light blue color indicates cells that definitely have an amplitude smaller than 0.042, the blue color indicates cells that definitely have an amplitude smaller than −0.039, and the grey color indicates cells that definitely have an amplitude larger than −0.039 and smaller than 0.042. A thin low-velocity oceanic crust would appear in Figure 5f as a pair of blue and red consecutive peaks with a thickness of about 5 km if it could be resolved by our RFs. It would appear as a pair of yellow and light blue consecutive peaks, or as white peaks, if it could not be resolved by our RFs. In Figure 5f, we cannot discover such consecutive peaks. We, therefore, find that there is no possibility of the existence of a low-velocity oceanic crust with a thickness of more than 5 km beneath A–A′, if it has more than 10% of S wave velocity reduction.
 It is, therefore, understood that the oceanic crust does not have a significant lower S wave velocity than the slab mantle beneath A–A′ and that the rock facies of the oceanic crust changes from lowsonite + amphibole + eclogite to amphibole + eclogite at depths shallower than 50 km. In the RF sections across the western part of Shikoku and Chugoku (Figure 1), the oceanic Moho is not detected deeper than 50–60 km by positive peaks [Shiomi et al., 2004; Shiomi et al., 2008]. The thermal structure of the PHS slab beneath north Kyushu is therefore similar to that beneath the western part of Shikoku and Chugoku, where the Shikoku Basin is subducting. However, the Shikoku Basin beneath north Kyushu, which is younger and hotter than the West Philippine Sea Basin, is subducting and can explain the phase change of the oceanic crust at shallower depths than that beneath central and south Kyushu.
4.2 Water Distribution in the Mantle Wedge
 The seismic velocity structure of the uppermost mantle beneath Kyushu has been estimated with seismic tomography [Zhao et al., 2000; Honda and Nakanishi, 2003; Wang and Zhao, 2006; Nakajima and Hasegawa, 2007; Xia et al., 2008; Hirose et al., 2008; Tahara et al., 2008; Zhao et al., 2011]. In these studies, a low-velocity (and high-Vp/Vs) region was detected in the fore-arc mantle and regarded to be a portion that was serpentinized by fluid dehydrated from the PHS slab. Abe et al. [2011a] discovered what is known as the “inverted Moho,” the continental Moho associated with negative RF peaks, beneath the fore-arc region (located a little north of box C–C′ (Figure 2)). The unusual occurrence of an inverted Moho has also been detected beneath Cascadia, Greece, and northern Chile [Bostock et al., 2002; Sodoudi et al., 2006; Sodoudi et al., 2011] and is regarded to represent the existence of a highly serpentinized mantle.
 In this study, the inverted Moho is estimated to be at a distance of between 40 km and 55 km beneath B–B′ (Figure 6a) and at a distance between 60 km and 70 km beneath C–C′ (Figure 7a). The fore-arc mantle beneath B–B′ and C–C′ is interpreted to have a lower S wave velocity than the continental lower crust. The absence of negative RF peaks, corresponding to the upper boundary of the subducted PHS slab beneath B–B′ and at distances of 55–75 km beneath C–C′, also implies that the fore-arc mantle has an S wave velocity that is as low as the hydrated oceanic crust. The RF amplitudes of the inverted Moho are between −0.103 and −0.066 beneath B–B′ (Figure 4c) and smaller than −0.103 beneath C–C′ (Figure 5c). According to the results of double-difference tomography by Saiga et al. , the S wave velocity of the continental lower crust above the inverted Moho is about 3.6 km/s. Assuming the S wave velocity of the continental lower crust as being 3.6 km/s, the S wave velocity of the mantle beneath the inverted Moho is estimated to be between 2.8 km/s and 3.2 km/s beneath B–B′ and lower than 2.8 km/s beneath C–C′, respectively. According to seismic velocities of rock samples measured by Christensen , the degree of serpentinization of the fore-arc mantle is between 60% and 80% beneath B–B′, and over 80% beneath C–C′, if the fore-arc mantle contains lizardite or chrysotile serpentinites. If it contains antigorite serpentinite, then the S wave velocity of the fore-arc mantle beneath the inverted Moho is lower than that of pure serpentinite. In this situation, the existence of free fluid with a high pore pressure would be necessary to explain such a low S wave velocity [Christensen, 2004]. According to Christensen , if the area of low velocity is colder than 300°C, lizardite or chrysotile serpentinite is likely to exist within the area. If the temperature of the area is 300–650°C, antigorite serpentinite and free fluid are likely to exist, and if the temperature is higher, only free fluid may exist.
 We generated RF sections along the dipping direction of the Wadati-Benioff zone, cut at every 0.1° of latitude. Each of the yellow stars in the map in Figure 10 represents the location of a cell that is the closest to the east coast of Kyushu out of all cells corresponding to the continental Moho with an amplitude greater than 0.048, in each section. The mantle beneath the continental Moho, represented by RF peaks with amplitudes of 0.048, is interpreted to have an S wave velocity of 3.9 km/s, which is explained by the presence of 70% of antigorite serpentinite [Christensen, 2004]. The distribution of these yellow stars indicates that the uppermost mantle that has a moderately low velocity extends landward in the northern part of central Kyushu. In the map of Figure 10, the line X–X′ shows the survey line of the seismic experiments conducted by Research Group for Explosion Seismology [1999a, 1999b]. Otsu  analyzed the experimental data and revealed that the Moho below the dashed line in the map in Figure 10 has a small velocity contrast. These results correspond with our interpretation of a low-velocity fore-arc mantle extending landward in the northern part of central Kyushu. Beneath the northern part of central Kyushu, dehydrated fluid would spread widely, while beneath the southern part of the central Kyushu, the fluid would be concentrated in a narrow area of the fore-arc mantle wedge (Figures 10b and 10c).
 RF peaks corresponding to the continental Moho beneath A–A′ and D–D′ are not inverted (Figures 5 and 8). This feature implies that the S wave velocity of the fore-arc mantle beneath A–A′ and D–D′ is higher than that of the continental lower crust. Negative RF peaks corresponding to the upper boundary of the PHS slab are clearly observed beneath D–D′ (Figure 8). This feature also implies that the S wave velocity of the fore-arc mantle is not as low as that of the oceanic crust. Negative peaks corresponding to the upper boundary of the PHS slab are not clearly detected beneath A–A′ (Figure 5). However, the oceanic crust would not have a much lower velocity than the slab mantle beneath A–A′, since positive peaks corresponding to the oceanic Moho are also not clearly detected, and the absence of negative peaks does not imply that the S wave velocity of the fore-arc mantle is low.
4.3 Water Transportation in the Mantle Wedge
 Our results indicate that the oceanic crust conveys fluid down to a depth of 70 km and that little fluid exists in the fore-arc mantle beneath south Kyushu, while a large volume of fluid exists in the fore-arc mantle beneath central Kyushu. We therefore assume that fluid dehydrated from the oceanic crust moves toward the back-arc side in the mantle wedge beneath south Kyushu (Figure 10d), while it moves toward the fore-arc side beneath central Kyushu (Figures 10b and 10c). Magmas erupted from active volcanoes on the volcanic front in south Kyushu are largely contaminated by slab-derived fluid [Shinjo et al., 2000]. Source magmas for volcanism on the volcanic front south of Kirishima may therefore be generated by a reduction in the solidus temperature of the mantle wedge material because of the dehydrated fluid and may be explained by the model of magma generation and upwelling described by Hasegawa and Nakajima . In a simulation of water transportation by Iwamori , a serpentinized layer on the subducting slab is thought to be a path of dehydrated fluid moving to the deeper back-arc side. Kawakatsu and Watada  detected a discontinuity with a downward increasing velocity, corresponding to the bottom of a low-velocity serpentinized layer beneath northeast Japan. Although we have not detected such a boundary beneath south Kyushu, there is a possibility of the existence of a serpentinized layer that does not have so sharp boundary, so low velocity, or is not so thick that it can be detected.
 The distribution of water in the mantle wedge beneath B–B′ and C–C′ implies that fluid dehydrated from the subducted oceanic crust is likely to move toward the fore arc, beneath the central part of Kyushu (Figures 10b and 10c). This feature may explain the gap in volcanism in central Kyushu (Figure 1). The direction of fluid movement may depend on the subduction velocity and the dip angle of the slab. Kawano et al.  suggested that the serpentinized layer is formed at the bottom of the mantle wedge by fluid dehydrated from the oceanic crust and that the dehydrated fluid prefers to move parallel, rather than vertically, to the subducted slab in the serpentinized layer. Such preferential movement would occur because of the strong anisotropy of permeability of the shear deformed serpentinized layer. Kawano et al.  indicated that fluid moves up dip if the percolation velocity of fluid is higher than the subduction velocity, but it moves down dip if the percolation velocity is lower than the subduction velocity. The pressure gradient in such a serpentinized layer, with respect to the direction of slab dip, is greater in a subduction zone where the slab dips more steeply. Therefore, fluid percolating in the serpentinized layer should move up dip faster on a steeper slab. Beneath the southern part of Kyushu, the PHS plate converges at a rate of a few millimeters per year faster than beneath the northern part [Seno et al., 1993]. The dip angle of the oceanic crust beneath the southern part (35°, D–D′) is lower than that beneath the central part (40°, B–B′; 45°, C–C′). This motion of the PHS plate and the variation in dip angle may facilitate the down dip fluid transportation beneath south Kyushu and the up dip fluid transportation beneath central Kyushu.
 Our results imply that the oceanic crust and the fore-arc mantle do not contain a lot of water beneath A–A′ (Figure 10a). Our results also imply that fluid dehydrated from the oceanic crust is accumulated in the fore-arc mantle beneath B–B′ (Figure 10b) and that fluid is not conveyed into deeper portions. Some magmas erupted from active volcanoes in the Beppu-Shimabara graben are not influenced by fluid dehydrated from the slab [Kita et al., 2001; Miyoshi et al., 2008]. Therefore, volcanic activities in the Beppu-Shimabara graben may not be caused by fluid-induced melting.
 According to the results of geochemical analyses by Kita et al.  and Miyoshi et al. , the volcanic rocks erupted from the Aso volcano have a greater contamination with slab-derived fluid than others in the Beppu-Shimabara graben, followed by those from Kuju, Unzen, and Yufu-Tsurumi volcanoes. According to the distribution of the low-velocity area, mantle materials beneath Aso would be the most hydrous and those beneath Yufu-Tsurumi and Unzen would be the least hydrous in the Beppu-Shimabara graben (Figure 10). Therefore, the degree of hydration of the mantle beneath each volcano interpreted from our analyses is correlated with the degree of fluid contamination of the magmas erupted from each volcano, as measured by previous geochemical studies. Beneath line B–B′ (Figures 6a–6c), RF amplitudes corresponding to the continental Moho largely vary with distance, and we can expect that the water content of the uppermost mantle also has a large lateral variation. Such a variation in water content may cause the variation in fluid contamination of magmas erupted at Aso, as indicated by Miyoshi et al. . In this study, we are not able to reveal the process of magma genesis of volcanoes in the Beppu-Shimabara graben. However, it is possible that magmas erupted from the graben are generated by mantle upwelling or partial melting of the slab [Tada, 1993; Sugimoto et al., 2006] and that the chemical composition of the volcanic rocks reflects the water content in the source region or on the path of magmas.
 We calculated the RFs using seismic waveform data from Hi-net and the J-array established in Kyushu, then migrated the RFs taking refraction into account at a steeply dipping discontinuity. We obtained the geometry of the continental Moho, the oceanic Moho, and the upper boundary of the PHS slab by stacking the RFs.
 Based on our RF analyses, we interpreted the velocity structure in the uppermost mantle beneath Kyushu to be as follows:
 The oceanic crust of the PHS slab has a lower S wave velocity than the slab mantle lying below it. This low-velocity signature extends to a depth of 70 km beneath south Kyushu, a depth of 80 km – 90 km beneath central Kyushu, but does not extend deeper than 50 km beneath north Kyushu. In the fore-arc mantle beneath central Kyushu, a region with a lower S wave velocity than the continental lower crust exists, while no such low velocity region exists in the fore-arc mantle beneath north Kyushu and south Kyushu. Beneath the southern part of central Kyushu, the low-velocity portion is confined near the edge of the mantle wedge, while the wide area of the fore-arc mantle has a lower velocity than the anhydrous mantle beneath the northern part of central Kyushu.
 From this velocity structure, water distribution and transportation in the uppermost mantle beneath Kyushu are interpreted as follows:
 The oceanic crust of the PHS slab is hydrated to a depth of 70 km beneath south Kyushu, to a depth of 80 km – 90 km beneath central Kyushu and to a depth of no more than 50 km beneath north Kyushu. The fore-arc mantle beneath central Kyushu contains hydrated materials and free fluid. Such a hydrated portion does not exist beneath north Kyushu and south Kyushu, and beneath north Kyushu, the oceanic crust does not convey water abundantly in the mantle wedge. Beneath south Kyushu, water dehydrated from the oceanic crust moves to the back-arc side and causes arc volcanism, where it moves to the fore-arc side and causes both a gap in volcanism and hydration of the fore-arc mantle beneath central Kyushu. The hydrated portion exists near the edge of the mantle wedge beneath the southern part of central Kyushu and widely beneath the north part of central Kyushu. The wide distribution of hydrated materials in the fore-arc mantle is likely to produce magmas partially contaminated by slab-derived fluid in the Beppu-Shimabara graben.
 We are grateful to Tatsuhiko Kawamoto for his useful suggestions. We are also thankful to our reviewer, Forough Sodoudi; an anonymous reviewer; the Editor of this publication, Robert Nowack; and the Associate Editor of this publication, for their many suggestions that have improved this paper immensely. We used seismic data which was observed by NIED, JMA, Kyushu University, and Kagoshima University. We also used the hypocentral data of JMA, and the Generic Mapping Tools of Wessel and Smith  to generate figures. This research has been supported by a Grant-in-Aid for Scientific Research (B) (24340103) from MEXT.