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Physics of the Earth and Planetary Interiors 115 Ž1999. 17–34 www.elsevier.comrlocaterpepi Interplate coupling in southwest Japan deduced from inversion analysis of GPS data Takeo Ito a b a,) , Shoichi Yoshioka a , Shin’ichi Miyazaki b Department of Earth and Planetary Sciences, Graduate School of Science, Kyushu UniÕersity, Hakozaki 6-10-1, Higashi ward, Fukuoka 812-8581, Japan Satellite Geodetic DiÕision, Geodetic ObserÕation Center, Geographical SurÕey Institute, Kitasato 1, Tsukuba, Ibaraki 305-0811, Japan Received 5 August 1998; received in revised form 16 April 1999; accepted 16 April 1999 Abstract Recently, the Geographical Survey Institute of Japan completed the installation of a GPS continuous observation network in Japan, which has enabled us to investigate real-time crustal movements. In this study, we attempt to obtain spatial distribution of interplate coupling and relative plate motion between subducting and overriding plates in southwest Japan, using horizontal and vertical deformation rates, which were observed at 247 GPS observation stations during the period from April 6, 1996 to March 20, 1998. For this purpose, we carried out an inversion analysis of geodetic data, incorporating Akaike’s Bayesian Information Criterion ŽABIC.. As a result, strong interplate coupling was found off Shikoku and Kumanonada regions, which corresponds well with the fault regions of the 1946 Nankai ŽM 8.1. and the 1944 Tonankai ŽM 8.0. earthquakes, respectively. We also found that interplate coupling becomes weak at depths deeper than about 30 to 40 km beneath the Shikoku and Kii peninsula. The recurrence time of great trench-type earthquakes was roughly estimated as 107 years, which is consistent with previous research. The direction of relative plate motion is oriented N538W, which is close to the direction predicted from the plate motion model. On the other hand, a large forward slip was found in the Hyuganada region off southeast of Kyushu. Since the coseismic displacements associated with the two 1996 Hyuganada earthquakes ŽM 6.6, M 6.6. are removed from the GPS data, this suggests that after-slip occurred near the source region andror that Kyushu moves southeastward stationarily due to other tectonic forces. q 1999 Elsevier Science B.V. All rights reserved. Keywords: GPS; Back slip; Interplate coupling; Relative plate motion; Forward slip 1. Introduction Southwest Japan is the region where the Amurian ŽAM. plate Žor the Eurasia ŽEU. plate., the Philippine Sea ŽPH. plate, and the Okhotsk ŽOK. plate Žor ) Corresponding author. Tel.: q81-92-642-2647; fax: q81-92642-2684; E-mail: [email protected] the North American ŽNA. plate. interact with each other ŽFig. 1.. The plate motion in southwest Japan, especially the eastward motion of the AM plate has been debated by many researchers Že.g., Zonenshain and Savostin, 1981; Kimura et al., 1986; Tsukuda, 1992; Ishibashi, 1995.. There are two theories concerning the location of the southern boundary of the AM plate: one places it along the Median Tectonic 0031-9201r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 1 - 9 2 0 1 Ž 9 9 . 0 0 0 6 3 - 1 18 T. Ito et al.r Physics of the Earth and Planetary Interiors 115 (1999) 17–34 Fig. 1. Map showing horizontal displacement rates relative to the stationary part of the Eurasian plate with confidence ellipses of 1 s at 247 GPS stations in southwest Japan during the period from April 6, 1996 to March 20, 1998. Coseismic crustal deformations associated with the 1996 Hyuganada earthquakes ŽOctober ŽM 6.6., December ŽM 6.6.. and the 1997 Kagoshima–Hokuseibu earthquakes ŽMarch ŽM 6.3., May ŽM 6.2.., which occurred during the observation period, were removed. The epicenters of the four events are shown with star symbols. The inset shows four plates in and around the Japanese islands. AM s Amurian Plate Žor EU s Eurasia plate.; OK s Okhotsk plate Žor NA s North American plate.; PA s Pacific plate; PH s Philippine Sea Plate. Line ŽMTL., and the other places it along the Nankai trough. Geophysical exploration of underground structure beneath the MTL ŽYoshikawa et al., 1992; Yuki et al., 1992; Ito et al., 1996. and fault simulation using strain data obtained by Geographical Survey Institute ŽGSI. of Japan ŽHashimoto and Jackson, 1993. have been conducted. However, we have not arrived at a conclusion to determine a preferred theory. Moreover, the spatial pattern of tectonic crustal movement in southwest Japan is complicated due to elastic strain accumulation and release associ- ated with the subduction of the PH plate along the Nankai trough Že.g., Thatcher, 1984; Savage and Thatcher, 1992; Tabei et al., 1996.. Great interplate earthquakes have occurred repeatedly along the Nankai trough, with recurrence interval of about 90 to 150 years Že.g., Shimazaki and Nakata, 1980; Thatcher, 1984.. The most recent events were the 1944 Tonankai ŽM 7.9. and the 1946 Nankai ŽM 8.0. earthquakes. It is believed that these events released accumulated stress in association with the subduction of the PH plate. Many studies have T. Ito et al.r Physics of the Earth and Planetary Interiors 115 (1999) 17–34 been done to determine the coseismic slip distribution of the two earthquakes, using geodetic data, seismic waves and tsunami data Že.g., Fitch and Scholz, 1971; Kanamori, 1972; Ando, 1975, 1982; Yoshioka et al., 1989; Yabuki and Matsu’ura, 1992; Satake, 1993; Sagiya and Thatcher, 1999.. Some studies have also attempted to obtain interseismic interplate coupling using geodetic data. In southwest Japan, Yoshioka Ž1991. investigated spatial distribution of the strength of interplate coupling along the Nankai trough, based on leveling, tide gauge, and trilateration data, using a three-dimension finite element method. However, the results were obtained using forward modeling, and the model was not satisfactory to evaluate the spatial distribution of interplate coupling objectively. Later, the strength of 19 interplate coupling and the direction of relative plate motion were estimated more objectively through inversion analysis of leveling and trilateration data in the Kanto–Tokai districts and southwest Japan ŽYoshioka et al., 1993, 1994; Sagiya, 1995.. During the last several years, the Geographical Survey Institute of Japan ŽGSI. has installed and maintained GPS continuous observation networks throughout the country. Recently, Nishimura et al. Ž1998. estimated interplate coupling in southwest Japan, using horizontal displacement rates of GPS data, on the basis of the least squares method. However, since their analysis is based on forward modeling, the obtained results cannot be evaluated objectively as well. In this study, we attempt to obtain interplate coupling, using an inversion analysis for continuous Fig. 2. An example of the time series obtained at the CHIYODA station Žlatitude 34.6778N, longitude 140.0888E.. Vertical and horizontal axes represent displacement Žmm. and time Žyear., respectively. Ža. Uncorrected time series of north–south component. Žb. Annual change of north–south component. Žc. Difference between uncorrected time series and annual change of north–south component. Žd. Uncorrected time series of vertical component. Že. Annual change of vertical component. Žf. Difference between uncorrected time series and annual change of vertical component. 20 T. Ito et al.r Physics of the Earth and Planetary Interiors 115 (1999) 17–34 GPS data obtained in southwest Japan. The real-time observations have enabled us to reveal detailed crustal movement in southwestern Japan, elucidating eastward motion of the AM plate. We used data of 247 horizontal and 237 vertical displacement rates from April 6, 1996 to March 20, 1998. The purpose of this study is to obtain the direction of relative plate motion and the spatial distribution of the strength of interplate coupling on the plate boundary between the subducting PH plate and the overriding continental plate through inversion analysis, using Akaike’s Bayesian Information Criterion ŽABIC. ŽYabuki and Matsu’ura, 1992.. 2. GPS data and their correction We employed Bernese version 4 software for analysis of GPS data. We used International GPS Service for Geodynamics ŽIGS. final orbits for satellite information and International Earth Rotation Service ŽIERS. bulletin B for Earth rotation parameters. Only the TSKB station, which is one of the IGS global sites in the GSI campus in Tsukuba, is used for the tie with IGS global site because we adopted a distributed strategy. We resolved ambiguities by the sigma dependent strategy Že.g., Rothacher and Mervart, 1996.. The reference frame we used is ITRF94 Fig. 3. Horizontal displacement rates which were obtained correcting the eastward motion of the Amurian plate. The area in the north of the boundary along the Median Tectonic Line, Arima–Takatsuki Tectonic Line, and the western part of Lake Biwa is regarded as the AM plate. We corrected the movement in this area as the motion of rigid body based on Euler vector Ž218S, 1088E, v s y0.0928rMyr. by Heki et al. Ž1998.. T. Ito et al.r Physics of the Earth and Planetary Interiors 115 (1999) 17–34 ŽITRF International Terrestrial Reference Frame.. Following Heki et al. Ž1998., we obtained the crustal velocity field relative to the EU plate by subtracting its absolute motion from ITRF velocities for each site because the kinematic part of ITRF94 is nnrNUVEL1a plate motion model ŽArgus and Gordon, 1991.. The horizontal displacement rates were calculated by a least-square approach ŽMiyazaki et al., 1998.. We did not use the full covariance information because the computation time is unrealistic. The scale of the formal error written in the digit file is 1 s . The root-mean-square is 3 mm on average, but some sites which had episodic displacement or transient deformation have larger values, reaching 7 mm. We excluded annual change of the data according to the method proposed by Miyazaki et al. Ž1998.. They modeled time series as a linear combination of constant, linear term, trigonometric function whose period is 1 year, and jumps for episodic events. One problem is that we did not estimate postseismic deformation because it strongly couples with annual variations. Fig. 2 shows an example of the time series obtained at the CHIYODA site Žlatitude 34.6778N, longitude 140.0888E.. Fig. 2Ža. and Žd. represent the uncorrected time series of north–south and vertical components, respectively. We clearly find that the scatter of the vertical component is larger than that of horizontal component. Fig. 2Žb. and Že. show north–south and vertical components of annual change, respectively. The annual change D can be expressed as the following form: D s A sin v Ž t y t 0 . q B sin2 v Ž t y t 1 . Ž 1. where A, B are amplitudes for annual and semi-annual changes, respectively, and v is angular frequency for annual changes. t 0 , t 1 are phases of annual and semi-annual changes, respectively. Fig. 2Žc. and Žf. are north-south and vertical components of corrected time series, respectively, excluding the calculated annual changes. The horizontal components of displacement rates of the GPS obtained by GSI show movements relative to the TSKB station Žlatitude 36.1038N, longitude 140.0888E.. Since it is difficult to estimate accurate interplate coupling from these data, we converted the GPS data into plate motion relative to 21 the stationary part of the EU plate. According to Heki Ž1996., the horizontal movement of the TSKB station relative to the stationary part of the EU plate is 2.7 mmryr to the north and 20.5 mmryr to the west. The result was obtained so as to minimize the difference in the horizontal displacement rates between the Very Long Baseline Interferometry ŽVLBI. observations and the model predictions by applying a small translation and rotation for the entire network. Therefore, as a first approximation, the addition of this correction to the horizontal displacement rates at all observation stations enables us to obtain plate motion of southwest Japan relative to the stationary part of the EU plate. Fig. 1 shows horizontal displacement rates relative to the stationary part of the EU plate with confidence ellipses of 1 s at all GPS stations in southwest Japan. Coseismic crustal deformations as- Table 1 Displacement rates of vertical component at 22 tidal stations. Ti: absolute uplift rates at tidal stations deduced from tidal records during the period from 1951 to 1987 ŽKato, 1989.. Gi: uplift rates at GPS stations nearest to the tidal stations. Vi s TiyGi. Negative values indicate subsidence. The locations of the tidal stations are shown in Fig. 4 No. Location Ti Žmmryr. Gi Žmmryr. Vi Žmmryr. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 y0.80 1.60 2.30 1.90 y3.70 y5.70 y1.60 y4.10 3.50 5.90 0.00 y1.40 y1.30 0.80 0.50 3.10 0.40 0.80 1.30 0.00 0.50 y1.30 0.12 Onisaki Owase Shirahama Kainan Sumoto Uno Komatsujima Muroto-misaki KochiŽgsi. Tosakure Tosashimizu Kure Tokuyama Matsuyama Oita Akune Misumi Hakata Shimonoseki Hagi Sakai Maizuru Average 4.03 0.54 y7.79 y8.01 y5.80 7.17 16.09 7.14 11.17 13.57 9.17 7.30 7.48 7.30 10.79 y3.02 7.39 7.32 7.03 7.48 7.59 y6.47 4.89 y4.83 1.06 10.09 9.91 2.10 y12.87 y17.69 y11.24 y7.67 y7.67 y9.17 y8.70 y8.78 y6.50 y10.29 6.12 y6.99 y6.52 y5.73 y7.48 y7.09 5.17 y4.76 22 T. Ito et al.r Physics of the Earth and Planetary Interiors 115 (1999) 17–34 sociated with the 1996 Hyuganada earthquakes ŽOctober 19 ŽM 6.6, depth 39 km., December 3 ŽM 6.6, depth 35 km.. and the 1997 Kagoshimaken–Hokuseibu earthquakes ŽMarch 26 ŽM 6.3, depth 8 km., May 13 ŽM 6.2, depth 8 km.., which occurred during the observation period, were removed. From the figure, large movements can be seen at the stations on the Pacific coast side, and the amount of the movement decreases farther inland. The direction is oriented nearly northwestward except for the stations in Kyushu. In the Chugoku district, however, the eastward component is dominant, suggesting eastward motion of the AM plate relative to the EU plate. Therefore, we removed the plate motion, using the Euler pole Ž218S, 1088E. and rotation rate Žy0.0928rMyr. of the AM plate relative to the EU plate ŽHeki et al., 1998., which were determined based on GPS observation. Here, we investigated the case for which the southern boundary of the AM plate is located along the MTL in Kyushu and Shikoku districts. In the Kinki district, we assumed that the boundary is along the Arima–Takatsuki tectonic line, referring to Hashimoto and Jackson Ž1993.. The area to the north of this boundary is regarded as the AM plate. Fig. 3 represents horizontal displacement rates that were obtained correcting the eastward motion of the AM plate. Comparing Fig. 1 with Fig. 3, we find that the EW component of the displacement rates is nearly zero in the Chugoku district. Fig. 4. Absolute vertical displacement rates with confidence ellipses of 1 s at 237 GPS stations during the period from April 6, 1996 to March 20, 1998. The locations of 22 tidal stations are also shown with symbols of open squares Žsee Table 1.. The upward and downward vectors represent uplift and subsidence, respectively. T. Ito et al.r Physics of the Earth and Planetary Interiors 115 (1999) 17–34 The vertical component of the GPS data also shows movement relative to the TSKB station. Here, we attempt to estimate absolute vertical displacement rate at each GPS station, which is necessary to estimate accurate back-slip distribution, using tidal records. Here, we regarded the sea level as an absolute standard, assuming that eustatic movement is negligible. We assumed that the absolute vertical rate at each tidal station in southwest Japan during the period from 1951 to 1987 estimated by Kato Ž1989. had been continuing for the observation period of the GPS data. Since Kato Ž1989. calculated absolute vertical rates based on the data of 30 years, we excluded tidal stations where coseismic and postseismic crustal deformations were evident during the period. We determined the amount of the correction so as to minimize the following quantity E: E s Ý Ž Ti y Ž Gi y D h . . 2 Ž 2. 23 the tidal station i, D h is the correction which should be added to all the GPS stations. We used the data at 22 tidal stations and obtained D h s y4.76 mmryr ŽTable 1.. Fig. 4 shows the obtained absolute vertical rates at all the GPS stations, together with the locations of the used tidal stations. Although we find that most of the GPS stations tend to subside, vertical movements reflecting subduction of the PH plate Že.g., Yoshioka et al., 1993, 1994. cannot be clearly seen in the figure. As can be seen in Figs. 1 and 4, the accuracy of the GPS data of the horizontal movements is much better than that of vertical movements. 3. Back-slip model and method of analysis i where Ti is absolute vertical rate at tidal station i, Gi is observed vertical rate at the GPS station nearest to In this section, we briefly describe the model used in this analysis, following Yoshioka et al. Ž1993, Fig. 5. Ža. Schematic illustration showing the back-slip model. The effects of locking at an intermediate depth Žleft. can be represented by the superposition of the effects of a uniform steady slip over the whole plate boundary Žright top. and a back slip at the intermediate depth Žright bottom. Žmodified from Yoshioka et al., 1993.. Žb. The forward-slip model. 24 T. Ito et al.r Physics of the Earth and Planetary Interiors 115 (1999) 17–34 1994.. Strain accumulation is considered to be caused by interaction between the subducting PH plate and the overlying continental plate. The situation is schematically illustrated in Fig. 5. Interplate coupling proceeds at the locked region along the plate boundary. On the other hand, decoupling is dominant along shallower and deeper portions of the plate boundary because of high pore pressure due to the existence of water and low viscosity due to high temperature, respectively. As a result, steady slip takes place at the shallower and the deeper portions, and tectonic stress accumulates in the locked region. Such a situation can be divided into two situations geometrically. One is the state that uniform steady slip proceeds over the whole plate boundary. The other is the state to give back slip in the locked region ŽSavage, 1983.. Assuming that we can disregard the former situation because surface deformation produced by the former has long wavelength and its amplitude is small, the present state of stress accumulation can be approximately expressed by giving the back slip in the locked region. On the other hand, stress release is represented by forward slip, whose slip direction is opposite that of the back slip. The application of the two-dimensional back-slip model by Savage Ž1983. to a three-dimensional case has already been done by Yoshioka et al. Ž1993, 1994. and Sagiya Ž1995.. In this study, we attempted to obtain spatial distribution of the magnitude of back slip and the direc- Fig. 6. Iso-depth contours Žin km. of the upper boundary of the Philippine Sea plate subducting beneath southwest Japan. The contour interval is 5 km. T. Ito et al.r Physics of the Earth and Planetary Interiors 115 (1999) 17–34 25 Fig. 7. The spatial distribution of slip rates on the plate boundary, inverted from the displacement rates of the GPS data. The slip motion on the overlying continental plate relative to the subducting Philippine Sea plate is shown. The contour lines denote the amount of back slip. The contour interval is 1.0 cmryr. The areas with low reliability Žthe ratio of the obtained back slip to estimation error is less than four. are shaded. tion of relative plate motion through inversion analysis ŽYabuki and Matsu’ura, 1992., using displacement rates of GPS data in southwest Japan. On the model source region where back slip or forward slip is given, we express spatial distribution of moment tensor corresponding to slip by superposing basis functions Žbi-cubic B-spline functions.. Here, we can express observation equations with N observation data as: d i s Ý A i j a j q ei j Ž i s 1, . . . , N . Ž 3. where d i are observed surface displacements, a j are coefficients of superposing basis functions Žmodel parameters., e i are random errors, and A i j are elastic response at a point i to a unit slip at a point j on the model source region. The response function A i j can be calculated by dislocation theory in a semi-infinite homogeneous perfect elastic body ŽMaruyama, 1964.. The more detailed form is given in ŽYabuki and Matsu’ura, 1992.. Our purpose is to find the model parameters as the best solution, and to estimate the back-slip distribution on the model source region. Here, we consider the likelihood function of T. Ito et al.r Physics of the Earth and Planetary Interiors 115 (1999) 17–34 26 a j . Assuming that the error e i to be NŽ0, s 2 E ., the likelihood function pŽ d < a; s 2 . of the model parameter a j can be expressed as: p Ž d < a; s 2 . s Ž 2ps 2 . yN r2 =exp y 5 E 5y1r2 1 2s 2 Ž d y Aa . =Ey1 Ž d y Aa . some degree. Here, we can denote the probability density function q Ž a; r . with a hyper-parameter r 2 that controls the roughness of the slip distribution as: q Ž a; r . s Ž 2pr 2 . t yK r2 5 L K 5 1r2 exp y 1 2r2 a t Wa Ž 5. Ž 4. where 5 E 5 denotes the absolute value of the determinant of E, and s 2 is unknown covariance for e i . On the other hand, the back-slip distribution has a prior information that the distribution is smooth to where W is a symmetric matrix, whose concrete expression is given in ŽYabuki and Matsu’ura, 1992.. K is the rank of the matrix W, and 5 L K 5 is the absolute value of the product of non-zero eigenvalues. We can estimate the back-slip distribution on the model source region, combining the prior infor- Fig. 8. Displacement rates at each GPS station calculated from the inverted back-slip distribution Žthick arrows. and the observed displacement rates Žthin arrows.. Ža. Horizontal displacement rates. Žb. Vertical displacement rates. T. Ito et al.r Physics of the Earth and Planetary Interiors 115 (1999) 17–34 27 Fig. 8 Žcontinued.. mation with the observation Eq. Ž3.. Here, we united the likelihood function from the data distribution of Eq. Ž4. with the probability density function from the prior information of Eq. Ž5. by using Bayes’ theorem. The Bayesian model is highly flexible with the two hyper-parameters, s 2 and r 2 . We can represent the model as: with: l Ž a; s 2 , r 2 d . To find the best estimates of the two hyperparameters, we used ABIC proposed by Akaike Ž1980. on the basis of the entropy maximization principle. It is a criterion to minimize the influence of the error included in the data and to derive hidden information to its maximum, in order to determine s Ž 2p . y Ž NqK .r2 syNryK 5 E 5y1r2 5 L K 5 1r2 =exp yS Ž a; s 2 , r 2 . Ž 6. S Ž a; s 2 , r 2 . 1 s t Ž d y Aa . Ey1 Ž d y Aa . 2s 2 1 q 2 a t Wa. 2r Ž 7. T. Ito et al.r Physics of the Earth and Planetary Interiors 115 (1999) 17–34 28 the hyper-parameters uniquely, which represent the degree of smoothness of the slip distribution. Once we have determined the two hyper-parameters, s 2 and r 2 , we can calculate the model parameter a. We can represent the solution for the model parameter a, ˆ using a 2 which is defined by s 2rr 2 as: aˆ s Ž At Ey1A q a 2 . y1 At Ey1 d. Ž 8. As a result, we can determine the back-slip distribution objectively and uniquely on the plate boundary, that is, the amount of interplate coupling and the direction of relative plate motion. The covariance for the model parameter aˆ is given by: C s sˆ 2 Ž At Ey1A q aˆ 2 W . y1 Ž 9. where sˆ 2 is the best estimate of s 2 . We can obtain the estimation error of each slip on the model source region from Eq. Ž9.. The optimal value of a which minimizes ABIC in this study was estimated to be 0.15, which is relatively small. From the definition of a 2 Žsee also Eqs. Ž6. and Ž7.., large value of a 2 indicates smooth distribution of back slip and forward slip. In this study, we constructed the model source region on the three-dimensional upper surface of the subducting PH plate obtained from spatial distribution of microearthquakes ŽSatake, 1993., whose strike direction is taken almost parallel to the axis of the Nankai ŽFig. 6.. Since the trough axis changes its direction abruptly in the region between Kyushu and Shikoku, we separated the model source regions into two parts. Since outside of the model source region is assumed to be completely decoupled in this analysis, we constructed relatively large model source regions. The sizes of the model source regions off southeast of Kyushu and Shikoku to Kii peninsula were taken to be 180 km = 200 km and 140 km = 400 km, respectively. We divided the respective model source regions into 9 = 10 and 7 = 20 subsections, and distributed 12 = 13 and 10 = 23 basis functions so as to cover the respective whole regions homogeneously. The distribution of slip rate on the model source region is represented by the superposition of the bi-cubic B-spline functions with various amplitudes. The boundary condition for the model source region is assumed to be semi-fixed, reducing numbers of bi-cubic B-spline functions which express distribution of slip rate on the model source regions. Therefore, stress concentration, which appears near the edge of the model source regions for conventional uniform slip model, is suppressed considerably in this study. In this study, we deduced 772 model parameters from the 247 horizontal and 237 vertical displacement rates of the GPS data, and determined the spatial distribution of slip rate. We excluded 10 vertical data from the data set because the observation errors of the 10 data are anomalously large, and because considering that data with large observation errors are not so important in our inversion analysis in which weight of the errors are considered. In this study, we carried out inversion analysis for both horizontal and vertical displacement rates, considering weight of confidence ellipse of 1 s for the respective components at each GPS station. As we described before, the accuracy of the GPS data of the horizontal movements is much better than that of vertical movements. For the model source region off Shikoku to Kii peninsula, we carried out inversion analysis, giving the constraint that the direction of back slip is within "458 of the direction of plate motion of the PH plate relative to the EU plate ŽSeno et al., 1993., using non-negative least-squares ŽNNLS. by Lawson and Hanson Ž1974.. 4. Results 4.1. Slip distributions on the model source regions Fig. 7 represents distributions of slip rate on the model source regions between the PH plate and the continental plate obtained from inversion analysis based on the GPS data of the crustal movements ŽFigs. 3 and 4.. In the model source region off Shikoku to Kii peninsula the average back-slip rate is 4.0 cmryr for the area with back slips greater than 3.0 cmryr, where interplate coupling appears to be strong. This corresponds well to the coseismic slip regions at the T. Ito et al.r Physics of the Earth and Planetary Interiors 115 (1999) 17–34 time of the 1944 Tonankai ŽM 7.9. and the 1946 Nankai ŽM 8.0. earthquakes ŽSagiya and Thatcher, 1999.. A weakly coupled region that separates these large back-slip regions is located beneath the Kii channel and its southern extensional region. The average direction of the back slip was obtained as N538W" 118 for the model source region off Shikoku to Kii peninsula. The direction differs by 48 from the direction of plate motion of the PH plate relative to the EU plate ŽN498W. ŽSeno et al., 1993. On the other hand, we find large forward slip, reaching 11 cmryr, on the model source region southeast off Kyushu. In Fig. 7, reliability, which is defined by the ratio of the obtained back slip to estimation error on the 29 model source region calculated from Eq. Ž9., is also shown. Reliability is low from the eastern part of Shikoku to the west of Kii peninsula, including the region beneath the Kii channel. The low reliability is probably due to the large distance between the model source region and the GPS stations: the model source region deepens abruptly beneath the Kii channel, and no GPS stations exist there. We also calculated distribution of slip rate on different model source regions so as to fill the gap between the two source regions in the present analysis. However, we hardly found a difference in distribution of slip rate on the original model source regions. From these considerations, we may say that the influence of the edge effects can be disregarded. Fig. 9. Map showing the rates of the converted 666 baseline length changes from the horizontal displacement rates of the GPS. The dashed and solid lines denote contraction and extension, respectively. The thickness of each line represents the displacement rate of baseline length change. 30 T. Ito et al.r Physics of the Earth and Planetary Interiors 115 (1999) 17–34 4.2. Surface displacement rates calculated from the inÕerted back-slip distribution Fig. 8Ža. and Žb., respectively, represent horizontal and vertical displacement rates at each GPS station calculated from the inverted back-slip distribution, together with the observed displacement rates. Concerning the horizontal movement, we find that most of the observed displacement rates are well explained by our model, except in the southern part of Kyushu, the western part of Shikoku, and the Chubu district. In the southern part of Kyushu, the observed horizontal displacement rates have south- ward components as compared to those in the northern region. The observation errors are large there, and we accordingly weighted the errors when we carried out inversion analysis. For these reasons, the fitting of horizontal movements between observation and calculation is considered to be poor. In the western part of Shikoku, the cause of the difference is probably due to large spatial variation of the directions of the observed horizontal movement. In the Chubu district, since there exists westward displacement rates with comparable magnitude in the inland region away from the eastern model source region, the calculation dose not fit the observation Fig. 10. The spatial distribution of slip rates on the plate boundary, inverted from the baseline length changes. The slip motion on the overlying continental plate relative to the subducting Philippine Sea plate is shown. The contour lines denote the amount of back slip. The contour interval is 1 cmryr. The areas with low reliability Žthe ratio of the obtained back slip to estimation error is less than four. are shaded. T. Ito et al.r Physics of the Earth and Planetary Interiors 115 (1999) 17–34 well. Therefore, the crustal movement in this region is considered to be caused by tectonic stresses other than subduction of the PH plate. Vertical movement is poorly fit in all regions. The reason is that the errors of the observation data of vertical movement are several times as large as those of the horizontal movement ŽFigs. 1 and 4., and we weighted the observation errors accordingly in the inversion analysis. 4.3. Slip distributions obtained from baseline length changes Until Section 4.2, we have discussed slip distributions obtained from the inversion of horizontal and vertical displacement rates of GPS data. However, we have to consider effect of fixed point for the horizontal data. To solve this problem, we converted the horizontal displacement rates of the GPS data to 666 baseline length changes ŽFig. 9.. For the data set, we carried out the similar inversion analysis. In this case, we also found that interplate coupling becomes weak at depths deeper than about 40 km beneath the Shikoku and Kii peninsula ŽFig. 10.. The direction of average back slips is oriented N538W" 38, which is close to the direction predicted from the plate motion model by Seno et al. Ž1993.. On the other hand, no slip occurs in the southeast off Kyushu where reliability is fairly low. 5. Discussion Our inversion analysis indicates the strong coupling between the PH and the continental plates in the model region off Shikoku to Kii peninsula ŽFigs. 7 and 10.. The strongly coupled region has been suggested by Hyndman et al. Ž1995. in which a transient thermal model using the finite element method was constructed ŽHyndman and Wang, 1993.. Their model allows comparison of the thermally estimated downdip extent of the seismogenic zone with that from seismicity, tsunami data and the crustal deformation data in the Nankai subduction zone. The locked zone by Hyndman et al. Ž1995. corresponds well with the large back-slip region obtained in this study. This result indicates that the geodetically obtained result is consistent with the 31 thermal model. In the south of the model source region, the Kinan seamount chain is ranging in the NS direction on the Shikoku basin. The subduction of such seamounts might be related to weak interplate coupling in this region ŽYoshioka, 1991.. The relation between seamounts and interplate coupling is discussed by Zhao et al. Ž1997., in which the morphology of the upper surface of the subducting Pacific plate beneath the Japanese islands was estimated using SP and sP converted waves at the upper boundary of the slab. The subducting seamounts have kept roughly their original shapes probably because the seamounts are stronger and less deformable than the inner slope materials, and are not scraped off at the trench so that the slab subducts at a steeper dip angle. Hence, the PH plate may subduct with steeper dip angle beneath the Kii channel than in other regions, corresponding to weak interplate coupling. Moreover, we find that the amount of the back slip becomes very small at depths deeper than about 30 to 40 km on the model source region, indicating weak interplate coupling there. This is probably due to ductile characteristics and flow of rocks due to the high temperature there. This depth is shallower than the depth of 60 km estimated from experimental studies of rock rheology in northeast Japan ŽShimamoto, 1990.. Combining a rheological model, which is represented by single crystal of olivine and plagioclase, with the thermal structure of the subduction zone, Shimamoto Ž1989. suggested the depth of transition from brittle or plastic deformation to ductile deformation to be about 60 km in northeast Japan. The difference in the depths in northeast and southwest Japan could be caused by the fact that the PH plate in southwest Japan is younger and warmer than the Pacific plate, which is subducting beneath northeast Japan, as suggested by previous studies Že.g., Yoshioka, 1991.. On the other hand, on the basis of the idea that the Nankai trough is the southern limit of the AM plate, we carried out a similar inversion analysis, after making necessary corrections for the horizontal GPS data. As a result, we obtained N778W" 148 as the direction of the average back slip, which is different from the direction of Seno et al. Ž1993. by 288. Comparing this with the result obtained assuming that the southern boundary of the AM plate is 32 T. Ito et al.r Physics of the Earth and Planetary Interiors 115 (1999) 17–34 along the MTL, the latter is closer to the results of the plate motion model by Seno et al. Ž1993. in terms of the direction of the average back slip. Therefore, we conclude that the idea that the MTL is the southern boundary of the AM plate is preferable, based on our inversion of the GPS data. We also estimated recurrence times of the Tonankai and the Nankai earthquakes from the results of the model source region off Shikoku to Kii peninsula. The amount of the average coseismic slip on the model source region was estimated to be 342 cm from the result of inversion analysis of coseismic geodetic data associated with the 1944 Tonankai and the 1946 Nankai earthquakes ŽSagiya and Thatcher, 1999.. On the other hand, the amount of the average back slip on the corresponding region obtained in this study is 3.2 cmryr. Dividing the amount of the average coseismic slip by that of the back slip, the recurrence time of the trench-type great earthquakes that have occurred at the Nankai trough is roughly estimated as 107 years, consistent with the recurrence interval of 90 to 150 years in this region Že.g., Ando, 1975; Shimazaki and Nakata, 1980; Thatcher, 1984.. Large forward slip was found on the model source region southeast off Kyushu for the inversion of the horizontal displacement rates. Since the forward slip appears in spite of the removal of the coseismic crustal deformations associated with the two 1996 Hyuganada earthquakes ŽOctober ŽM 6.6., December ŽM 6.6.. from the GPS data, a possible explanation of the forward slip might be after-slip of the Hyuganada earthquakes. However, horizontal displacement rates of GPS observation before the 1996 Hyuganada earthquakes had already shown southeastward movements in Kyushu ŽGeographical Survey Institute, 1996.. Also, no slip can be found on the model source region southeast off Kyushu for the inversion of rates of the baseline length changes. These indicate that deformation of Kyushu dose not behave like an elastic body but a rigid body. Therefore, the NS oriented extension in Kyushu associated with the expansion of the Okinawa trough ŽShiono et al., 1980; Tada, 1980. andror southeastward drag of Kyushu due to the upwelling of mantle material beneath the East China Sea Že.g., Seno, 1998. may be the cause of the southeastward displacement rates in Kyushu. 6. Conclusions In this study, we calculated the distribution of interseismic slip rate on the plate boundary between the subducting Philippine Sea plate and the continental plate in southwest Japan, based on the displacement rates obtained from the continuous GPS observations by the Geographical Survey Institute of Japan. The obtained results are as follows. Ž1. We found back slip of more than 3 cmryr on the model source regions off Shikoku and Kumanonada, indicating strong interplate coupling. These correspond well to the large coseismic slip areas of the 1946 Nankai ŽM 8.0. and the 1944 Tonankai ŽM 7.9. earthquakes, respectively. Weak interplate coupling can be found in the region beneath off Kii channel and in the region deeper than about 30 to 40 km. Ž2. We estimated the recurrence time of the trench-type great earthquakes along the Nankai trough to be about 107 years from coseismic slip and back slip obtained from inversion analyses of the coseismic crustal deformations associated with the Nankai and the Tonankai earthquakes, and the GPS data in this study, respectively. The recurrence time is consistent with the results obtained in the previous studies. Ž3. The average direction of the back slip is N538W on the model source region off Shikoku to Kii peninsula, which is concordant with the direction of N498W from the plate motion model by Seno et al. Ž1993.. Ž4. In the Hyuganada region off southeast of Kyushu, although we excluded coseismic crustal deformations associated with the 1996 Hyuganada earthquakes ŽOctober ŽM 6.6., December ŽM 6.6.. and the 1997 Satsuma earthquakes ŽMarch ŽM 6.3., May ŽM 6.2.., we obtained large forward slip from inversion analysis of the horizontal and vertical displacement rates. The forward slip corresponds to the process of stress release, indicating after-slip in the vicinity of the coseismic slip region of these events. However, from the inversion using baseline length changes, we found that no slips can be seen in the southeast off Kyushu. These indicates that deformation of Kyushu does not behave like an elastic body but a rigid body. The N–S oriented extension in Kyushu associated with expansion of the Okinawa trough andror southeastward drag of Kyushu due to T. Ito et al.r Physics of the Earth and Planetary Interiors 115 (1999) 17–34 the upwelling of mantle material beneath the East China Sea may be a preferable cause of the southeastward horizontal displacement rates in Kyushu. Ž5. We inverted the GPS data for two cases, assuming that the southern boundary of the Amurian plate is located along the Median Tectonic Line and the Nankai trough. Comparing the two cases, the former is closer to the results of the plate motion model than the latter in terms of the direction of the average back slip. Therefore, the idea that the Median Tectonic Line is the southern boundary of the Amurian plate is preferable from our inversion analysis of the GPS data. Acknowledgements We are thankful to T. Yabuki for allowing us to use his source code for geodetic data inversion. We are indebted to B.A. Romanowicz, K. Hudnut and R. 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