Interplate Coupling in Southwest Japan Deduced from Inversion Analysis of GPS Data

Physics of the Earth and Planetary Interiors 115Ž. 1999 17±34 www.elsevier.comrlocaterpepi

Interplate coupling in southwest Japan deduced from inversion analysis of GPS data

Takeo Ito a,), Shoichi Yoshioka a, Shin'ichi Miyazaki b a Department of Earth and Planetary Sciences, Graduate School of Science, Kyushu UniÕersity, Hakozaki 6-10-1, Higashi ward, Fukuoka 812-8581, Japan b 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 CriterionŽ. ABIC . As a result, strong interplate coupling was found off Shikoku and Kumanonada regions, which corresponds well with the fault regions of the 1946 NankaiŽ. M 8.1 and the 1944 Tonankai Ž M 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 earthquakesŽ. M 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 the North AmericanŽ. NA plate . interact with each otherŽ. Fig. 1 . The plate motion in southwest Japan, Southwest Japan is the region where the Amurian especially the eastward motion of the AM plate has Ž.AM plate Ž or the Eurasia Ž. EU plate . , the Philip- been debated by many researchersŽ e.g., Zonenshain pine SeaŽ. PH plate, and the Okhotsk Ž OK . plate Ž or and Savostin, 1981; Kimura et al., 1986; Tsukuda, 1992; Ishibashi, 1995. . There are two theories con- ) Corresponding author. Tel.: q81-92-642-2647; fax: q81-92- cerning the location of the southern boundary of the 642-2684; E-mail: [email protected] AM plate: one places it along the Median Tectonic

Fig. 1. Map showing horizontal displacement rates relative to the stationary part of the Eurasian plate with confidence ellipses of 1s 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 earthquakesŽ October Ž M 6.6 . , December Ž M 6.6 .. and the 1997 Kagoshima±Hokuseibu earthquakes Ž March Ž M 6.3 . , MayŽ.. M 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. AMsAmurian PlateŽ. or EUsEurasia plate ; OKsOkhotsk plate Ž or NAsNorth American plate. ; PAsPacific plate; PHsPhilippine Sea Plate.

LineŽ. MTL , and the other places it along the Nankai ated with the subduction of the PH plate along the trough. Geophysical exploration of underground Nankai troughŽ e.g., Thatcher, 1984; Savage and structure beneath the MTLŽ Yoshikawa et al., 1992; Thatcher, 1992; Tabei et al., 1996. . Yuki et al., 1992; Ito et al., 1996. and fault simula- Great interplate earthquakes have occurred repeat- tion using strain data obtained by Geographical Sur- edly along the Nankai trough, with recurrence inter- vey InstituteŽ. GSI of Japan Ž Hashimoto and Jack- val of about 90 to 150 yearsŽ e.g., Shimazaki and son, 1993. have been conducted. However, we have Nakata, 1980; Thatcher, 1984. . The most recent not arrived at a conclusion to determine a preferred events were the 1944 TonankaiŽ. M 7.9 and the 1946 theory. Moreover, the spatial pattern of tectonic NankaiŽ. M 8.0 earthquakes. It is believed that these crustal movement in southwest Japan is complicated events released accumulated stress in association with due to elastic strain accumulation and release associ- the subduction of the PH plate. Many studies have T. Ito et al.rPhysics of the Earth and Planetary Interiors 115() 1999 17±34 19 been done to determine the coseismic slip distribu- interplate coupling and the direction of relative plate tion of the two earthquakes, using geodetic data, motion were estimated more objectively through in- seismic waves and tsunami dataŽ e.g., Fitch and version analysis of leveling and trilateration data in Scholz, 1971; Kanamori, 1972; Ando, 1975, 1982; the Kanto±Tokai districts and southwest Japan Yoshioka et al., 1989; Yabuki and Matsu'ura, 1992; Ž.Yoshioka et al., 1993, 1994; Sagiya, 1995 . During Satake, 1993; Sagiya and Thatcher, 1999. . the last several years, the Geographical Survey Insti- Some studies have also attempted to obtain inter- tute of JapanŽ. GSI has installed and maintained GPS seismic interplate coupling using geodetic data. In continuous observation networks throughout the southwest Japan, YoshiokaŽ. 1991 investigated spa- country. Recently, Nishimura et al.Ž. 1998 estimated tial distribution of the strength of interplate coupling interplate coupling in southwest Japan, using hori- along the Nankai trough, based on leveling, tide zontal displacement rates of GPS data, on the basis gauge, and trilateration data, using a three-dimension of the least squares method. However, since their finite element method. However, the results were analysis is based on forward modeling, the obtained obtained using forward modeling, and the model was results cannot be evaluated objectively as well. not satisfactory to evaluate the spatial distribution of In this study, we attempt to obtain interplate interplate coupling objectively. Later, the strength of coupling, using an inversion analysis for continuous

Fig. 2. An example of the time series obtained at the CHIYODA stationŽ. latitude 34.6778N, longitude 140.0888E . Vertical and horizontal axes represent displacementŽ. mm and time Ž year . , respectively. Ž. a Uncorrected time series of north±south component. Ž. b Annual change of north±south component.Ž. c Difference between uncorrected time series and annual change of north±south component.Ž. d Uncorrected time series of vertical component.Ž. e Annual change of vertical component. Ž. f Difference between uncorrected time series and annual change of vertical component. 20 T. Ito et al.rPhysics of the Earth and Planetary Interiors 115() 1999 17±34

GPS data obtained in southwest Japan. The real-time 2. GPS data and their correction observations have enabled us to reveal detailed crustal movement in southwestern Japan, elucidating east- We employed Bernese version 4 software for ward motion of the AM plate. We used data of 247 analysis of GPS data. We used International GPS horizontal and 237 vertical displacement rates from Service for GeodynamicsŽ. IGS final orbits for satel- April 6, 1996 to March 20, 1998. The purpose of this lite information and International Earth Rotation Ser- study is to obtain the direction of relative plate viceŽ. IERS bulletin B for Earth rotation parameters. motion and the spatial distribution of the strength of Only the TSKB station, which is one of the IGS interplate coupling on the plate boundary between global sites in the GSI campus in Tsukuba, is used the subducting PH plate and the overriding continen- for the tie with IGS global site because we adopted a tal plate through inversion analysis, using Akaike's distributed strategy. We resolved ambiguities by the Bayesian Information CriterionŽ.Ž ABIC Yabuki and sigma dependent strategyŽ e.g., Rothacher and Mer- Matsu'ura, 1992. . vart, 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 vectorŽ. 218S, 1088E, vsy0.0928rMyr by Heki et al. Ž.1998 . T. Ito et al.rPhysics of the Earth and Planetary Interiors 115() 1999 17±34 21

Ž.ITRF International Terrestrial Reference Frame . the stationary part of the EU plate. According to Following Heki et al.Ž. 1998 , we obtained the crustal HekiŽ. 1996 , the horizontal movement of the TSKB velocity field relative to the EU plate by subtracting station relative to the stationary part of the EU plate its absolute motion from ITRF velocities for each is 2.7 mmryr to the north and 20.5 mmryr to the site because the kinematic part of ITRF94 is nnr- west. The result was obtained so as to minimize the NUVEL1a plate motion modelŽ Argus and Gordon, difference in the horizontal displacement rates be- 1991. . tween the Very Long Baseline InterferometryŽ. VLBI The horizontal displacement rates were calculated observations and the model predictions by applying a by a least-square approachŽ. Miyazaki et al., 1998 . small translation and rotation for the entire network. We did not use the full covariance information be- Therefore, as a first approximation, the addition of cause the computation time is unrealistic. The scale this correction to the horizontal displacement rates at of the formal error written in the digit file is 1s . The all observation stations enables us to obtain plate root-mean-square is 3 mm on average, but some sites motion of southwest Japan relative to the stationary which had episodic displacement or transient defor- part of the EU plate. mation have larger values, reaching 7 mm. Fig. 1 shows horizontal displacement rates rela- We excluded annual change of the data according tive to the stationary part of the EU plate with to the method proposed by Miyazaki et al.Ž. 1998 . confidence ellipses of 1s at all GPS stations in They modeled time series as a linear combination of southwest Japan. Coseismic crustal deformations as- 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 Table 1 Displacement rates of vertical component at 22 tidal stations. variations. Fig. 2 shows an example of the time Ti: absolute uplift rates at tidal stations deduced from tidal records series obtained at the CHIYODA siteŽ latitude during the period from 1951 to 1987Ž. Kato, 1989 . Gi: uplift rates 34.6778N, longitude 140.0888E.Ž.Ž. . Fig. 2 a and d at GPS stations nearest to the tidal stations. VisTiyGi. Nega- represent the uncorrected time series of north±south tive values indicate subsidence. The locations of the tidal stations and vertical components, respectively. We clearly are shown in Fig. 4 find that the scatter of the vertical component is No. Location TiŽ.Ž.Ž. mmryr Gi mmryr Vi mmryr larger than that of horizontal component. Fig. 2Ž. b 1 Onisaki y0.80 4.03 y4.83 andŽ. e show north±south and vertical components 2 Owase 1.60 0.54 1.06 y of annual change, respectively. The annual change D 3 Shirahama 2.30 7.79 10.09 4 Kainan 1.90 y8.01 9.91 can be expressed as the following form: 5 Sumoto y3.70 y5.80 2.10 6 Uno y5.70 7.17 y12.87 s y q y y y D A sinv Ž.t t01B sin2v Ž.t t Ž.1 7 Komatsujima 1.60 16.09 17.69 8 Muroto-misaki y4.10 7.14 y11.24 Ž. y where A, B are amplitudes for annual and semi-an- 9 Kochi gsi 3.50 11.17 7.67 10 Tosakure 5.90 13.57 y7.67 nual changes, respectively, and v is angular fre- 11 Tosashimizu 0.00 9.17 y9.17 y y quency for annual changes. t01, t are phases of 12 Kure 1.40 7.30 8.70 annual and semi-annual changes, respectively. Fig. 13 Tokuyama y1.30 7.48 y8.78 2Ž. c and Ž. f are north-south and vertical components 14 Matsuyama 0.80 7.30 y6.50 y of corrected time series, respectively, excluding the 15 Oita 0.50 10.79 10.29 16 Akune 3.10 y3.02 6.12 calculated annual changes. 17 Misumi 0.40 7.39 y6.99 The horizontal components of displacement rates 18 Hakata 0.80 7.32 y6.52 of the GPS obtained by GSI show movements rela- 19 Shimonoseki 1.30 7.03 y5.73 tive to the TSKB stationŽ latitude 36.1038N, longi- 20 Hagi 0.00 7.48 y7.48 y tude 140.0888E. . Since it is difficult to estimate 21 Sakai 0.50 7.59 7.09 22 Maizuru y1.30 y6.47 5.17 accurate interplate coupling from these data, we Average 0.12 4.89 y4.76 converted the GPS data into plate motion relative to 22 T. Ito et al.rPhysics of the Earth and Planetary Interiors 115() 1999 17±34 sociated with the 1996 Hyuganada earthquakesŽ Oc- Ž.y0.0928rMyr of the AM plate relative to the EU tober 19Ž.Ž M 6.6, depth 39 km , December 3 M 6.6, plateŽ. Heki et al., 1998 , which were determined depth 35 km.. and the 1997 Kagoshimaken±Hoku- based on GPS observation. Here, we investigated the seibu earthquakesŽŽ March 26 M 6.3, depth 8 km . , case for which the southern boundary of the AM May 13Ž.. M 6.2, depth 8 km , which occurred during plate is located along the MTL in Kyushu and the observation period, were removed. From the Shikoku districts. In the Kinki district, we assumed figure, large movements can be seen at the stations that the boundary is along the Arima±Takatsuki on the Pacific coast side, and the amount of the tectonic line, referring to Hashimoto and Jackson movement decreases farther inland. The direction is Ž.1993 . The area to the north of this boundary is oriented nearly northwestward except for the stations regarded as the AM plate. Fig. 3 represents horizon- in Kyushu. In the Chugoku district, however, the tal displacement rates that were obtained correcting eastward component is dominant, suggesting east- the eastward motion of the AM plate. Comparing ward motion of the AM plate relative to the EU Fig. 1 with Fig. 3, we find that the EW component plate. Therefore, we removed the plate motion, using of the displacement rates is nearly zero in the the Euler poleŽ. 218S, 1088E and rotation rate Chugoku district.

Fig. 4. Absolute vertical displacement rates with confidence ellipses of 1s 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 squaresŽ. see Table 1 . The upward and downward vectors represent uplift and subsidence, respectively. T. Ito et al.rPhysics of the Earth and Planetary Interiors 115() 1999 17±34 23

The vertical component of the GPS data also the tidal station i, Dh is the correction which should shows movement relative to the TSKB station. Here, be added to all the GPS stations. We used the data at we attempt to estimate absolute vertical displacement 22 tidal stations and obtained Dhsy4.76 mmryr rate at each GPS station, which is necessary to Ž.Table 1 . estimate accurate back-slip distribution, using tidal Fig. 4 shows the obtained absolute vertical rates records. Here, we regarded the sea level as an abso- at all the GPS stations, together with the locations of lute standard, assuming that eustatic movement is the used tidal stations. Although we find that most of negligible. We assumed that the absolute vertical rate the GPS stations tend to subside, vertical movements at each tidal station in southwest Japan during the reflecting subduction of the PH plateŽ e.g., Yoshioka period from 1951 to 1987 estimated by KatoŽ. 1989 et al., 1993, 1994. cannot be clearly seen in the had been continuing for the observation period of the figure. As can be seen in Figs. 1 and 4, the accuracy GPS data. Since KatoŽ. 1989 calculated absolute of the GPS data of the horizontal movements is vertical rates based on the data of 30 years, we much better than that of vertical movements. 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: s y yD 2 3. Back-slip model and method of analysis E Ý Ž.TiiŽ.G h Ž.2 i where Tiiis absolute vertical rate at tidal station i, G In this section, we briefly describe the model used is observed vertical rate at the GPS station nearest to in this analysis, following Yoshioka et al.Ž 1993,

Fig. 5.Ž. a Schematic illustration showing the back-slip model. The effects of locking at an intermediate depthŽ. left can be represented by the superposition of the effects of a uniform steady slip over the whole plate boundaryŽ. right top and a back slip at the intermediate depth Ž.Žright bottom modified from Yoshioka et al., 1993 .Ž. . b The forward-slip model. 24 T. Ito et al.rPhysics of the Earth and Planetary Interiors 115() 1999 17±34

1994. . Strain accumulation is considered to be caused other is the state to give back slip in the locked by interaction between the subducting PH plate and regionŽ. Savage, 1983 . Assuming that we can disre- the overlying continental plate. The situation is gard the former situation because surface deforma- schematically illustrated in Fig. 5. Interplate cou- tion produced by the former has long wavelength pling proceeds at the locked region along the plate and its amplitude is small, the present state of stress boundary. On the other hand, decoupling is dominant accumulation can be approximately expressed by along shallower and deeper portions of the plate giving the back slip in the locked region. On the boundary because of high pore pressure due to the other hand, stress release is represented by forward existence of water and low viscosity due to high slip, whose slip direction is opposite that of the back temperature, respectively. As a result, steady slip slip. The application of the two-dimensional back-slip takes place at the shallower and the deeper portions, model by SavageŽ. 1983 to a three-dimensional case and tectonic stress accumulates in the locked region. has already been done by Yoshioka et al.Ž 1993, Such a situation can be divided into two situations 1994.Ž. and Sagiya 1995 . geometrically. One is the state that uniform steady In this study, we attempted to obtain spatial distri- slip proceeds over the whole plate boundary. The bution of the magnitude of back slip and the direc-

Fig. 6. Iso-depth contoursŽ. in km of the upper boundary of the Philippine Sea plate subducting beneath southwest Japan. The contour interval is 5 km. T. Ito et al.rPhysics 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 reliabilityŽ. the ratio of the obtained back slip to estimation error is less than four are shaded.

tion of relative plate motion through inversion analy- where dijare observed surface displacements, a are sisŽ. Yabuki and Matsu'ura, 1992 , using displace- coefficients of superposing basis functionsŽ model ment rates of GPS data in southwest Japan. parameters. , eiijare random errors, and A are elas- On the model source region where back slip or tic response at a point i to a unit slip at a point j on forward slip is given, we express spatial distribution the model source region. The response function Aij of moment tensor corresponding to slip by superpos- can be calculated by dislocation theory in a semi-in- ing basis functionsŽ. bi-cubic B-spline functions . finite homogeneous perfect elastic bodyŽ Maruyama, Here, we can express observation equations with N 1964.Ž . The more detailed form is given in Yabuki observation data as: and Matsu'ura, 1992. . Our purpose is to find the model parameters as the best solution, and to esti- s q s diijjiÝ Aa eiŽ.Ž.1,...,N 3 mate the back-slip distribution on the model source j region. Here, we consider the likelihood function of 26 T. Ito et al.rPhysics of the Earth and Planetary Interiors 115() 1999 17±34

2 aji. Assuming that the error e to be NŽ 0,s E., the some degree. Here, we can denote the probability likelihood function pdaŽ < ;s 2 . of the model parame- density function qaŽ.;r with a hyper-parameter r 2 ter aj can be expressed as: that controls the roughness of the slip distribution as: y r <55s 22s ps N 2 y1r2 pdaŽ.; Ž.2 E yKr2 r 1 qaŽ.;r s Ž.2pr2 55 L 1 2exp y aWat 1 K 2 r 2 =exp y Ž.dyAa t 2s 2 Ž.5

y =Ed1 Ž.yAa Ž.4 where W is a symmetric matrix, whose concrete expression is given inŽ. Yabuki and Matsu'ura, 1992 . 55 55 where E denotes the absolute value of the determi- K is the rank of the matrix W, and LK is the 2 nant of E, and s is unknown covariance for ei. absolute value of the product of non-zero eigenval- On the other hand, the back-slip distribution has a ues. We can estimate the back-slip distribution on prior information that the distribution is smooth to the model source region, combining the prior infor-

Fig. 8. Displacement rates at each GPS station calculated from the inverted back-slip distributionŽ. thick arrows and the observed displacement ratesŽ.Ž. thin arrows . a Horizontal displacement rates. Ž. b Vertical displacement rates. T. Ito et al.rPhysics of the Earth and Planetary Interiors 115() 1999 17±34 27

Fig. 8Ž. continued .

mation with the observation Eq.Ž. 3 . Here, we united with: the likelihood function from the data distribution of SaŽ.;s 2 ,r 2 Eq.Ž. 4 with the probability density function from the Ž. 1 t y prior information of Eq. 5 by using Bayes' theo- s Ž.Ž.dyAa E1 dyAa rem. The Bayesian model is highly flexible with the 2s 2 two hyper-parameters, s 2 and r 2. We can represent 1 the model as: q aWat .7Ž. 2 r 2 To find the best estimates of the two hyper- la;s 22,r d Ž. parameters, we used ABIC proposed by Akaike Ž.1980 on the basis of the entropy maximization s psryŽ.NqK r2 yN yK 55y1r21 5L 5r2 Ž.2 E K principle. It is a criterion to minimize the influence of the error included in the data and to derive hidden = y s 22r exp SaŽ.; , Ž.6 information to its maximum, in order to determine 28 T. Ito et al.rPhysics of the Earth and Planetary Interiors 115() 1999 17±34 the hyper-parameters uniquely, which represent the region is assumed to be semi-fixed, reducing num- degree of smoothness of the slip distribution. Once bers of bi-cubic B-spline functions which express we have determined the two hyper-parameters, s 2 distribution of slip rate on the model source regions. and r 2, we can calculate the model parameter a.We Therefore, stress concentration, which appears near can represent the solution for the model parameter aÃ, the edge of the model source regions for conven- using a 2 which is defined by s 2rr 2 as: tional uniform slip model, is suppressed considerably in this study. y1 aÃs Ž.AEt y12 Aqa AEt y1 d.8 Ž.In this study, we deduced 772 model parameters from the 247 horizontal and 237 vertical displacement rates of the GPS data, and determined the As a result, we can determine the back-slip distribu- spatial distribution of slip rate. We excluded 10 tion objectively and uniquely on the plate boundary, vertical data from the data set because the observa- that is, the amount of interplate coupling and the tion errors of the 10 data are anomalously large, and direction of relative plate motion. The covariance for because considering that data with large observation the model parameter aÃ is given by: errors are not so important in our inversion analysis

y in which weight of the errors are considered. In this y 1 CssÃÃ2 Ž.AEt 12 Aqa W Ž.9 study, we carried out inversion analysis for both horizontal and vertical displacement rates, consider- where sÃ 2 is the best estimate of s 2. We can obtain ing weight of confidence ellipse of 1s for the the estimation error of each slip on the model source respective components at each GPS station. As we region from Eq.Ž. 9 . The optimal value of a which described before, the accuracy of the GPS data of the minimizes ABIC in this study was estimated to be horizontal movements is much better than that of 0.15, which is relatively small. From the definition vertical movements. of a 2 ŽŽ.Ž..see also Eqs. 6 and 7 , large value of a 2 For the model source region off Shikoku to Kii indicates smooth distribution of back slip and for- peninsula, we carried out inversion analysis, giving ward slip. the constraint that the direction of back slip is within In this study, we constructed the model source "458 of the direction of plate motion of the PH region on the three-dimensional upper surface of the plate relative to the EU plateŽ. Seno et al., 1993 , subducting PH plate obtained from spatial distribu- using non-negative least-squaresŽ. NNLS by Lawson tion of microearthquakesŽ. Satake, 1993 , whose strike and HansonŽ. 1974 . direction is taken almost parallel to the axis of the NankaiŽ. Fig. 6 . Since the trough axis changes its direction abruptly in the region between Kyushu and Shikoku, we separated the model source regions into 4. Results two parts. Since outside of the model source region is assumed to be completely decoupled in this analysis, we constructed relatively large model source 4.1. Slip distributions on the model source regions regions. The sizes of the model source regions off southeast of Kyushu and Shikoku to Kii peninsula Fig. 7 represents distributions of slip rate on the were taken to be 180 km=200 km and 140 km=400 model source regions between the PH plate and the km, respectively. We divided the respective model continental plate obtained from inversion analysis source regions into 9=10 and 7=20 subsections, based on the GPS data of the crustal movements and distributed 12=13 and 10=23 basis functions Ž.Figs. 3 and 4 . so as to cover the respective whole regions homoge- In the model source region off Shikoku to Kii neously. The distribution of slip rate on the model peninsula the average back-slip rate is 4.0 cmryr for source region is represented by the superposition of the area with back slips greater than 3.0 cmryr, the bi-cubic B-spline functions with various ampli- where interplate coupling appears to be strong. This tudes. The boundary condition for the model source corresponds well to the coseismic slip regions at the T. Ito et al.rPhysics of the Earth and Planetary Interiors 115() 1999 17±34 29 time of the 1944 TonankaiŽ. M 7.9 and the 1946 model source region calculated from Eq.Ž. 9 , is also NankaiŽ. M 8.0 earthquakes Ž Sagiya and Thatcher, shown. Reliability is low from the eastern part of 1999. . A weakly coupled region that separates these Shikoku to the west of Kii peninsula, including the large back-slip regions is located beneath the Kii region beneath the Kii channel. The low reliability is channel and its southern extensional region. probably due to the large distance between the model The average direction of the back slip was ob- source region and the GPS stations: the model source tained as N538W"118 for the model source region region deepens abruptly beneath the Kii channel, and off Shikoku to Kii peninsula. The direction differs by no GPS stations exist there. 48 from the direction of plate motion of the PH plate We also calculated distribution of slip rate on relative to the EU plateŽ.Ž N498W Seno et al., 1993 .different model source regions so as to fill the gap On the other hand, we find large forward slip, between the two source regions in the present analy- reaching 11 cmryr, on the model source region sis. However, we hardly found a difference in distri- southeast off Kyushu. bution of slip rate on the original model source In Fig. 7, reliability, which is defined by the ratio regions. From these considerations, we may say that of the obtained back slip to estimation error on the 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.rPhysics of the Earth and Planetary Interiors 115() 1999 17±34

4.2. Surface displacement rates calculated from the ward components as compared to those in the north- inÕerted back-slip distribution ern region. The observation errors are large there, and we accordingly weighted the errors when we Fig. 8Ž. a and Ž. b , respectively, represent horizon- carried out inversion analysis. For these reasons, the tal and vertical displacement rates at each GPS sta- fitting of horizontal movements between observation tion calculated from the inverted back-slip distribu- and calculation is considered to be poor. In the tion, together with the observed displacement rates. western part of Shikoku, the cause of the difference Concerning the horizontal movement, we find that is probably due to large spatial variation of the most of the observed displacement rates are well directions of the observed horizontal movement. In explained by our model, except in the southern part the Chubu district, since there exists westward dis- of Kyushu, the western part of Shikoku, and the placement rates with comparable magnitude in the Chubu district. In the southern part of Kyushu, the inland region away from the eastern model source observed horizontal displacement rates have south- 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 reliabilityŽ. the ratio of the obtained back slip to estimation error is less than four are shaded. T. Ito et al.rPhysics of the Earth and Planetary Interiors 115() 1999 17±34 31 well. Therefore, the crustal movement in this region thermal model. In the south of the model source is considered to be caused by tectonic stresses other region, the Kinan seamount chain is ranging in the than subduction of the PH plate. NS direction on the Shikoku basin. The subduction Vertical movement is poorly fit in all regions. The of such seamounts might be related to weak inter- reason is that the errors of the observation data of plate coupling in this regionŽ. Yoshioka, 1991 . The vertical movement are several times as large as those relation between seamounts and interplate coupling of the horizontal movementŽ. Figs. 1 and 4 , and we is discussed by Zhao et al.Ž. 1997 , in which the weighted the observation errors accordingly in the morphology of the upper surface of the subducting inversion analysis. Pacific plate beneath the Japanese islands was estimated using SP and sP converted waves at the upper 4.3. Slip distributions obtained from baseline length boundary of the slab. The subducting seamounts changes have kept roughly their original shapes probably because the seamounts are stronger and less de- Until Section 4.2, we have discussed slip distribu- formable than the inner slope materials, and are not tions obtained from the inversion of horizontal and scraped off at the trench so that the slab subducts at vertical displacement rates of GPS data. However, a steeper dip angle. Hence, the PH plate may subduct we have to consider effect of fixed point for the with steeper dip angle beneath the Kii channel than horizontal data. To solve this problem, we converted in other regions, corresponding to weak interplate the horizontal displacement rates of the GPS data to coupling. 666 baseline length changesŽ. Fig. 9 . For the data Moreover, we find that the amount of the back set, we carried out the similar inversion analysis. In slip becomes very small at depths deeper than about this case, we also found that interplate coupling 30 to 40 km on the model source region, indicating becomes weak at depths deeper than about 40 km weak interplate coupling there. This is probably due beneath the Shikoku and Kii peninsulaŽ. Fig. 10 . The to ductile characteristics and flow of rocks due to the direction of average back slips is oriented N538W" high temperature there. This depth is shallower than 38, which is close to the direction predicted from the the depth of 60 km estimated from experimental plate motion model by Seno et al.Ž. 1993 . On the studies of rock rheology in northeast Japan other hand, no slip occurs in the southeast off Kyushu Ž.Shimamoto, 1990 . Combining a rheological model, where reliability is fairly low. which is represented by single crystal of olivine and plagioclase, with the thermal structure of the subduction zone, ShimamotoŽ. 1989 suggested the depth of 5. Discussion transition from brittle or plastic deformation to ductile deformation to be about 60 km in northeast Our inversion analysis indicates the strong cou- Japan. The difference in the depths in northeast and pling between the PH and the continental plates in southwest Japan could be caused by the fact that the the model region off Shikoku to Kii peninsulaŽ Figs. PH plate in southwest Japan is younger and warmer 7 and 10. . The strongly coupled region has been than the Pacific plate, which is subducting beneath suggested by Hyndman et al.Ž. 1995 in which a northeast Japan, as suggested by previous studies transient thermal model using the finite element Ž.e.g., Yoshioka, 1991 . method was constructedŽ. Hyndman and Wang, 1993 . On the other hand, on the basis of the idea that Their model allows comparison of the thermally the Nankai trough is the southern limit of the AM estimated downdip extent of the seismogenic zone plate, we carried out a similar inversion analysis, with that from seismicity, tsunami data and the after making necessary corrections for the horizontal crustal deformation data in the Nankai subduction GPS data. As a result, we obtained N778W"148 as zone. The locked zone by Hyndman et al.Ž. 1995 the direction of the average back slip, which is corresponds well with the large back-slip region different from the direction of Seno et al.Ž. 1993 by obtained in this study. This result indicates that the 288. Comparing this with the result obtained assum- geodetically obtained result is consistent with the ing that the southern boundary of the AM plate is 32 T. Ito et al.rPhysics of the Earth and Planetary Interiors 115() 1999 17±34 along the MTL, the latter is closer to the results of 6. Conclusions the plate motion model by Seno et al.Ž. 1993 in terms of the direction of the average back slip. In this study, we calculated the distribution of Therefore, we conclude that the idea that the MTL is interseismic slip rate on the plate boundary between the southern boundary of the AM plate is preferable, the subducting Philippine Sea plate and the continen- based on our inversion of the GPS data. tal plate in southwest Japan, based on the displace- We also estimated recurrence times of the To- ment rates obtained from the continuous GPS obser- nankai and the Nankai earthquakes from the results vations by the Geographical Survey Institute of Japan. of the model source region off Shikoku to Kii penin- The obtained results are as follows. sula. The amount of the average coseismic slip on Ž.1 We found back slip of more than 3 cmryr on the model source region was estimated to be 342 cm the model source regions off Shikoku and Kumanon- from the result of inversion analysis of coseismic ada, indicating strong interplate coupling. These cor- geodetic data associated with the 1944 Tonankai and respond well to the large coseismic slip areas of the the 1946 Nankai earthquakesŽ Sagiya and Thatcher, 1946 NankaiŽ. M 8.0 and the 1944 Tonankai Ž. M 7.9 1999. . On the other hand, the amount of the average earthquakes, respectively. Weak interplate coupling back slip on the corresponding region obtained in can be found in the region beneath off Kii channel this study is 3.2 cmryr. Dividing the amount of the and in the region deeper than about 30 to 40 km. average coseismic slip by that of the back slip, the Ž.2 We estimated the recurrence time of the recurrence time of the trench-type great earthquakes trench-type great earthquakes along the Nankai that have occurred at the Nankai trough is roughly trough to be about 107 years from coseismic slip and estimated as 107 years, consistent with the recur- back slip obtained from inversion analyses of the rence interval of 90 to 150 years in this regionŽ e.g., coseismic crustal deformations associated with the Ando, 1975; Shimazaki and Nakata, 1980; Thatcher, Nankai and the Tonankai earthquakes, and the GPS 1984. . data in this study, respectively. The recurrence time Large forward slip was found on the model source is consistent with the results obtained in the previous region southeast off Kyushu for the inversion of the studies. horizontal displacement rates. Since the forward slip Ž.3 The average direction of the back slip is appears in spite of the removal of the coseismic N538W on the model source region off Shikoku to crustal deformations associated with the two 1996 Kii peninsula, which is concordant with the direction Hyuganada earthquakesŽŽ. October M 6.6 , December of N498W from the plate motion model by Seno et Ž..M 6.6 from the GPS data, a possible explanation al.Ž. 1993 . of the forward slip might be after-slip of the Hyu- Ž.4 In the Hyuganada region off southeast of ganada earthquakes. However, horizontal displace- Kyushu, although we excluded coseismic crustal de- ment rates of GPS observation before the 1996 Hyu- formations associated with the 1996 Hyuganada ganada earthquakes had already shown southeast- earthquakesŽŽ. October M 6.6 , December Ž.. M 6.6 ward movements in KyushuŽ Geographical Survey and the 1997 Satsuma earthquakesŽŽ. March M 6.3 , Institute, 1996. . Also, no slip can be found on the MayŽ.. M 6.2 , we obtained large forward slip from model source region southeast off Kyushu for the inversion analysis of the horizontal and vertical dis- inversion of rates of the baseline length changes. placement rates. The forward slip corresponds to the These indicate that deformation of Kyushu dose not process of stress release, indicating after-slip in the behave like an elastic body but a rigid body. There- vicinity of the coseismic slip region of these events. fore, the NS oriented extension in Kyushu associated However, from the inversion using baseline length with the expansion of the Okinawa troughŽ Shiono et changes, we found that no slips can be seen in the al., 1980; Tada, 1980. andror southeastward drag of southeast off Kyushu. These indicates that deforma- Kyushu due to the upwelling of mantle material tion of Kyushu does not behave like an elastic body beneath the East China SeaŽ. e.g., Seno, 1998 may but a rigid body. The N±S oriented extension in be the cause of the southeastward displacement rates Kyushu associated with expansion of the Okinawa in Kyushu. trough andror southeastward drag of Kyushu due to T. Ito et al.rPhysics of the Earth and Planetary Interiors 115() 1999 17±34 33 the upwelling of mantle material beneath the East Heki, K., 1996. Horizontal and vertical movements from three-di- China Sea may be a preferable cause of the south- mensional very long baseline interferometry kinematic refer- eastward horizontal displacement rates in Kyushu. ence frame: implication for the reversal timescale revision. J. Geophys. Res. 101, 3187±3198. Ž.5 We inverted the GPS data for two cases, Heki, K., Miyazaki, S., Takahashi, H., Kasahara, M., Kimata, F., assuming that the southern boundary of the Amurian Miura, S., Seno, T., Vasilenko, N., Ivashchenko, A., Korcha- plate is located along the Median Tectonic Line and gin, F., An, G., 1998. Re-determination of the movement of the Nankai trough. Comparing the two cases, the the Amurian plate. Program and Abstracts of the Seismologi- former is closer to the results of the plate motion cal Society of Japan 1998, fall meeting, C28, in Japanese. Hyndman, F.D., Wang, K., 1993. Thermal constraints on the zone model than the latter in terms of the direction of the of major thrust earthquake failure: the Cascadia subduction average back slip. Therefore, the idea that the Me- zone. J. Geophys. Res. 98Ž. B2 , 2039±2060. dian Tectonic Line is the southern boundary of the Hyndman, F.D., Wang, K., Yamano, M., 1995. Thermal con- Amurian plate is preferable from our inversion anal- straints on the seismogenic portion of the southwestern Japan subduction thrust. J. Geophys. Res. 100, 15373±15392. ysis of the GPS data. Ishibashi, K., 1995. The 1995 Hyogo±Ken Nanbu earthquake and seismic activity in large area, considering Eastern deforming margin of the Amurian plateŽ. preliminary report . 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