interplate coupling in southwest japan deduced from...

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

Interplate coupling in southwest Japan deduced from inversionanalysis 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, Fukuoka812-8581, 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 networkin Japan, which has enabled us to investigate real-time crustal movements. In this study, we attempt to obtain spatialdistribution 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 fromApril 6, 1996 to March 20, 1998. For this purpose, we carried out an inversion analysis of geodetic data, incorporating

Ž .Akaike’s Bayesian Information Criterion ABIC . As a result, strong interplate coupling was found off Shikoku andŽ . ŽKumanonada regions, which corresponds well with the fault regions of the 1946 Nankai M 8.1 and the 1944 Tonankai M

.8.0 earthquakes, respectively. We also found that interplate coupling becomes weak at depths deeper than about 30 to 40km beneath the Shikoku and Kii peninsula. The recurrence time of great trench-type earthquakes was roughly estimated as107 years, which is consistent with previous research. The direction of relative plate motion is oriented N538W, which isclose to the direction predicted from the plate motion model. On the other hand, a large forward slip was found in theHyuganada region off southeast of Kyushu. Since the coseismic displacements associated with the two 1996 Hyuganada

Ž .earthquakes M 6.6, M 6.6 are removed from the GPS data, this suggests that after-slip occurred near the source regionandror that Kyushu moves southeastward stationarily due to other tectonic forces. q 1999 Elsevier Science B.V. All rightsreserved.

Keywords: GPS; Back slip; Interplate coupling; Relative plate motion; Forward slip

1. Introduction

Southwest Japan is the region where the AmurianŽ . Ž Ž . .AM plate or the Eurasia EU plate , the Philip-

Ž . Ž . Žpine Sea PH plate, and the Okhotsk OK plate or

) Corresponding author. Tel.: q81-92-642-2647; fax: q81-92-642-2684; E-mail: [email protected]

Ž . .the North American NA plate interact with eachŽ .other Fig. 1 . The plate motion in southwest Japan,

especially the eastward motion of the AM plate hasŽbeen debated by many researchers e.g., Zonenshain

and Savostin, 1981; Kimura et al., 1986; Tsukuda,.1992; Ishibashi, 1995 . There are two theories con-

cerning the location of the southern boundary of theAM plate: one places it along the Median Tectonic

0031-9201r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved.Ž .PII: S0031-9201 99 00063-1

( )T. Ito et al.rPhysics of the Earth and Planetary Interiors 115 1999 17–3418

Fig. 1. Map showing horizontal displacement rates relative to the stationary part of the Eurasian plate with confidence ellipses of 1s at 247GPS stations in southwest Japan during the period from April 6, 1996 to March 20, 1998. Coseismic crustal deformations associated with

Ž Ž . Ž .. Ž Ž .the 1996 Hyuganada earthquakes October M 6.6 , December M 6.6 and the 1997 Kagoshima–Hokuseibu earthquakes March M 6.3 ,Ž ..May M 6.2 , which occurred during the observation period, were removed. The epicenters of the four events are shown with star symbols.

Ž . ŽThe inset shows four plates in and around the Japanese islands. AMsAmurian Plate or EUsEurasia plate ; OKsOkhotsk plate or.NAsNorth American plate ; PAsPacific plate; PHsPhilippine Sea Plate.

Ž .Line MTL , and the other places it along the Nankaitrough. Geophysical exploration of underground

Žstructure beneath the MTL Yoshikawa et al., 1992;.Yuki et al., 1992; Ito et al., 1996 and fault simula-

tion using strain data obtained by Geographical Sur-Ž . Žvey Institute GSI of Japan Hashimoto and Jack-

.son, 1993 have been conducted. However, we havenot arrived at a conclusion to determine a preferredtheory. Moreover, the spatial pattern of tectoniccrustal movement in southwest Japan is complicateddue to elastic strain accumulation and release associ-

ated with the subduction of the PH plate along theŽNankai trough e.g., Thatcher, 1984; Savage and

.Thatcher, 1992; Tabei et al., 1996 .Great interplate earthquakes have occurred repeat-

edly along the Nankai trough, with recurrence inter-Žval of about 90 to 150 years e.g., Shimazaki and.Nakata, 1980; Thatcher, 1984 . The most recentŽ .events were the 1944 Tonankai M 7.9 and the 1946

Ž .Nankai M 8.0 earthquakes. It is believed that theseevents released accumulated stress in association withthe 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-tion of the two earthquakes, using geodetic data,

Žseismic waves and tsunami data e.g., Fitch andScholz, 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 inter-

seismic interplate coupling using geodetic data. InŽ .southwest Japan, Yoshioka 1991 investigated spa-

tial distribution of the strength of interplate couplingalong the Nankai trough, based on leveling, tidegauge, and trilateration data, using a three-dimensionfinite element method. However, the results wereobtained using forward modeling, and the model wasnot satisfactory to evaluate the spatial distribution ofinterplate coupling objectively. Later, the strength of

interplate coupling and the direction of relative platemotion were estimated more objectively through in-version analysis of leveling and trilateration data inthe Kanto–Tokai districts and southwest JapanŽ .Yoshioka et al., 1993, 1994; Sagiya, 1995 . Duringthe last several years, the Geographical Survey Insti-

Ž .tute of Japan GSI has installed and maintained GPScontinuous observation networks throughout the

Ž .country. Recently, Nishimura et al. 1998 estimatedinterplate coupling in southwest Japan, using hori-zontal displacement rates of GPS data, on the basisof the least squares method. However, since theiranalysis is based on forward modeling, the obtainedresults cannot be evaluated objectively as well.

In this study, we attempt to obtain interplatecoupling, using an inversion analysis for continuous

Ž .Fig. 2. An example of the time series obtained at the CHIYODA station latitude 34.6778N, longitude 140.0888E . Vertical and horizontalŽ . Ž . Ž . Ž .axes represent displacement mm and time year , respectively. a Uncorrected time series of north–south component. b Annual changeŽ . Ž .of north–south component. c Difference between uncorrected time series and annual change of north–south component. d Uncorrected

Ž . Ž .time series of vertical component. e Annual change of vertical component. f Difference between uncorrected time series and annualchange of vertical component.


GPS data obtained in southwest Japan. The real-timeobservations have enabled us to reveal detailed crustalmovement in southwestern Japan, elucidating east-ward motion of the AM plate. We used data of 247horizontal and 237 vertical displacement rates fromApril 6, 1996 to March 20, 1998. The purpose of thisstudy is to obtain the direction of relative platemotion and the spatial distribution of the strength ofinterplate coupling on the plate boundary betweenthe subducting PH plate and the overriding continen-tal plate through inversion analysis, using Akaike’s

Ž . ŽBayesian Information Criterion ABIC Yabuki and.Matsu’ura, 1992 .

2. GPS data and their correction

We employed Bernese version 4 software foranalysis of GPS data. We used International GPS

Ž .Service for Geodynamics IGS final orbits for satel-lite information and International Earth Rotation Ser-

Ž .vice IERS bulletin B for Earth rotation parameters.Only the TSKB station, which is one of the IGSglobal sites in the GSI campus in Tsukuba, is usedfor the tie with IGS global site because we adopted adistributed strategy. We resolved ambiguities by the

Žsigma dependent strategy e.g., Rothacher and Mer-.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 theboundary along the Median Tectonic Line, Arima–Takatsuki Tectonic Line, and the western part of Lake Biwa is regarded as the AM plate.

Ž .We corrected the movement in this area as the motion of rigid body based on Euler vector 218S, 1088E, vsy0.0928rMyr by Heki et al.Ž .1998 .


Ž .ITRF International Terrestrial Reference Frame .Ž .Following Heki et al. 1998 , we obtained the crustal

velocity field relative to the EU plate by subtractingits absolute motion from ITRF velocities for eachsite because the kinematic part of ITRF94 is nnr-

ŽNUVEL1a plate motion model Argus and Gordon,.1991 .

The horizontal displacement rates were calculatedŽ .by a least-square approach Miyazaki et al., 1998 .

We did not use the full covariance information be-cause the computation time is unrealistic. The scaleof the formal error written in the digit file is 1s . Theroot-mean-square is 3 mm on average, but some siteswhich had episodic displacement or transient defor-mation have larger values, reaching 7 mm.

We excluded annual change of the data accordingŽ .to the method proposed by Miyazaki et al. 1998 .

They modeled time series as a linear combination ofconstant, linear term, trigonometric function whoseperiod is 1 year, and jumps for episodic events. Oneproblem is that we did not estimate postseismicdeformation because it strongly couples with annualvariations. Fig. 2 shows an example of the time

Žseries obtained at the CHIYODA site latitude. Ž . Ž .34.6778N, longitude 140.0888E . Fig. 2 a and d

represent the uncorrected time series of north–southand vertical components, respectively. We clearlyfind that the scatter of the vertical component is

Ž .larger than that of horizontal component. Fig. 2 bŽ .and e show north–south and vertical components

of annual change, respectively. The annual change Dcan be expressed as the following form:

DsA sinv ty t qB sin2v ty t 1Ž . Ž . Ž .0 1

where A, B are amplitudes for annual and semi-an-nual changes, respectively, and v is angular fre-quency for annual changes. t , t are phases of0 1

annual and semi-annual changes, respectively. Fig.Ž . Ž .2 c and f are north-south and vertical components

of corrected time series, respectively, excluding thecalculated annual changes.

The horizontal components of displacement ratesof the GPS obtained by GSI show movements rela-

Žtive to the TSKB station latitude 36.1038N, longi-.tude 140.0888E . Since it is difficult to estimate

accurate interplate coupling from these data, weconverted the GPS data into plate motion relative to

the stationary part of the EU plate. According toŽ .Heki 1996 , the horizontal movement of the TSKB

station relative to the stationary part of the EU plateis 2.7 mmryr to the north and 20.5 mmryr to thewest. The result was obtained so as to minimize thedifference in the horizontal displacement rates be-

Ž .tween the Very Long Baseline Interferometry VLBIobservations and the model predictions by applying asmall translation and rotation for the entire network.Therefore, as a first approximation, the addition ofthis correction to the horizontal displacement rates atall observation stations enables us to obtain platemotion of southwest Japan relative to the stationarypart of the EU plate.

Fig. 1 shows horizontal displacement rates rela-tive to the stationary part of the EU plate withconfidence ellipses of 1s at all GPS stations insouthwest Japan. Coseismic crustal deformations as-

Table 1Displacement rates of vertical component at 22 tidal stations.Ti: absolute uplift rates at tidal stations deduced from tidal records

Ž .during the period from 1951 to 1987 Kato, 1989 . Gi: uplift ratesat GPS stations nearest to the tidal stations. VisTiyGi. Nega-tive values indicate subsidence. The locations of the tidal stationsare shown in Fig. 4

Ž . Ž . Ž .No. Location Ti mmryr Gi mmryr Vi mmryr

1 Onisaki y0.80 4.03 y4.832 Owase 1.60 0.54 1.063 Shirahama 2.30 y7.79 10.094 Kainan 1.90 y8.01 9.915 Sumoto y3.70 y5.80 2.106 Uno y5.70 7.17 y12.877 Komatsujima y1.60 16.09 y17.698 Muroto-misaki y4.10 7.14 y11.24

Ž .9 Kochi gsi 3.50 11.17 y7.6710 Tosakure 5.90 13.57 y7.6711 Tosashimizu 0.00 9.17 y9.1712 Kure y1.40 7.30 y8.7013 Tokuyama y1.30 7.48 y8.7814 Matsuyama 0.80 7.30 y6.5015 Oita 0.50 10.79 y10.2916 Akune 3.10 y3.02 6.1217 Misumi 0.40 7.39 y6.9918 Hakata 0.80 7.32 y6.5219 Shimonoseki 1.30 7.03 y5.7320 Hagi 0.00 7.48 y7.4821 Sakai 0.50 7.59 y7.0922 Maizuru y1.30 y6.47 5.17

Average 0.12 4.89 y4.76


Žsociated with the 1996 Hyuganada earthquakes Oc-Ž . Žtober 19 M 6.6, depth 39 km , December 3 M 6.6,

..depth 35 km and the 1997 Kagoshimaken–Hoku-Ž Ž .seibu earthquakes March 26 M 6.3, depth 8 km ,

Ž ..May 13 M 6.2, depth 8 km , which occurred duringthe observation period, were removed. From thefigure, large movements can be seen at the stationson the Pacific coast side, and the amount of themovement decreases farther inland. The direction isoriented nearly northwestward except for the stationsin Kyushu. In the Chugoku district, however, theeastward component is dominant, suggesting east-ward motion of the AM plate relative to the EUplate. Therefore, we removed the plate motion, using

Ž .the Euler pole 218S, 1088E and rotation rate

Ž .y0.0928rMyr of the AM plate relative to the EUŽ .plate Heki et al., 1998 , which were determined

based on GPS observation. Here, we investigated thecase for which the southern boundary of the AMplate is located along the MTL in Kyushu andShikoku districts. In the Kinki district, we assumedthat the boundary is along the Arima–Takatsukitectonic line, referring to Hashimoto and JacksonŽ .1993 . The area to the north of this boundary isregarded as the AM plate. Fig. 3 represents horizon-tal displacement rates that were obtained correctingthe eastward motion of the AM plate. ComparingFig. 1 with Fig. 3, we find that the EW componentof the displacement rates is nearly zero in theChugoku district.

Fig. 4. Absolute vertical displacement rates with confidence ellipses of 1s at 237 GPS stations during the period from April 6, 1996 toŽ .March 20, 1998. The locations of 22 tidal stations are also shown with symbols of open squares see Table 1 . The upward and downward

vectors represent uplift and subsidence, respectively.


The vertical component of the GPS data alsoshows movement relative to the TSKB station. Here,we attempt to estimate absolute vertical displacementrate at each GPS station, which is necessary toestimate accurate back-slip distribution, using tidalrecords. Here, we regarded the sea level as an abso-lute standard, assuming that eustatic movement isnegligible. We assumed that the absolute vertical rateat each tidal station in southwest Japan during the

Ž .period from 1951 to 1987 estimated by Kato 1989had been continuing for the observation period of the

Ž .GPS data. Since Kato 1989 calculated absolutevertical rates based on the data of 30 years, weexcluded tidal stations where coseismic and post-seismic crustal deformations were evident during theperiod. We determined the amount of the correctionso as to minimize the following quantity E:

2Es T y G yDh 2Ž . Ž .Ž .Ý i i

i

where T is absolute vertical rate at tidal station i, Gi i

is observed vertical rate at the GPS station nearest to

the tidal station i, Dh is the correction which shouldbe added to all the GPS stations. We used the data at22 tidal stations and obtained Dhsy4.76 mmryrŽ .Table 1 .

Fig. 4 shows the obtained absolute vertical ratesat all the GPS stations, together with the locations ofthe used tidal stations. Although we find that most ofthe GPS stations tend to subside, vertical movements

Žreflecting subduction of the PH plate e.g., Yoshioka.et al., 1993, 1994 cannot be clearly seen in the

figure. As can be seen in Figs. 1 and 4, the accuracyof the GPS data of the horizontal movements ismuch better than that of vertical movements.

3. Back-slip model and method of analysis

In this section, we briefly describe the model usedŽin this analysis, following Yoshioka et al. 1993,

Ž . Ž .Fig. 5. a Schematic illustration showing the back-slip model. The effects of locking at an intermediate depth left can be represented byŽ .the superposition of the effects of a uniform steady slip over the whole plate boundary right top and a back slip at the intermediate depth

Ž . Ž . Ž .right bottom modified from Yoshioka et al., 1993 . b The forward-slip model.


.1994 . Strain accumulation is considered to be causedby interaction between the subducting PH plate andthe overlying continental plate. The situation isschematically illustrated in Fig. 5. Interplate cou-pling proceeds at the locked region along the plateboundary. On the other hand, decoupling is dominantalong shallower and deeper portions of the plateboundary because of high pore pressure due to theexistence of water and low viscosity due to hightemperature, respectively. As a result, steady sliptakes place at the shallower and the deeper portions,and tectonic stress accumulates in the locked region.Such a situation can be divided into two situationsgeometrically. One is the state that uniform steadyslip proceeds over the whole plate boundary. The

other is the state to give back slip in the lockedŽ .region Savage, 1983 . Assuming that we can disre-

gard the former situation because surface deforma-tion produced by the former has long wavelengthand its amplitude is small, the present state of stressaccumulation can be approximately expressed bygiving the back slip in the locked region. On theother hand, stress release is represented by forwardslip, whose slip direction is opposite that of the backslip. The application of the two-dimensional back-slip

Ž .model by Savage 1983 to a three-dimensional caseŽhas already been done by Yoshioka et al. 1993,

. Ž .1994 and Sagiya 1995 .In this study, we attempted to obtain spatial distri-

bution of the magnitude of back slip and the direc-

Ž .Fig. 6. Iso-depth contours in km of the upper boundary of the Philippine Sea plate subducting beneath southwest Japan. The contourinterval is 5 km.


Fig. 7. The spatial distribution of slip rates on the plate boundary, inverted from the displacement rates of the GPS data. The slip motion onthe overlying continental plate relative to the subducting Philippine Sea plate is shown. The contour lines denote the amount of back slip.

Ž .The contour interval is 1.0 cmryr. The areas with low reliability the ratio of the obtained back slip to estimation error is less than four areshaded.

tion of relative plate motion through inversion analy-Ž .sis Yabuki and Matsu’ura, 1992 , using displace-

ment rates of GPS data in southwest Japan.On the model source region where back slip or

forward slip is given, we express spatial distributionof moment tensor corresponding to slip by superpos-

Ž .ing basis functions bi-cubic B-spline functions .Here, we can express observation equations with Nobservation data as:

d s A a qe is1, . . . , N 3Ž . Ž .Ýi i j j ij

where d are observed surface displacements, a arei jŽcoefficients of superposing basis functions model

.parameters , e are random errors, and A are elas-i i j

tic response at a point i to a unit slip at a point j onthe model source region. The response function Ai j

can be calculated by dislocation theory in a semi-in-Žfinite homogeneous perfect elastic body Maruyama,

. Ž1964 . The more detailed form is given in Yabuki.and Matsu’ura, 1992 . Our purpose is to find the

model parameters as the best solution, and to esti-mate the back-slip distribution on the model sourceregion. Here, we consider the likelihood function of


Ž 2 .a . Assuming that the error e to be N 0,s E , thej iŽ < 2 .likelihood function p d a;s of the model parame-

ter a can be expressed as:j

yNr2 y1r22 2< 5 5p d a;s s 2ps EŽ .Ž .

=1 texp y dyAaŽ .22s

= y1E dyAa 4Ž . Ž .

5 5where E denotes the absolute value of the determi-nant of E, and s 2 is unknown covariance for e .i

On the other hand, the back-slip distribution has aprior information that the distribution is smooth to

some degree. Here, we can denote the probabilityŽ . 2density function q a;r with a hyper-parameter r

that controls the roughness of the slip distribution as:

1yKr2 1r22 t5 5q a;r s 2pr L exp y a WaŽ . Ž . K 22 r

5Ž .

where W is a symmetric matrix, whose concreteŽ .expression is given in Yabuki and Matsu’ura, 1992 .

5 5K is the rank of the matrix W, and L is theK

absolute value of the product of non-zero eigenval-ues. We can estimate the back-slip distribution onthe model source region, combining the prior infor-

Ž .Fig. 8. Displacement rates at each GPS station calculated from the inverted back-slip distribution thick arrows and the observedŽ . Ž . Ž .displacement rates thin arrows . a Horizontal displacement rates. b Vertical displacement rates.


Ž .Fig. 8 continued .

Ž .mation with the observation Eq. 3 . Here, we unitedthe likelihood function from the data distribution of

Ž .Eq. 4 with the probability density function from theŽ .prior information of Eq. 5 by using Bayes’ theo-

rem. The Bayesian model is highly flexible with thetwo hyper-parameters, s 2 and r 2. We can representthe model as:

2 2l a;s ,r dŽ .Ž .y NqK r2 y1r2 1r2yN yK 5 5 5 5s 2p s r E LŽ . K

= 2 2exp yS a;s ,r 6Ž .Ž .

with:

S a;s 2 ,r 2Ž .1 t y1s dyAa E dyAaŽ . Ž .22s

1tq a Wa. 7Ž .22 r

To find the best estimates of the two hyper-parameters, we used ABIC proposed by AkaikeŽ .1980 on the basis of the entropy maximizationprinciple. It is a criterion to minimize the influenceof the error included in the data and to derive hiddeninformation to its maximum, in order to determine


the hyper-parameters uniquely, which represent thedegree of smoothness of the slip distribution. Oncewe have determined the two hyper-parameters, s 2

and r 2, we can calculate the model parameter a. Wecan represent the solution for the model parameter a,ˆusing a 2 which is defined by s 2rr 2 as:

y1t y1 2 t y1as A E Aqa A E d. 8Ž . Ž .ˆ

As a result, we can determine the back-slip distribu-tion objectively and uniquely on the plate boundary,that is, the amount of interplate coupling and thedirection of relative plate motion. The covariance forthe model parameter a is given by:ˆ

y12 t y1 2Css A E Aqa W 9Ž . Ž .ˆ ˆ

where s 2 is the best estimate of s 2. We can obtainˆthe estimation error of each slip on the model source

Ž .region from Eq. 9 . The optimal value of a whichminimizes ABIC in this study was estimated to be0.15, which is relatively small. From the definition

2 Ž Ž . Ž .. 2of a see also Eqs. 6 and 7 , large value of a

indicates smooth distribution of back slip and for-ward slip.

In this study, we constructed the model sourceregion on the three-dimensional upper surface of thesubducting PH plate obtained from spatial distribu-

Ž .tion of microearthquakes Satake, 1993 , whose strikedirection is taken almost parallel to the axis of the

Ž .Nankai Fig. 6 . Since the trough axis changes itsdirection abruptly in the region between Kyushu andShikoku, we separated the model source regions intotwo parts. Since outside of the model source regionis assumed to be completely decoupled in this analy-sis, we constructed relatively large model sourceregions. The sizes of the model source regions offsoutheast of Kyushu and Shikoku to Kii peninsulawere taken to be 180 km=200 km and 140 km=400km, respectively. We divided the respective modelsource regions into 9=10 and 7=20 subsections,and distributed 12=13 and 10=23 basis functionsso as to cover the respective whole regions homoge-neously. The distribution of slip rate on the modelsource region is represented by the superposition ofthe bi-cubic B-spline functions with various ampli-tudes. The boundary condition for the model source

region is assumed to be semi-fixed, reducing num-bers of bi-cubic B-spline functions which expressdistribution of slip rate on the model source regions.Therefore, stress concentration, which appears nearthe edge of the model source regions for conven-tional uniform slip model, is suppressed considerablyin this study.

In this study, we deduced 772 model parametersfrom the 247 horizontal and 237 vertical displace-ment rates of the GPS data, and determined thespatial distribution of slip rate. We excluded 10vertical data from the data set because the observa-tion errors of the 10 data are anomalously large, andbecause considering that data with large observationerrors are not so important in our inversion analysisin which weight of the errors are considered. In thisstudy, we carried out inversion analysis for bothhorizontal and vertical displacement rates, consider-ing weight of confidence ellipse of 1s for therespective components at each GPS station. As wedescribed before, the accuracy of the GPS data of thehorizontal movements is much better than that ofvertical movements.

For the model source region off Shikoku to Kiipeninsula, we carried out inversion analysis, givingthe constraint that the direction of back slip is within"458 of the direction of plate motion of the PH

Ž .plate relative to the EU plate Seno et al., 1993 ,Ž .using non-negative least-squares NNLS by Lawson

Ž .and Hanson 1974 .

4. Results

4.1. Slip distributions on the model source regions

Fig. 7 represents distributions of slip rate on themodel source regions between the PH plate and thecontinental plate obtained from inversion analysisbased on the GPS data of the crustal movementsŽ .Figs. 3 and 4 .

In the model source region off Shikoku to Kiipeninsula the average back-slip rate is 4.0 cmryr forthe area with back slips greater than 3.0 cmryr,where interplate coupling appears to be strong. Thiscorresponds well to the coseismic slip regions at the


Ž .time of the 1944 Tonankai M 7.9 and the 1946Ž . ŽNankai M 8.0 earthquakes Sagiya and Thatcher,

.1999 . A weakly coupled region that separates theselarge back-slip regions is located beneath the Kiichannel and its southern extensional region.

The average direction of the back slip was ob-tained as N538W"118 for the model source regionoff Shikoku to Kii peninsula. The direction differs by48 from the direction of plate motion of the PH plate

Ž . Ž .relative to the EU plate N498W Seno et al., 1993On the other hand, we find large forward slip,

reaching 11 cmryr, on the model source regionsoutheast off Kyushu.

In Fig. 7, reliability, which is defined by the ratioof the obtained back slip to estimation error on the

Ž .model source region calculated from Eq. 9 , is alsoshown. Reliability is low from the eastern part ofShikoku to the west of Kii peninsula, including theregion beneath the Kii channel. The low reliability isprobably due to the large distance between the modelsource region and the GPS stations: the model sourceregion deepens abruptly beneath the Kii channel, andno GPS stations exist there.

We also calculated distribution of slip rate ondifferent model source regions so as to fill the gapbetween the two source regions in the present analy-sis. However, we hardly found a difference in distri-bution of slip rate on the original model sourceregions. From these considerations, we may say thatthe 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 dashedand solid lines denote contraction and extension, respectively. The thickness of each line represents the displacement rate of baseline lengthchange.


4.2. Surface displacement rates calculated from theinÕerted back-slip distribution

Ž . Ž .Fig. 8 a and b , respectively, represent horizon-tal and vertical displacement rates at each GPS sta-tion calculated from the inverted back-slip distribu-tion, together with the observed displacement rates.Concerning the horizontal movement, we find thatmost of the observed displacement rates are wellexplained by our model, except in the southern partof Kyushu, the western part of Shikoku, and theChubu district. In the southern part of Kyushu, theobserved horizontal displacement rates have south-

ward components as compared to those in the north-ern region. The observation errors are large there,and we accordingly weighted the errors when wecarried out inversion analysis. For these reasons, thefitting of horizontal movements between observationand calculation is considered to be poor. In thewestern part of Shikoku, the cause of the differenceis probably due to large spatial variation of thedirections of the observed horizontal movement. Inthe Chubu district, since there exists westward dis-placement rates with comparable magnitude in theinland region away from the eastern model sourceregion, 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 theoverlying continental plate relative to the subducting Philippine Sea plate is shown. The contour lines denote the amount of back slip. The

Ž .contour interval is 1 cmryr. The areas with low reliability the ratio of the obtained back slip to estimation error is less than four areshaded.


well. Therefore, the crustal movement in this regionis considered to be caused by tectonic stresses otherthan subduction of the PH plate.

Vertical movement is poorly fit in all regions. Thereason is that the errors of the observation data ofvertical movement are several times as large as those

Ž .of the horizontal movement Figs. 1 and 4 , and weweighted the observation errors accordingly in theinversion analysis.

4.3. Slip distributions obtained from baseline lengthchanges

Until Section 4.2, we have discussed slip distribu-tions obtained from the inversion of horizontal andvertical displacement rates of GPS data. However,we have to consider effect of fixed point for thehorizontal data. To solve this problem, we convertedthe horizontal displacement rates of the GPS data to

Ž .666 baseline length changes Fig. 9 . For the dataset, we carried out the similar inversion analysis. Inthis case, we also found that interplate couplingbecomes weak at depths deeper than about 40 km

Ž .beneath the Shikoku and Kii peninsula Fig. 10 . Thedirection of average back slips is oriented N538W"

38, which is close to the direction predicted from theŽ .plate motion model by Seno et al. 1993 . On the

other hand, no slip occurs in the southeast off Kyushuwhere reliability is fairly low.

5. Discussion

Our inversion analysis indicates the strong cou-pling between the PH and the continental plates in

Žthe model region off Shikoku to Kii peninsula Figs..7 and 10 . The strongly coupled region has been

Ž .suggested by Hyndman et al. 1995 in which atransient thermal model using the finite element

Ž .method was constructed Hyndman and Wang, 1993 .Their model allows comparison of the thermallyestimated downdip extent of the seismogenic zonewith that from seismicity, tsunami data and thecrustal deformation data in the Nankai subduction

Ž .zone. The locked zone by Hyndman et al. 1995corresponds well with the large back-slip regionobtained in this study. This result indicates that thegeodetically obtained result is consistent with the

thermal model. In the south of the model sourceregion, the Kinan seamount chain is ranging in theNS direction on the Shikoku basin. The subductionof such seamounts might be related to weak inter-

Ž .plate coupling in this region Yoshioka, 1991 . Therelation between seamounts and interplate coupling

Ž .is discussed by Zhao et al. 1997 , in which themorphology of the upper surface of the subductingPacific plate beneath the Japanese islands was esti-mated using SP and sP converted waves at the upperboundary of the slab. The subducting seamountshave kept roughly their original shapes probablybecause the seamounts are stronger and less de-formable than the inner slope materials, and are notscraped off at the trench so that the slab subducts ata steeper dip angle. Hence, the PH plate may subductwith steeper dip angle beneath the Kii channel thanin other regions, corresponding to weak interplatecoupling.

Moreover, we find that the amount of the backslip becomes very small at depths deeper than about30 to 40 km on the model source region, indicatingweak interplate coupling there. This is probably dueto ductile characteristics and flow of rocks due to thehigh temperature there. This depth is shallower thanthe depth of 60 km estimated from experimentalstudies of rock rheology in northeast JapanŽ .Shimamoto, 1990 . Combining a rheological model,which is represented by single crystal of olivine andplagioclase, with the thermal structure of the subduc-

Ž .tion zone, Shimamoto 1989 suggested the depth oftransition from brittle or plastic deformation to duc-tile deformation to be about 60 km in northeastJapan. The difference in the depths in northeast andsouthwest Japan could be caused by the fact that thePH plate in southwest Japan is younger and warmerthan the Pacific plate, which is subducting beneathnortheast Japan, as suggested by previous studiesŽ .e.g., Yoshioka, 1991 .

On the other hand, on the basis of the idea thatthe Nankai trough is the southern limit of the AMplate, we carried out a similar inversion analysis,after making necessary corrections for the horizontalGPS data. As a result, we obtained N778W"148 asthe direction of the average back slip, which is

Ž .different from the direction of Seno et al. 1993 by288. Comparing this with the result obtained assum-ing that the southern boundary of the AM plate is


along the MTL, the latter is closer to the results ofŽ .the plate motion model by Seno et al. 1993 in

terms of the direction of the average back slip.Therefore, we conclude that the idea that the MTL isthe southern boundary of the AM plate is preferable,based on our inversion of the GPS data.

We also estimated recurrence times of the To-nankai and the Nankai earthquakes from the resultsof the model source region off Shikoku to Kii penin-sula. The amount of the average coseismic slip onthe model source region was estimated to be 342 cmfrom the result of inversion analysis of coseismicgeodetic data associated with the 1944 Tonankai and

Žthe 1946 Nankai earthquakes Sagiya and Thatcher,.1999 . On the other hand, the amount of the average

back slip on the corresponding region obtained inthis study is 3.2 cmryr. Dividing the amount of theaverage coseismic slip by that of the back slip, therecurrence time of the trench-type great earthquakesthat have occurred at the Nankai trough is roughlyestimated as 107 years, consistent with the recur-

Žrence interval of 90 to 150 years in this region e.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 thehorizontal displacement rates. Since the forward slipappears in spite of the removal of the coseismiccrustal deformations associated with the two 1996

Ž Ž .Hyuganada earthquakes October M 6.6 , DecemberŽ ..M 6.6 from the GPS data, a possible explanationof the forward slip might be after-slip of the Hyu-ganada earthquakes. However, horizontal displace-ment rates of GPS observation before the 1996 Hyu-ganada earthquakes had already shown southeast-

Žward movements in Kyushu Geographical Survey.Institute, 1996 . Also, no slip can be found on the

model source region southeast off Kyushu for theinversion of rates of the baseline length changes.These indicate that deformation of Kyushu dose notbehave like an elastic body but a rigid body. There-fore, the NS oriented extension in Kyushu associated

Žwith the expansion of the Okinawa trough Shiono et.al., 1980; Tada, 1980 andror southeastward drag of

Kyushu due to the upwelling of mantle materialŽ .beneath the East China Sea e.g., Seno, 1998 may

be the cause of the southeastward displacement ratesin Kyushu.

6. Conclusions

In this study, we calculated the distribution ofinterseismic slip rate on the plate boundary betweenthe subducting Philippine Sea plate and the continen-tal plate in southwest Japan, based on the displace-ment rates obtained from the continuous GPS obser-vations by the Geographical Survey Institute of Japan.The obtained results are as follows.

Ž .1 We found back slip of more than 3 cmryr onthe model source regions off Shikoku and Kumanon-ada, indicating strong interplate coupling. These cor-respond well to the large coseismic slip areas of the

Ž . Ž .1946 Nankai M 8.0 and the 1944 Tonankai M 7.9earthquakes, respectively. Weak interplate couplingcan be found in the region beneath off Kii channeland in the region deeper than about 30 to 40 km.

Ž .2 We estimated the recurrence time of thetrench-type great earthquakes along the Nankaitrough to be about 107 years from coseismic slip andback slip obtained from inversion analyses of thecoseismic crustal deformations associated with theNankai and the Tonankai earthquakes, and the GPSdata in this study, respectively. The recurrence timeis consistent with the results obtained in the previousstudies.

Ž .3 The average direction of the back slip isN538W on the model source region off Shikoku toKii peninsula, which is concordant with the directionof N498W from the plate motion model by Seno et

Ž .al. 1993 .Ž .4 In the Hyuganada region off southeast of

Kyushu, although we excluded coseismic crustal de-formations associated with the 1996 Hyuganada

Ž Ž . Ž ..earthquakes October M 6.6 , December M 6.6Ž Ž .and the 1997 Satsuma earthquakes March M 6.3 ,

Ž ..May M 6.2 , we obtained large forward slip frominversion analysis of the horizontal and vertical dis-placement rates. The forward slip corresponds to theprocess of stress release, indicating after-slip in thevicinity of the coseismic slip region of these events.However, from the inversion using baseline lengthchanges, we found that no slips can be seen in thesoutheast off Kyushu. These indicates that deforma-tion of Kyushu does not behave like an elastic bodybut a rigid body. The N–S oriented extension inKyushu associated with expansion of the Okinawatrough andror southeastward drag of Kyushu due to


the upwelling of mantle material beneath the EastChina Sea may be a preferable cause of the south-eastward horizontal displacement rates in Kyushu.

Ž .5 We inverted the GPS data for two cases,assuming that the southern boundary of the Amurianplate is located along the Median Tectonic Line andthe Nankai trough. Comparing the two cases, theformer is closer to the results of the plate motionmodel than the latter in terms of the direction of theaverage back slip. Therefore, the idea that the Me-dian Tectonic Line is the southern boundary of theAmurian plate is preferable from our inversion anal-ysis of the GPS data.

Acknowledgements

We are thankful to T. Yabuki for allowing us touse his source code for geodetic data inversion. Weare indebted to B.A. Romanowicz, K. Hudnut and R.Burgmann for their critical reviews. W. Spakman is¨gratefully acknowledged for providing graphic soft-ware. We also thank S. Takenaka and H. San-shadokoro for their valuable comments and kind helpthrough calculation.

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