Secular Crustal Deformation and Interplate Coupling of the Japanese Islands As Deduced from Continuous GPS Array, 1996–2001 ⁎ Gamal El-Fiky A, , Teruyuki Kato B

Tectonophysics 422 (2006) 1–22 www.elsevier.com/locate/tecto

Secular crustal deformation and interplate coupling of the Japanese Islands as deduced from continuous GPS array, 1996–2001 ⁎ Gamal El-Fiky a, , Teruyuki Kato b

a Construction Engineering and Utilities Department, Faculty of Eng., Zagazig Univ., El-Zagazig, Egypt b Earthquake Research Institute, University of Tokyo, Tokyo, Japan Received 23 September 2005; received in revised form 31 March 2006; accepted 25 April 2006 Available online 10 July 2006

Abstract

Data from the nation-wide GPS continuous tracking network that has been operated by the Geographical Survey Institute of Japan since April 1996 were used to study crustal deformation in the Japanese Islands. We first extracted site coordinate from daily SINEX files for the period from April 1, 1996 to February 24, 2001. Since raw time series of station coordinates include coseismic and postseismic displacements as well as seasonal variation, we model each time series as a combination of linear and trigonometric functions and jumps for episodic events. Estimated velocities were converted into a kinematic reference frame [Heki, K., 1996. Horizontal and vertical crustal movements from three-dimensional very long baseline interferometry kinematic reference frame: implication for reversal timescale revision. J. Geophys. Res., 101: 3187–3198.] to discuss the crustal deformation relative to the stable interior of the Eurasian plate. A Least-Squares Prediction technique has been used to segregate the signal and noise in horizontal as well as vertical velocities. Estimated horizontal signals (horizontal displacement rates) were then differentiated in space to calculate principal components of strain. Dilatations, maximum shear strains, and principal axes of strain clearly portray tectonic environments of the Japanese Islands. On the other hand, the interseismic vertical deformation field of the Japanese islands is derived for the same GPS data interval. The GPS vertical velocities are combined with 31 year tide gage records to estimate absolute vertical velocity. The results of vertical deformation show that (1) the existence of clear uplift of about 6 mm/yr in Shikoku and Kii Peninsula, whereas pattern of subsidence is observed in the coast of Kyushu district. This might reflect strong coupling between the Philippine Sea plate and overriding plate at the Nankai Trough and weak coupling off Kyushu, (2) no clear vertical deformation pattern exists along the Pacific coast of northeastern Japan. This might be due to the long distance between the plate boundary (Japan trench) and overriding plate where GPS sites are located, (3) significant uplift is observed in the southwestern part of Hokkaido and in northeastern Tohoku along the Japan Sea coast. This is possibly due to the viscoelastic rebound of the 1983 Japan Sea (Mw 7.7) and the 1993 Hokkaido–Nansei–Oki (Mw 7.8) earthquakes and/or associated with distributed compression of incipient subduction there. We then estimate the elastic deformation of the Japanese Islands caused by interseismic loading of the Pacific and Philippine Sea subduction plates. The elastic models account for most of the observed horizontal velocity field if the subduction movement of the Philippine Sea Plate is 100% locked and if that of the Pacific Plate is 70% locked. However, the best fit for vertical velocity ranges from 80% to 100% coupling factor in southwestern Japan and only 50% in northeastern Japan. Since horizontal data does not permit the separation of rigid plate motion and interplate coupling because horizontal velocities include

⁎ Corresponding author. E-mail address: [email protected] (G. El-Fiky).

0040-1951/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.tecto.2006.04.021 2 G. El-Fiky, T. Kato / Tectonophysics 422 (2006) 1–22 both contributions, we used the vertical velocities to discriminate between them. So, we can say there is strong interplate coupling (80%–100%) over the Nankaido subduction zone, whereas it is about 50% only over the Kurile–Japan trench. © 2006 Elsevier B.V. All rights reserved.

Keywords: Crustal deformation; Interplate coupling; Continuous GPS array; Japanese Islands

1. Introduction the Sagami Trough. Relative motion among these plates accumulates tectonic stress in the lithosphere and causes The Japanese Islands are located at a complex plate observable crustal deformation. The occurrence of large boundary. The convergence of four plates including the earthquake along plate boundaries and crustal faults re- Eurasian (EUR) or Amurian (AMR), the Pacific (PAC), leases such tectonic stress. Consequently, study of the Philippine Sea (PHS) plate, and North American crustal deformation is a key to understand the physical (NAM) or the Okhotsk (OKH) predominates (Fig. 1). process in the crust as well as to forecast crustal activity. The oceanic PAC is descending beneath the continental Dense arrays of continuous GPS tracking networks NAM (or OKH) at the Kurile–Japan trench, and oceanic provide us with an ideal tool for monitoring crustal PHS plate is descending beneath the EUR at the Suruga– deformation. In Japan, the Geographical Survey Institute Nankai Trough and beneath NAM (or OKH) plate along (GSI) started to establish the dense GPS array of

Fig. 1. Major plate boundaries in and near the Japanese Islands. EUR or AMR: Eurasian or Amurain plate, NAM or OHK: North American or Okhotsk plate, PHS: Philippine Sea plate, and PAC: Pacific plate. Source regions of recent conspicuous earthquakes which might affect on the GPS data are shown. Arrows indicate the relative plate motion directions. G. El-Fiky, T. Kato / Tectonophysics 422 (2006) 1–22 3

Fig. 2. An example of the time series at site number 950155 (39.93°E, 40.58°N). (a) Uncorrected time series of E–W component. (b) Annual change of E–W component. (c) Difference between uncorrected time series and annual change of E–W component. (d), (e), and (f) are same but for vertical component. continuous tracking network in the Kanto–Tokai region horizontal signals (horizontal displacement rates) were in 1992 and has further expanded it to cover the entire differentiated in space to calculate principal components nation. The GSI has been operating in 610 sites, for of strain. continuous monitoring of the daily site coordinates since One problem in employing only the horizontal velocity April 1996. The number of sites increased to 1200 by components as data for crustal deformations studies is that 2004, with average site intervals of about 20 km (e.g., it is difficult to segregate rigid plate motions from inter- Miyazaki et al., 1998; Sagiya et al., 2000). The array is plate coupling strain. This is because horizontal velocities now considered one of the most fundamental infra- include both effects (Aoki and Scholz, 2003). So, rigid structures for monitoring crustal activity in Japan. plate motions could be mapped into the interplate coupling. Details of the operation and analysis of this GPS array This problem can be solved by using vertical velocities to are described in Tada et al. (1997), Miyazaki et al. separate between the rigid plate motions and interplate (1997), and Sagiya (2004a). coupling. On the other hand, the repeatability of horizontal In the present study, we try to delineate the horizontal components of GPS coordinates is highly precise com- crustal strains as well as the interseismic vertical defor- pared with that of their vertical components. So, vertical mation field of the Japanese Islands, using data for about component has rarely been used in scientific discussions. five years from the GPS array. For this purpose, we first Here, we try to estimate the interseismic vertical velocity extracted site coordinate from daily SINEX files for the field for Japanese Islands using GSI's GPS array data period from April 1, 1996 to February, 24, 2001, and between 1996 and 2001. The estimated GPS vertical vel- estimated site velocities by modelling each time series as a cities are combined with 31 year tide gage records to obtain combination of step functions, trigonometric functions, absolute vertical velocity. and a linear function. A Least-Squares Prediction (LSP) Finally, we investigate the origin of the GPS defor- technique has been used to segregate the signal and noise mation in the Japanese Islands by comparing velocity in horizontal as well as vertical velocities. Estimated fields determined from GPS data with those calculated velocities are converted to a kinematic reference frame from the elastic dislocation models involving interplate (Heki, 1996) to discuss the crustal deformation relative to motion at the subduction zones in northeastern and the stable interior of the Eurasian plate. Finally, estimated southwestern Japan. We then show that most of this GPS 4 G. El-Fiky, T. Kato / Tectonophysics 422 (2006) 1–22 velocity field can indeed be accounted for by full elastic sites. (c) and (f) are E–W and vertical components of coupling along the Philippine thrust zones and only 50% corrected time series (difference between uncorrected coupling for the Pacific locked zone. We compare the time series and annual variation), respectively. Finally, GPS-derived strain with those obtained from seismo- the estimated velocities are converted into a kinematic logical and geological data and show that they are qua- reference frame (Heki, 1996) to discuss the crustal litatively similar but that the GPS deformation is much deformation relative to the stable interior of the Eurasian larger that the other two. plate. Fig. 3 shows the horizontal component of the velocity vectors relative to the stable part of the Eurasian 2. Time series and horizontal velocity field plate with 95% confidence error ellipses. Coseismic crustal deformation associated with large earthquakes Processing of the data of GSI's GPS array with the IGS which occurred during the observation period, were precise orbit yields daily coordinates of all stations. We estimated as formulated in Eq. (1), e.g., the 1996 Hyu- used daily GPS data from April 1, 1996 to February 24, ganada earthquakes (MJMA 6.6 on October 19 and MJMA 2001. The period spans about 5 years, which give rea- 6.6 on December 3) southeast off Kyushu (Nishimura et sonably reliable displacement vectors (e.g., Miyazaki et al., 1998), the 1997 Kagoshimaken–Hokuseibu earth- al., 1997; Kato et al., 1998). Here, the horizontal and quakes (MJMA 6.3 of March 26 and MJMA 6.2 on May vertical velocities are calculated by a least-square 13), and the 2000 Tottori earthquake (Mw 7.3). In approach following the procedure described in Sagiya et addition, several artificial steps caused by replacements al. (2000). They modelled time series as a linear of GPS antennas and receivers were found and removed. combination of constant, linear term, trigonometric We tried to remove abrupt displacements resulting from function, and jumps for episodic events. So, the following coseismic and volcanic events in the time series, how- function is fitted to the three components of the GPS data ever, it is difficult to remove postseismic deformation of each station separately. because it strongly couples with annual variations. After removing the annual variation from original ⁎ ⁎ ⁎ dðtÞ¼A1 þ A2 t þ A3 Sinð2ktÞþA4 Cosð2ktÞ time series of GPS data, the standard deviation of the þ HðtÞ: ð1Þ velocities ranges from 0.11 to 0.42 mm/yr for horizontal components and from 0.16 to 1.38 mm/yr for vertical where, A1, A2, A3,andA4 are constants. The first two components. Since most of the coordinate time series are terms on the right side indicate the linear trend with time t, well approximated by fitting method mentioned above, the next two terms (trigonometric function) are the we may consider that the horizontal components of sinusoidal annual variation where A3 and A4 are the velocity shown in Fig. 3 are representative of present amplitudes of the annual change, and the last term, H(t), secular deformation of the Japanese islands. represents the coseismic steps or jumps for episodic The main characteristics of the horizontal velocity events. Here, jumps for episodicP events are estimated as a field shown in Fig. 3 are; (1) a westward motion of the m ð − kÞ sum of Heaviside functions k¼1 en;kH t tn ,wheren northeastern part of Japan. The magnitude of the velocity is number of GPS sites, en,k is the magnitude of the k-th is about 35 mm/yr on the Pacific coast and decreases k step which occurred at tn. These jumps or steps of relative gradually to less than 10 mm/yr to the west along the coordinates in time series might be associated with Japan Sea coast. This may be due to the subduction of the earthquakes, volcanic activity, and GPS antenna and Pacific plate at the plate interface along the Japan Trench. replacements. We should note that the second term in the This deformation might be also due to the eastward above equation, A2, represents the displacement of each motion of China continental block (El-Fiky and Kato, component to be estimated. 1999b; Ito et al., 2000). (2) A northwestward movement After fitting the above equation to the three com- of the southwestern part of Japan (except for Kyushu). ponents of the GPS data, we estimated the displacement The velocity is also about 35 mm/yr on the Pacific coast rate components for all stations by solving least-squares of the southwestern Japan and decreases to less than problems. Fig. 2 shows an example of the time series 10 mm/yr inland toward the west. This is attributed to the obtained at the 950155 site (139.93°E, 40.58°N). Fig. 2a effects of the subducting Philippine Sea plate under the and d represent the time series of raw data of E–W Japanese Islands along the Nankai Trough (Sagiya, component, and vertical component, respectively. (b) 1995; Ito, 2004). (3) A trenchward movement of south- and (e) show E–W and vertical components of annual ern Kyushu and the Ryukyu Islands to the southeast. This variation, respectively. The amplitude of estimated is attributed to the backarc opening process at the Oki- annual variation ranges up to 5 mm among the GPS nawa Trough (Tada, 1984; Sagiya et al., 2000). (4) G. El-Fiky, T. Kato / Tectonophysics 422 (2006) 1–22 5

Chugoku district (western Japan), which has been 3. Estimation of crustal strains assumed to be a part of the EUR (e.g., Seno et al., 1996), is moving eastward relative to the EUR with a rate 3.1. Least-squares prediction technique of about 10 mm/yr. This suggests that the Chugoku district is on another plate, which could be the Amurian It is well known that the estimated velocity field plate (e.g., Cook et al., 1986; Wei and Seno, 1998), or a depends on the assumption of fixed point or the reference separate plate moving eastward by ∼10 mm/yr relative frame used in the analysis. Therefore, estimation of crustal to EUR (e.g., Zonenshain and Savostin, 1981). On the strain, which is independent of fixed point or reference other hand, the estimated GPS velocity vectors are frame, is important to understand the physical processes in parallel to the Pacific subduction vector in northern the crust in the study area. There are a variety of methods Japan (83 mm/yr in 296°) with respect to North to delineate crustal strains (e.g., Tsuboi, 1932; Frank, American plate (e.g., DeMets et al., 1994) and to the 1966; Bibby, 1975; Rikitake, 1976; Savage, 1978; Philippine Sea plate subduction vector in southwestern Brunner et al., 1981; Dermanis, 1981). However, all of Japan (48 mm/yr in 310°, with respect to Eurasian plate, these studies use a discrete approach where the area within Seno et al., 1993). a particular triangle or block is assumed to have uniform

Fig. 3. Yearly averaged velocity vectors with error ellipses (1σ) obtained from the continuous GPS observation network in the Japanese Islands for the period April 1996 to February 2001. 6 G. El-Fiky, T. Kato / Tectonophysics 422 (2006) 1–22 infinitesimal strains. The reality is such that the land by using a statistical approach that assumes the signal has deforms rather continuously except where/when a fault spatial correlation whereas the noise does not. Such spatial displaces the land surface. Thus, a more appropriate correlation is represented by the covariance of the data, to technique to represent crustal strains in a continuous which an “empirical covariance function (ECF)”—is manner may have to be used. Some researchers have used fitted. By using the empirical covariance function, hori- algebraic polynomials of specified degree to describe zontal displacement (or rate) can be estimated at any crustal strains (e.g., Dermanis et al., 1981; Kato and arbitrary point in the study area. Nakajima, 1989). Also, recently, Shen et al. (1996) used Here, we employed the LSP to estimate the crustal an assumed distances decaying constant to relate the strains using the GPS data. In this study, the strain observed displacement rate with the strain rate tensor. components were calculated following the method However, such purely mathematical approach could described by El-Fiky and Kato (1999a). sometimes yield spurious results. We would rather use some physical information included in data itself. One of 3.2. Results of crustal strains relevant techniques is the Least-Squares Prediction (LSP) whereby tectonic signal in the data is extracted by the To estimate the crustal strains from GPS data, we statistical analysis of data (El-Fiky et al., 1997; El-Fiky used the horizontal velocity vectors shown in Fig. 3. The and Kato, 1999a). LSP technique was first developed by average velocities are subtracted from all of the site Moritz (1962) for gravity data and was applied to crustal velocities to remove the systematic bias. Then, we deformation data by El-Fiky et al. (1997) and El-Fiky and applied the LSP as described above to each of the vector Kato (1999a). The method segregates signal (rate of hori- components (East–West and North–South) indepen- zontal movement in the present case) and noise in the data dently. ECF for each of the components are fitted to the

Fig. 4. The rates of areal dilatation of the Japanese Islands as estimated by the LSP technique for the period from April 1, 1996 to February 24, 2001. Unit is 0.1×Micro strain/yr. G. El-Fiky, T. Kato / Tectonophysics 422 (2006) 1–22 7 data. After that, ECFs are used to reconstruct displace- Here we have to note that dilatation strain rate is ment vectors (signal) at grid points (8 km×8 km) mesh dominant affected by subducting plate (if the direction covering the Japanese Islands. Then estimated velocities of subducting plate is perpendicular to trench axis). On at grid points are differentiated in space to obtain rate of the other hand, the maximum shear strain rate is domi- crustal strains in this data period. The rates of strain nant affected by earthquake. Figs. 46 are the thus parameters were estimated in this analysis as follows estimated rates of dilatational strains, rates of maximum (El-Fiky and Kato, 1999a): shear strains, and rates of principal axes of strains, respectively. 2 2 0.5 Rate of maximum shear strain γmax ={(exx −eyy) +γxy} ε Δ γ Rate of principal axes of strain 1 =0.5 ( + max) 3.3. Discussion Rate of principal axes of strain ε2 =0.5 (Δ−γmax) Direction of ε θ=0.5 tan−1 {γxy /(e −e )} 1 xx yy Since the coordinate time series are well approximated by Eq. (1), the coseismic crustal deformation are Where Δ is the rate of dilatation strain (Δ=exx +eyy); estimated and removed from the present GPS data, and γxy is the rate of shear strain {γxy =0.5 (eyx +exy)}; θ is the estimated strains are almost the same for the above the direction ε1 of measured from x-axis anticlockwise; mentioned four intervals, we may think that the crustal and eyx and exy are the rates of linear strains components. strains shown in Figs. 46 are representative of a present

Fig. 5. Distribution of the maximum shear strain rates in the Japanese Islands as estimated by LSP for the period from April 1, 1996 to February 24, 2001. Unit is 0.1×Micro strain/yr. Epicenters of shallow earthquakes (d≤40 km) determined by NEIC are also plotted. 8 G. El-Fiky, T. Kato / Tectonophysics 422 (2006) 1–22

Fig. 6. Magnitude and orientation of rates of principal strains axes in the Japanese Islands as estimated by LSP for the period from April 1, 1996 to February 24, 2001. secular deformation of the Japanese Islands. Though the present GPS array. This might support the incipient strains in these figures are estimated from a relatively subduction and the new plate boundary in this region as short interval of data (5 years), they may well portray suggested by several researchers (e.g., Nakamura, 1983; characteristics of the tectonic deformation in the Seno et al., 1996). On the other hand, widespread com- Japanese Islands. pressional strain in Fig. 4 is somewhat different from data The dilatational strain rates shown in Fig. 4 indicate obtained by conventional surveys. Ishikawa and Hashi- that the Japanese Islands are under a compressional strain moto (1999) analysed the strains in the Japanese Islands regime. This may be due to the subducting Pacific plate by the triangulation data for the last 100 years and showed from the east and Philippine Sea plate from the southeast that the dilatational strain is positive in most of Tokoku (Fig. 1). The deformation might be also due to the and Kyushu districts, which significantly differ from the eastward extraction of China continental block by the present results. The present study shows that only the collision of India toward north (e.g., Kato et al., 1998). southwestern parts of Kyushu are dilating positively. The Rapid compressional strain (>0.12 Micro strain/yr) is discrepancy in the Tohoku district may have to be ex- found in the central and eastern Hokkaido, central amined carefully because many interplate earthquakes Tohoku, the Japan Sea coast of Tohoku, and all over have occurred in this region during the past 100 years and the Shikoku district. The rapid compressional strain along may have affected strains in the area. Although none of the the Japan Sea coast is an important issue derived from the large interplate earthquakes have occurred in the Tohoku G. El-Fiky, T. Kato / Tectonophysics 422 (2006) 1–22 9

Fig. 7. Distribution of tidal stations of Geographical Survey Institute (GSI) used in this study.

area during the study period, significant postseismic de- the source region of the Narugo earthquake (MJMA 5.9) of formation may have occurred. This may be significant in August 11, 1996. South Kanto is the region where the the northern part of the area after the Sanriku earthquake Philippine Sea plate converges with the North American of 1994 (Mb 7.5) (Heki et al., 1997; Kato et al., 1998; El- (or Okhotsk) plate and seismic and volcanic activities are Fiky and Kato, 1999b). very high. On the other hand, the strain rates in this region Maximum shear strain rates (Fig. 5) show some patches might be partly attributed to the silent earthquake off Boso of rapid strain. They are found in eastern Hokkaido, peninsula in May 1996, which was followed by a number southern Tohoku, southern Kanto, Shikoku, and north- of small earthquakes (Sagiya, 2004b). High maximum eastern Kyushu. All of these areas coincide with seis- shear in the Shikoku region may be due to the oblique mically active regions. To compare the maximum shear subduction along the Nankai Trough (e.g., El-Fiky et al., strains with seismicity, epicentres of shallow earthquakes 1999), eastward motion of the Amurain plate (Heki et al., (<40 km) are plotted in Fig. 5. Eastern Hokkaido is an area 1999), and/or N–S oriented extension in Kyushu where a couple of large offshore earthquakes occurred; associated with expansion of the Okinawa Trough 1993 Kushiro earthquake and 1994 Hokkaido–Toho–Oki (Tada, 1984; Kato et al., 1998). Finally, maximum shear earthquake (e.g., Tsuji et al., 1995). A wide area in the strain in northeastern Kyushu is most prominent. As southern part of Tohoku has high maximum shear. The mentioned earlier, the coseismic deformation associated maximum shear strain area coincides with the area of with large earthquakes such as the Hyuganada earth- active seismicity in the central Tohoku district. It also quakes of October 19th (MJMA 6.6) and December 3rd includes the focal areas of large earthquakes such as 1962 (MJMA 6.3), 1996, which occurred off the Pacific coast of (M 6.5), 1970 (M 6.2), and 1998 (MJMA 6.1), and lies near Kyushu (Fig. 1) are estimated and removed. Thus, the 10 G. El-Fiky, T. Kato / Tectonophysics 422 (2006) 1–22

Table 1 with that of their horizontal components. So, vertical Tide gage locations with their velocities components of GPS data have been neglected in many Site Location Velocity Velocity Ci scientific discussions. Here, we try to estimate the inter- (V i) mm/yr (V i) mm/yr (mm/yr) Longitude Latitude t g seismic vertical velocity field for Japanese Islands using ABU 139.62 35.13 −1.56 −2.10 0.54 GSI's GPS array data. We investigate and discuss crustal AKU 130.28 31.72 2.10 −0.61 2.71 deformation of the Japanese Islands in terms of vertical ASA 140.83 40.84 2.12 3.33 −1.21 velocity. HOS 131.47 32.02 −0.78 −4.14 3.36 After removing the annual variation from original − − KAI 135.07 34.27 1.44 1.88 0.42 time series of GPS data, we estimated the vertical rate KAR 129.85 33.48 0.80 5.70 −4.91 KAS 138.57 37.40 5.34 9.00 −3.66 for all stations by solving least-squares problems as KAT 140.27 35.17 −0.64 1.45 −2.09 mentioned above. Although these procedures allow us KUR 133.40 33.41 4.89 3.31 1.58 to obtain a vertical velocity field, it does not reflect the MIK 136.17 36.23 −0.85 5.98 −6.83 absolute vertical velocity field because the GPS data we − − NEZ 139.51 38.23 2.12 6.56 8.68 used are processed relative to Tsukuba site (140.0875°E, OGI 138.47 38.06 0.24 2.40 −2.16 OGA 139.78 39.97 4.27 9.47 −5.20 36.10568°N). On the other hand, tidal gage data can ONI 136.87 34.82 4.09 3.82 0.27 represent absolute vertical velocity if they corrected for OSH 140.60 43.29 2.22 3.89 −1.67 the different sources of errors including the eustatic SOM 140.84 38.03 −4.46 −2.53 −1.93 change of sea level. Thus, the GPS vertical velocity field − WAJ 136.89 37.38 1.57 8.35 6.78 is linked with tidal gage data to obtain absolute vertical Average −2.13 velocities. First we need to obtain vertical velocities at each tide gage. The sea level observations in the Japanese Islands rates of high maximum shear of strains in northeastern started in the beginning of the 20th century and are still Kyushu may be due to postseismic effect of these being continued. The locations of tidal stations used in earthquakes. The slow thrust slip event of May 1997 this study are shown in Fig. 7. Raw tidal data contain following the above Hyuganada earthquakes, also, might various effects such as ocean tides, ocean currents, have contributed to this high strain rate as suggested by atmospheric pressure, eustatic change of sea level, and Hirose et al. (1999) and Ozawa et al. (2001). vertical crustal deformation. In order to estimate the Fig. 6 shows rates and directions of principal strain linear trend of vertical movements at the 17 tidal stations axes. NW–SE compression is predominant in the south- used in this study for the period from 1970 to 2001 from western Japan. This may be due to the compressional records, we used the method introduced by Kato and force acting at the convergent plate boundary between the Tsumura (1979). By this method we can remove Philippine Sea plate and the continental plate (e.g., Tabei seasonal or annual variations, such as atmospheric et al., 1996). The northeastern Japan exhibits east–west pressure and ocean tides, using the yearly mean sea level compressional strains due to the Pacific plate converging data. Then, the yearly mean sea level is decomposed into toward west, whose directions are consistent with the ocean current effects and the vertical crustal deforma- results obtained from old triangulation data by Shen-Tu tion. It should be noted that, although the eustatic and Holt (1996),andEl-Fiky and Kato (1999a), but the change of sea level has been estimated to be about 2.0± rates are about two to three times larger relative to their 0.9 mm/yr by many studies (e.g., Barnett, 1984; result. In the Kyushu Island, even though the east–west Douglas, 1991; Savage and Thatcher, 1992; Peltier compressional strain is predominant, a north–south and Tushingham, 1998), the present method does not extension is also evident in northern par of Kyushu. introduce any correction for it. To solve the problem, the Tada (1984) used the conventional surveys and hypoth- eustatic correction is assumed to be 1.8 mm/yr esized that Kyushu area is under the extensional force due (Douglas, 1991) in the present analysis. The vertical to the rifting at the Beppu–Shimabara Graben in the velocities at the tidal stations used in the present are northern Kyushu. The present GPS data is consistent with listed in Table 1. Since velocities obtained from tide the conventional strain data in this region. gage data represent absolute velocities, the estimated GPS vertical velocities relative to Tsukuba must be 4. Vertical deformation adjusted to the tide gage reference frame. First, we select a GPS site which is collocated with the tidal gage or It is well known that repeatability of vertical com- nearest to each tide gage. Then the obtained GPS ponents of GPS coordinates is much poorer compared vertical velocities are adjusted to the tide gage velocities G. El-Fiky, T. Kato / Tectonophysics 422 (2006) 1–22 11 by giving the fowling correction (Aoki and Scholz, such technique may be the least-squares prediction, 2003): which is discussed above for the horizontal velocities (El- Fiky et al., 1997). The method uses discrete values of Xn ¼ 1 ð i− i ÞðÞ vertical velocity to segregate the noise from the observed C Vt Vg 2 n i¼1 data and obtain continuous distribution of rate of vertical deformation. We divided the Japanese Islands into cells where, C is the correction which should be added to all the of 8 km × 8 km, and we estimated the rate of vertical GPS estimated velocities, n is the number of tidal stations, deformation at all grid points from the observed absolute i i Vt the velocity of i-th tidal gage, and Vg the velocity of the vertical data at the GPS sites. Fig. 9 shows the distribution i-th GPS sites. We used the data of 17 tidal stations and of predicted vertical velocities in the Japanese islands for obtained C=−2.13 mm/yr (Table 1). Fig. 8 shows the the present interval (1996/04–2001/02). obtained absolute vertical velocities at the GPS sites. We then try to estimate vertical deformation of tecto- 4.1. Discussion nic origin using these absolute vertical rates. Here, we have to consider an important problem that the estimated It is widely accepted in the Japanese Islands that the vertical velocity is usually contaminated by some noise landward limit of the coupled region coincides approx- (e.g., observation errors and local deformations due to imately with the coastline in northeastern and south- water pumping or other artificial causes) which may have western parts of Japan (Hyndman et al., 1995; Le Pichon to be removed. Thus an appropriate method for et al., 1998). The elastic deformation induced by sub- segregating the continuous vertical deformation which duction of oceanic plates produces subsidence seawards is of tectonic origin and the noise is indispensable. One of of this limit and uplift landwards of this limit during the

Fig. 8. Estimated absolute vertical velocities at GPS sites with the associated error ellipses for the period from April 1, 1996 to February 24, 2001. 12 G. El-Fiky, T. Kato / Tectonophysics 422 (2006) 1–22

Fig. 9. Distribution of rates of vertical crustal movements as estimated by LSP in the Japanese Islands from the period from April 1, 1996 to February 24, 2001.

interseismic interval. Thus, the coastline is supposed to subduction along the Suruga Trough. (3) Distribution of coincide with the change from subsidence to uplift. the vertical deformation in northeastern part of Japanese Fig. 9 shows the distribution of estimated vertical Islands does not show a clear evidence for interplate velocities in the Japanese islands. Although this figure is coupling along the Kurile–Japan Trench. This might be estimated from only five years of GPS data, it shows due to the Japan Trench plate boundary being too far clearly some characteristics of vertical tectonic defor- ocean-ward from the GPS sites or might be due to a mation pattern in the Japanese Island. The striking weak coupling between the Pacific plate and overriding characteristics of this velocity field are; (1) a clear uplift plate at the Japan Kurile–Japan Trench. (4) Most of the pattern of up to 6 mm/yr along the Shikoku district and Kyushu district is subsiding and no clear uplift area is Kii Peninsula parallel to the plate boundary in this area. seen along its Pacific coast. This indicates a weak or no This is attributed to the strong interplate coupling be- interplate coupling between the EUR and PHS there. tween the overriding plate and the subducting Philippine This is expected from the absence of great earthquakes Sea plate at Nankai Trough. (2) A clear subsidence in this area (e.g., Shiono et al., 1980). (5) A clear uplift pattern of up to 7 mm/yr in Tokai area approximately area of up to 6 mm/yr in the northern part of the Japan parallel to the Suruga Trough. The direction of this tilt is Sea coast of Tohoku district. This might be related to approximately parallel to the direction of the movement incipient subduction and the formation of a new plate of the Izu block relative to the Eurasian plate (Fig. 3). boundary in this region. This subduction is represented The vertical deformation in this region may be due to the by earthquakes such as the 1964 Niigata earthquake (Mw G. El-Fiky, T. Kato / Tectonophysics 422 (2006) 1–22 13

7.5), the 1983 Japan Sea earthquake (Mw 7.7), and the 5. Elastic modelling of interseismic deformation 1993 Hokkaido Nansei–Oki earthquake (Mw 7.8) (Kobayashi, 1983; Nakamura, 1983; Seno et al., 1996). The GPS-derived strain rates (Figs. 46) are in good The convergence rate of the plate boundary along the west qualitative agreement with those obtained from seismo- side of northeastern Japan is less than 20 mm/yr (Seno et logical and geological data (e.g., Research Group for al., 1996), about one-fourth of that of the east side at the Active Faults in Japan, 1991; Tsukahara and Kobayashi, Japan Trench. However, this convergence may cause 1991). Wesnousky et al. (1982) and Shen-Tu et al. remarkable deformation at the GPS sites because the plate (1995) estimated the rates of horizontal strain and boundary in the Japan Sea is much closer to the land than principal axes of the Japanese Islands from a 400-year the Japan Trench. (6) Another uplifted area of up to 8 mm/ earthquake catalog and the geomorphological data of yr is observed along southwestern part of Hokkaido Quaternary faults. Although the directions of the district. This uplift is consistent with uplift determined maximum compressive strains of geological data are from leveling observations in 1993 and 1998 (GSI, 1999). in harmony with those obtained from seismological This may due to the above mentioned incipient subduction data, the seismic strain release rate is about 30–50% in the Japan Sea or might indicate the long-term larger than the geological strain rate. Since most of the postseismic vertical deformation of the 1993 Hokkaido– historical earthquakes are located in the offshore area, Nansei–Oki (Mw 7.8) earthquake. where no Quaternary faults are mapped, the geological

Fig. 10. The rectangles adopted to approximate the locked portions of the Pacific slab and Philippine Sea used slab. The dashed lines indicate the location of cross-sections in Figs. 13–16. 14 G. El-Fiky, T. Kato / Tectonophysics 422 (2006) 1–22 strain rates may underestimate the strain rate. Therefore, Cohen, 1994; Mazzotti et al., 2000). We thus follow the considering the possible unmapped faults, and the elastic back-slip dislocation approach of Savage (1983). uncertainties in the fault slip rates, the difference We ignored viscoelasticity and used a purely elastic between the seismic strain rate and the geological strain model in the present analysis. The downdip extent of the rate may not be significant. locked zone can be obtained from modelling the large The principal axes of deformation estimated in the amount of deformation that occurs during great earth- present study are in agreement with those of seismological quakes and approximately coincides with the maximum and geological data. However, we have a considerable extent of interplate thrust events. In southwest Japan, difference in the rates; the present GPS-derived strain rate Hyndman et al. (1995) have determined the geometry of is generally one order of magnitude higher than long-term the locked thrust plane based on the analysis of the strain rate estimated from seismological and geological Nankaido and Tonankai great earthquakes. They showed data. This difference may be due to aseismic strain re- that the downdip extent of the locked zone is thermally sulting from pure folding and/or aseismic slip (Wes- controlled. In northern Japan, Shen-Tu and Holt (1996) nousky et al., 1982; Kaizuka and Imaizumi, 1984; Shen- have determined the geometry of the locked zone based Tu et al., 1995). Since both the seismic and geological on the locations of interplate seismicity (Byrne et al., strains rates are small compared with the GPS-derived 1988; Hasegawa et al., 1994; Kawakatsu and Seno, strain rates, only the aseismic strain due to pure folding 1993). would account for part of the difference between the GPS The geometries of the thrust planes we use in this and seismic/geological strain rates. However, Quaternary study are shown in Figs. 10 and 11. The Nankaido folding does not seem to be a pervasive feature in Japan Trough dislocation surface strikes N 60°E, with a locked (e.g., Research Group for Active Faults in Japan, 1991; section down to 20 km depth and a transition zone to Shen-Tu et al., 1995). Therefore, this difference should be 30 km (with a dip of 7°–12°). The downdip widths of explained by the non-permanent elastic strain present in the two portions are 150 and 45 km, respectively. In the the geodetic data transmitted from the subduction zones Tonankai region, the subduction is steeper. The locked (e.g., Wesnousky et al., 1982; Hashimoto and Jackson, zone extends to a depth of 23 km but is only 115 km in 1993; Shen-Tu et al., 1995; Le Pichon et al., 1998). Here width and the transition zone extends to 38 km and is we try to investigate this interpretation using the dis- 40 km in width (Fig. 11)(Hyndman et al., 1995). Even location model for crustal deformation data in the Japa- though the previous studies and the pattern of crustal nese Islands. We use the above five-year solution for the deformation discussed above indicate a very weak velocities of GPS stations of the Japanese arrays (hori- coupling off the Kyushu region, we selected the fault zontal and vertical) to estimate elastic deformation caused shown in Fig. 10 which extends from 20 km to 57 km in by interseismic loading of the Pacific and the Philippine depth (Yamasaki and Seno, 2005). We ignored central subduction plans. Japan (Kanto–Tokai region) in our elastic modelling In the simplest tectonic model, elastic strain accumulation along a subduction zone in interseismic period is assumed to result from a constant rate of elastic strain build-up produced by the locking of the thrust zone, this elastic deformation being instantaneously released during the earthquakes. The locked thrust surface can then be treated as an edge dislocation in an elastic half-space with a constant back-slip (normal-slip) rate during the interseismic phase (Savage, 1983). If the back-slip vector estimated by this model is equal to the subduction vector, full coupling is realized and no aseismic slip is allowed. A smaller back-slip rate implies weaker coupling and larger aseismic slip. Although the issue of permanent deformation build up is still being debated, the approximation of purely elastic behavior of the subduction system during the interseismic period is a reasonable approach, and the Fig. 11. Simplified geometries adopted for the Philippine Sea slab in differences with the deformation estimated by more Tonankai and Nankai (top). Black lines correspond to locked zone, complex model do not exceed a few perdent (e.g., grey lines to the transition zone. Same for the Pacific slab (bottom). G. El-Fiky, T. Kato / Tectonophysics 422 (2006) 1–22 15 due to the complexities related to the Izu–Bonin al., 1994; Kawakatsu and Seno, 1993). The downdip collision. We calculated the subduction velocity from extent of the coupled zone is 200 km with a transition the predicted Eurasian/Philippine Sea rotation pole zone 40 km long. The Japan Trench subduction plane given by Seno et al. (1993). It ranges from 50 mm/yr strikes about N 20°E based on the bathymetric data. The toward N312°W off Kyushu to 43 mm/yr toward maximum depth of the locked part of the plane is about N310°W off Kii peninsula. 55 km and the transition extends down to 75 km depth, For the Pacific slab, we adopt the geometry proposed with a dip of 13.5°–30°. For the subduction velocity in by Shen-Tu et al. (1995) on the basis of the interplate northeast Japan we define the slip and its direction on seismicity (Yoshii, 1979; Byrne et al., 1988; Hasegawa et each subduction thrust plane using the NUVEL-1A

Fig. 12. Elastic modelling of northeastern and southwestern Japan thrust zones with an approximation of the locked portions by rectangles shown in Fig. 10. Computations were performed for 100% and 70% for Philippine Sea slab and for Pacific slab respectively. 16 G. El-Fiky, T. Kato / Tectonophysics 422 (2006) 1–22

Pacific/North American plate motion Euler vector velocity agree closely with the observed values. Fig. 13 (DeMets et al., 1994). It ranges from 83 mm/yr toward shows the elastic modelling along cross-sections of N296°W off south Tohoku to 82 mm/yr toward N298°W Nankaido (Shikoku) and Tonankai (Kii peninsula) thrust off Hokkaido. Recently several kinematic and geodetic zones (see Fig. 10 for location) in southwestern part of researches have shown that northeastern Japan belongs Japan. The variation of the magnitudes of the horizontal either to the North American plate or Okhotsk plate (e.g., velocity is plotted with respect to the distance to the DeMets, 1992; Yoshioka et al., 1993, Shen-Tu et al., Nankai Trough (Fig. 13). Computed curves along cross- 1995; Seno et al., 1996). Both models predict essentially sections in this figure are for 100%, 80%, and 60% the same plate motion velocity along the Japan Trench coupling factor. To see how well the predicated velocities (Seno et al., 1996). We used three sets of rectangular fit the observed velocities, total variability is calculated planes, one for Hokkaido, one for northern part of using variance and residual variance as given below: Tohoku, and third one is for the southern part of Tohoku, Total variance ðTVÞ as shown in Fig. 10. This is to fit its azimuthal variation X 1 2 and because of the expected variation in coupling along ¼ ðXi−X¯Þ ; Residual Variance ðRVÞ the length of the plate interface. The expected variation is N 1 X in part due to the postseismic effect of the 1994 Sanriku– ¼ ðX −X Þ2 N i ie Oki earthquake. Panels A and B of Fig. 12 show the horizontal velocity Where Xi denote the observed velocity of point i (i=1,2, ¯ of the modelling for the Pacific slab and Philippine Sea …N), X is the average of the observed velocities, Xie is the slab, respectively. The coupling factor used in this figure estimated (predicted) velocities of point i. is 70% for the Pacific slab and 100% for the Philippine Sea slab. In the southern part of Japan, the elastic effect is RV Then : % Variability ¼ 1− 100 not significant in the northern part of Shikoku district and TV Kii peninsula, north of the Medium Tectonic Line (MTL) (Fig. 11b). As seen in this figure, both the estimated 100% variability here means that the fitting line lies directions and magnitudes for the predicted horizontal on the observation. The best fit for horizontal velocity is

Fig. 13. Elastic modelling of southwestern Japan thrust zones, (a) is for Tonankai, and (b) is for Nankaido. The magnitude of observed horizontal velocity (dots with 2σ error bars) is plotted with respect to the distance to the trench. Computed curves along cross-sections for 100%, 80%, and 60% coupling factor. G. El-Fiky, T. Kato / Tectonophysics 422 (2006) 1–22 17 obtained for about 100% coupling factor in these two China Sea (e.g., Seno, 1999) may be the cause of the regions. On the other hand, the predicted vertical southeastern horizontal displacement rates in Kyushu. velocity for Nankaido and Tonankai also agrees well Figs. 12b and 14 show the modelling for the Pacific with the estimated one (Fig. 14). The best fit for vertical slab. We use three sets of rectangles to model the locked velocity ranges from 80% to 100% coupling factor in and the transition planes for Hokkaido and Tohoku as these two regions. The predicted vertical velocity agrees shown in Figs. 10 and 11. The agreement in direction well with the interseismic vertical velocity as given by and magnitudes of the estimated elastic and observed Hyndman et al. (1995). As mentioned above, the horizontal velocities is fairly good. In Fig. 12a, we can interseismic coupling produces uplift on land north of see that the estimated elastic velocities reduce gradually the coast and subsidence at sea south of it. This is the to about 10 mm/yr on the Japan Sea coast. This agrees same pattern of vertical motion as the permanent plastic with the observed GPS velocities in that region (Fig. 3). vertical motion that has prevailed for the last 2–5 Myr Note also that the estimated elastic velocities in the (Le Pichon et al., 1998). This supports the hypothesis northern part of Tohoku are slightly greater than the that permanent plastic and elastic deformations are observed ones. This might be due the postseismic effect essentially collinear (Le Pichon et al., 1998). of the 1994 Sanriku–Oki earthquake in the observed In contrast, the elastic modelling in Fig. 12a does not velocities. On the other hand, the elastic effect is not show any indication for coupling in the Kyushu region. significant in the western and southwestern parts of This is expected as no earthquake of magnitude 8 or Hokkaido (Fig. 11a). greater has been reported in this area, though moderate Fig. 13 shows the estimated curves for the horizontal earthquakes occur frequently there (e.g., Shiono et al., velocity compared with the observed values along the 1980). This suggests that deformation of Kyushu does three cross-sections, the Hokkaido cross-section to the behave like an elastic body but a rigid body. Therefore, north and the northern and southern Tohoku sections to the N–S oriented extension in Kyushu (Fig. 6) the south (see Fig. 10 for location). Computed curves associated with the expansion of the Okinawa Trough along cross-sections in this figure are for 100%, 80%, (Tada, 1984) and/or southeastern drag of Kyushu due to 60%, and 50% coupling factor. As shown, systematic the upwelling of mantel material beneath the Eastern differences exist among the cross-sections. The best fit for

Fig. 14. Computed vertical velocity compared with observed velocity (dots with 2σ error bars) of southwestern Japan thrust zones, (a) is for Tonankai, and (b) is for Nankaido. 18 G. El-Fiky, T. Kato / Tectonophysics 422 (2006) 1–22 horizontal velocity is obtained for about 70%, 50%, and showed that weak coupling was recovered in the 80% coupling factor in Hokkaido, northern Tohoku, and coseismic rupture area 3.3 yr after the earthquake. On southern Tohoku, respectively. The relatively low inter- the other hand, the predicted vertical velocity for plate coupling in the northern Tohoku might be due to the Hokkaido and Tohoku does not recover the observed postseismic effect of the 1994 Sanriku–Oki earthquake. one well (Fig. 15). The best fit for vertical velocity in these This is consistent with the results of Nishimura et al. two regions is obtained for about 50% coupling factor. (2004). They studied the temporal change of interplate As stated above, the observed horizontal velocities in coupling in northeastern Japan using the GPS array for the both northeast and southwest Japan are consistent with period from 1995 April to 2002 March. They pointed out those predicted by elastic back-slip model (Fig. 12). In that after-slip of the 1994 Sanriku–Oki earthquake addition, the vertical velocities in southwest Japan agree occurred over the coseismic rupture area and its downdip well with the model (Fig. 14). However, in the northeast extension on the plate boundary and continued only in the Japan the observed vertical velocities deviate from that of downdip extension and decayed with time. They also the elastic model (Fig. 16). Heki (2004) discussed this

Fig. 15. Elastic modelling of northeastern Japan thrust zones, (a) is for the horizontal velocity of Hokkaido cross-section, (b) is for the horizontal velocity of northern cross-section (39°N–41°N), (c) is for the horizontal velocity of southern cross-section (37°N–41°N). Computed curves along cross-sections for 100%, 80%, 60%, and 50% coupling factor. Dots indicate the observed velocities and bars represent 2σ uncertainty. G. El-Fiky, T. Kato / Tectonophysics 422 (2006) 1–22 19

Fig. 16. Computed vertical velocity compared with observed velocity (dots with 2σ error bars) of northeastern Japan. (a) Is for Hokkaido, (b) is for northern cross-section of Tohoku district, and (c) is for southern cross-section of Tohoku district. Computed curves along cross-sections for 100%, 80%, 60%, and 50% coupling factor. problem and summarized the following reasons for the So both possible causes (1) and (2) listed above are not discrepancy: (1) viscous flow effect, (2) wrong estimation reasonable. For the vertical deformation, we might get of coupling strength and/or convergence rates, (3) a better agreement between the model and observations by tectonic factor causing the northeast Japan fore-arc to extending the coupled zone to a depth of 100–120 km subside and keeping southwest Japan stationary. It is (Suwa et al., 2003). However, this would be inconsistent known that the crustal deformation might vary during an with our knowledge of seismogenic depth in northeast earthquake cycle due to viscosity relaxation in the Japan where interplate thrust earthquakes occurs at depths asthenosphere. But as mentioned above, Cohen (1994) shallower than 50–60 km (e.g., Hasegawa et al., 1991). studied such cyclic components under various conditions, So, Heki (2004) adopted possibility (3) and hypothesized and showed that the difference between purely elastic that a tectonic factor of basal subduction erosion gives rise behavior of the subduction system and the one with a to the observed fore-arc vertical velocity by loss of upper more complex viscous model not exceed a few per cent. plate materials including both mantle and crust. He 20 G. El-Fiky, T. Kato / Tectonophysics 422 (2006) 1–22 estimated the basal subduction erosion rate to be 15 mm/ the signal and noise in horizontal as well as vertical yr down to a slab depth of 90 km which is somewhat faster velocity. Then, the estimated horizontal signals (hori- than the geological average. zontal displacement rates) were differentiated in space Aoki and Scholz (2003) used the GPS data to study to calculate principal components of strain. Calculated vertical velocity in the Japanese Islands and they strains seem to portray the tectonic environments of the pointed out that horizontal data does not permit the Japanese Islands; (1) dilatational strains show that the separation of rigid plate motion and interplate coupling Japanese Islands are under the compressive strain because horizontal displacements contain both effects. regime induced by the subducting Pacific and Philippine Therefore rigid plate motion could be mapped into the Sea plates, (2) maximum shear strains show a good interplate coupling leading to a misunderstanding of its agreement with recent crustal activities, and (3) spatial distribution. This problem can be avoided by principal axes of the strains indicate that the Japanese using the vertical velocities to discriminate between the Islands are under the influence from the converging rigid plate motions and interplate coupling. That is why oceanic plates. The secular vertical deformation field of we used both horizontal and vertical velocities in this the Japanese islands was also derived for the same of study. The obtained results in this study confirmed the GPS data. We combined the GPS vertical velocities with above conclusion of Aoki and Scholz (2003). That is the 31 year tide gage data to obtain absolute vertical estimated coupling factor from horizontal velocity is velocity. The estimated pattern of vertical velocity usually higher than the one obtained from the vertical shows the following. (1) A clear uplift pattern of about velocity. Based on this and summing up the present 6 mm/yr in the Shikoku district and Kii Peninsula, study, we can say there is strong interplate coupling whereas subsidence pattern is seen in the coast of (80%–100%) in the Nankaido and Tonankai regions, Kyushu district. This is consistent with the strong where it is only 50% in Kurile–Japan Trench. coupling between the Philippine Sea plate and overrid- Similar results of low seismic coupling along the Japan ing plate at the Nankai Trough and weak coupling off and Kurile trenches have been obtained from 100 years of Kyushu. (2) No clear uplift pattern is seen along the geodetic and leveling data (Hashimoto and Jackson, Pacific coast of northeastern part of Japan. This might be 1993; Shen-Tu and Holt, 1996; El-Fiky and Kato, 1999b). due to the plate boundary is too far seaward from the In contrast, Le Pichon et al. (1998) estimated the coupling GPS sites or might be due to weak coupling there. (3) factor using 1 yr (1995) of the GPS data to about 80% for Significant uplift is observed in southwestern Hokkaido northeastern Japan. Since they used the horizontal and in northeastern Japan along the Japan Sea coast of velocity only for studying the coupling in northeastern Tohoku district. This uplift might be due to the long- Japan which might include the contributions of both of the term postseismic rebound of the 1983 Japan Sea (Mw rigid plate motion and interplate coupling as mentioned 7.7) and the 1993 Hokkaido–Nansei–Oki (Mw 7.8) above, their estimated value seems to be overestimated. earthquakes and/or associated with the convergence For the Nankai subduction, the obtained results here are plate of incipient subduction there. Finally, we investi- consistent with previous results on the basis of analysis of gate the origin of the present GPS deformation in the GPS, long-term geodetic and leveling data (Savage and Japanese Islands by comparing velocity fields deter- Thatcher, 1992; Hyndman et al., 1995; Ozawa et al., mined from GPS data with those calculated from the 1999; El-Fiky et al., 1999). elastic dislocation models involving interplate motion at the subduction zones in southwestern and northeastern 6. Conclusion Japan. Since horizontal data does not permit the separation of rigid plate motion and interplate coupling Data from the nation-wide GPS continuous tracking because horizontal velocities include both effects, we network of Japan for the period from April 1, 1996 to used the vertical velocities to discriminate between February 24, 2001 has been used to study secular crustal them. We then showed that most of the GPS velocity deformation in the Japanese Islands. We first model each field can indeed be accounted for by full elastic coupling time series of the GPS components as a linear com- along Philippine locked thrust zone and only 50% bination of linear function, trigonometric function, and coupling for the Pacific locked zone. jumps for episodic events. Estimated velocities after fitting are converted into a kinematic reference frame Acknowledgments (Heki, 1996) to allow discussion of crustal deformation relative to the stable interior of the Eurasian plate. We We are grateful to the staff of the Geographical used Least-Squares Prediction technique to segregate Survey Institute for providing the GPS data. We thank G. El-Fiky, T. Kato / Tectonophysics 422 (2006) 1–22 21

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