Interseismic Deformation at the Nankai Subduction Zone and the Median Tectonic Line, Southwest Japan Yosuke Aoki and Christopher H

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. B10, 2470, doi:10.1029/2003JB002441, 2003

Interseismic deformation at the Nankai subduction zone and the Median Tectonic Line, southwest Japan Yosuke Aoki and Christopher H. Scholz1 Lamont-Doherty Earth Observatory of Columbia University, Palisades, New York, USA Received 10 February 2003; revised 9 June 2003; accepted 7 July 2003; published 11 October 2003.

[1] GPS velocities in the vicinity of the Nankai Trough, southwest Japan, were inverted into three components: interplate loading due to Nankai Trough subduction, deformation associated with deep slip on the Median Tectonic Line (MTL), and the residual rigid plate motion. The results show a gradual decrease of interplate seismic coupling between 25 and 40 km depth on the Nankai Trough interface. This is consistent with the deep slip model, in which the fault extends as a ductile shear zone, with a depth-variable interplate strain accumulation rate. The top 20 km of the interface may not be fully coupled, although the resolution is poor there. The low coupling at shallow depths is consistent with the accretionary prism detected by seismic surveys. The MTL slip rate is estimated to be between 0.00 and 5.50 mm/yr if we assume a vertical fault and between 0.00 and 3.88 mm/yr if we assume a north dipping fault. Combining our results with a geological estimate (4–9 mm/yr) and a geodetic estimate with a denser network (5 mm/yr) suggests that the MTL slip rate may be near the upper bound of our geodetic estimate, that is, 4–5 mm/yr. The rigid plate motion with respect to the stable Eurasian craton was estimated to be very small, indicating that southwestern Japan is on the Eurasian plate rather than a separate plate. INDEX TERMS: 1206 Geodesy and Gravity: Crustal movements—interplate (8155); 1208 Geodesy and Gravity: Crustal movements—intraplate (8110); 1243 Geodesy and Gravity: Space geodetic surveys; 8158 Tectonophysics: Plate motions—present and recent (3040); 8159 Tectonophysics: Rheology—crust and lithosphere; KEYWORDS: southwest Japan, Nankai Trough, Median Tectonic Line, brittle-plastic transition zone, three-dimensional deformation Citation: Aoki, Y., and C. H. Scholz, Interseismic deformation at the Nankai subduction zone and the Median Tectonic Line, southwest Japan, J. Geophys. Res., 108(B10), 2470, doi:10.1029/2003JB002441, 2003.

1. Introduction strains by differentiation of velocities avoids this problem [Mazzotti et al., 2000], but the spatial resolution of the [2] Interseismic crustal deformation in southwest Japan is interplate coupling is then poor because the spatial differ- dominated by the interplate coupling between the Philippine entiation of displacement data results in the introduction of Sea Plate (PHS) and the overriding southwest Japan (SWJ) additional noise. with a relative velocity of 50 mm/yr [Seno et al., 1993] [4] These previous studies focused on seismic potential (Figure 1). Accumulated stress is released as periodic M8 and did not discuss much the details of the strain accumu- thrust earthquakes, such as the 1946 Nankaido, 1854 Ansei, lation at the subduction zone. The Nankaido region is an and 1707 Genroku earthquakes [Ando, 1975]. ideal place to explore this because of the dense geodetic [3] The recent development of a continuous Global network, the proximity of the trench to the geodetic surveys, Positioning System (GPS) network in the Japanese islands and a shallow-dipping subduction interface, which allow allows us to obtain the spatial variation of interplate better resolution of the depth variation of the interplate coupling between the PHS and SWJ [Ito et al.,1999; coupling than a vertical fault such as the San Andreas fault. Mazzotti et al., 2000; Miyazaki and Heki, 2001]. Aoki and Here we will discuss the interplate coupling with emphasis Scholz [2003] pointed out, however, that horizontal veloc- on the mechanism of interseismic strain accumulation at a ities contain both rigid plate motion and the interplate fault, using three-dimensional GPS data. coupling effect, so that rigid plate motion could be mapped [5] About 230 km north of the Nankai Trough, there into the interplate coupling effect. Employing volumetric exists the contact of a pair of metamorphic belts separated by a dextral fault called the Median Tectonic Line (MTL;

1 Figure 1), south of which is the low T/P (temperature-to- Also at Department of Earth and Environmental Sciences, Columbia pressure ratio) Sanbagawa belt and north of which is the University, New York, USA. high T/P Ryoke belt [Scholz, 1980]. Geological and trilat- Copyright 2003 by the American Geophysical Union. eration data show that the MTL slip rate is 4–9 mm/yr 0148-0227/03/2003JB002441$09.00 [Tsutsumi and Okada, 1996] and 5 ± 3 mm/yr [Hashimoto

ETG 5 - 1 ETG 5 - 2 AOKI AND SCHOLZ: DEFORMATION IN SW JAPAN

and Jackson, 1993], respectively. Because of the lack of 130 135 140 145 historical large earthquakes for at least past 400 years [Tsutsumi and Okada, 1996], it is important for seismic 45 (a) 45 hazard assessment to estimate the slip rate of the MTL precisely. This has been difficult, however, because deformation due to the MTL is much smaller than the interplate 40 NA 40 EUR coupling effect at the Nankai Trough, so that the deformation due to the MTL is masked by the interplate coupling 35 effect. Miyazaki and Heki [2001] estimated the slip rate at 35 MTL qualitatively to be 2–3 mm/yr, but they also acknowl- PAC MTL PHS edged that more GPS sites are needed to qualitatively assess 30 50mm/yr 30 the MTL slip rate. Tabei et al. [2002] recently estimated the MTL slip rate to be 5 mm/yr from densely occupied 130 135 140 145 campaign GPS measurements. 133 134 135 36 36 2. Data Set (b) X [6] We obtained three-dimensional velocities from contin- 7 uous GPS data operated by the Geographical Survey Institute of Japan (GSI) between 1996 and 1999. The data in 2000 and

later were omitted to avoid the coseismic and postseismic 6 effects of the 2000 Tottori earthquake (Mw = 6.6). Vertical

35 35 velocities of each station were obtained by the method 5 described by Aoki and Scholz [2003] and horizontal velocities were obtained in the new reference frame for the stable Eurasian craton of Steblov et al. [2003], who constructed the 4 new reference frame of the Eurasian and North American 40 plates by analyzing GPS data across Russia. Typical uncer- 3 34 34 tainties for velocities are 1 mm/yr for both horizontal and vertical velocities. Table 1 shows a list of GPS sites used in 30 2 this study with their velocities and uncertainties. 30 [7] The velocity field in Figure 1 is a superposition

1 of (1) interplate coupling between the PHS and SWJ, (2) deformation due to the deep slip at the MTL, and 20 (3) the SWJ rigid plate motion. It is appropriate to assume 33 33 0 20 that horizontal velocities contain all three, while vertical velocities contain only 1. -1 10 3. Model Setting 10 -2 [8] We employed a two-dimensional model for interplate 32 Y 32 coupling (Figure 2) in which the interplate coupling coef- km -3 30mm/yr Vertical velocity ficient is a function of depth only. Some attempts have been made to image both the lateral and depth variation of the 0 50 (mm/yr) interplate coupling along the Nankai Trough [e.g., Ito et al., 1999; Miyazaki and Heki, 2001], but we used a two- 133 134 135 dimensional model to gain better resolution of the depth variation by simplifying the problem. [9] The three-dimensional velocity of each GPS site was Figure 1. (a) Tectonic setting around the studied region rotated into vertical, MTL-normal, and MTL-parallel com- indicated by a square. The Median Tectonic Line (MTL) is ponents (see Figure 1). Note that the vertical velocities are also shown by a solid line. EUR, NA, PAC, and PHS stand due to the downdip component of interplate coupling, the for the Eurasian, North American, Pacific, and Philippine MTL-normal velocity is a superposition of the downdip Sea Plates. (b) GPS velocity field in the studied area with component of the interplate coupling and the MTL-normal the depth contour of the plate interface between PHS and component of rigid plate motion, and the MTL-parallel EUR. Vertical velocities are obtained by the method of Aoki velocity is a superposition of the arc-parallel component and Scholz [2003], and horizontal velocities are according of the interplate coupling, rigid plate motion, and MTL deep to a new reference frame by Steblov et al. [2003] with slip. Although the Nankai Trough is not precisely parallel to respect to the stable Eurasian craton. Also appended are the MTL, we assumed that the MTL-normal direction is the lines along X and perpendicular to Y for which the downdip direction of the Nankai Trough to simplify the interplate coupling and the MTL slip rate are estimated. problem. This assumption should be valid because the strike of the Nankai Trough differs only 15 from the MTL. AOKI AND SCHOLZ: DEFORMATION IN SW JAPAN ETG 5 - 3

[10] We employed the back-slip model of Savage [1983] (Figure 2) in which the overriding plate is down dragged at Table 1. Coordinates, Velocities, and Their Standard Deviations the same velocity as the subducting plate when the interplate of GPS Sites Used in This Studya coupling is full and the overriding plate does not deform at Latitude, Longitude, East, mm/yr North, mm/yr Up, mm/yr all when no interplate coupling occurs. The shape of the Code N E Ve se Vn sn Vu su plate interface is taken from Sagiya and Thatcher [1999], 940072 35.587 134.331 À12.54 1.39 À14.04 1.67 À2.14 0.63 who compiled it from the distribution of microseismicity. 940073 35.490 133.699 À1.66 1.57 À0.06 1.08 0.07 0.53 [11] Figure 2 shows two models for the deep slip of the 940077 34.549 133.528 À1.87 1.39 5.32 0.85 0.47 0.47 MTL, one which assumes a vertical fault and the other 940080 34.286 134.024 À4.13 1.21 6.73 0.84 5.18 0.36 940081 33.927 134.626 À13.09 0.58 8.21 0.74 5.37 0.29 which assumes a 35 north dipping fault. The MTL is 940082 33.316 134.122 À25.57 0.78 26.53 0.09 À3.34 0.67 classically understood to be a vertical strike-slip fault 950346 34.998 134.404 À3.68 1.43 1.00 1.07 1.02 0.44 [e.g., Tsutsumi and Okada, 1996], but a recent seismic 950357 34.670 134.520 À3.03 1.44 2.21 1.01 2.11 0.38 reflection survey shows that the MTL may dip to the north 950378 35.457 134.047 À0.71 1.63 0.67 1.06 1.22 0.43 30–40 from surface to a depth of at least 5 km [Ito et al., 950379 35.346 133.439 À4.04 1.41 0.91 1.05 0.61 0.50 950380 35.266 134.237 À3.73 1.44 1.03 1.05 À0.02 0.51 1996]. Their survey has no resolution at greater depths. We 950382 36.285 133.240 0.45 1.71 0.86 1.05 4.00 0.36 accordingly constructed two models for the MTL, one 950389 35.264 133.793 À2.51 1.59 À0.93 1.12 1.91 0.45 vertical and one dipping to the north. 950390 35.100 134.320 7.73 1.46 20.80 0.25 À0.79 0.53 [12] We assumed that the top 15 km of the MTL is locked 950391 35.021 134.235 À2.91 1.46 1.43 1.04 1.40 0.42 950392 35.003 133.735 À2.69 1.50 0.89 1.01 1.37 0.46 completely and the deeper part is slips freely in both models 950393 34.983 133.961 À2.60 1.45 3.28 0.96 1.49 0.41 [Savage and Burford, 1973]. We fixed the locking depth to 950394 34.810 133.598 À0.43 1.46 6.94 0.79 1.12 0.46 be 15 km according to the result of Tabei et al. [2002], that 950395 34.791 133.929 À11.44 1.20 À7.01 1.40 À2.61 0.63 is, we did not attempt to image the shape of the brittle- 950396 34.658 134.166 À6.46 1.27 À0.49 1.13 À3.14 0.65 950397 34.439 133.797 3.54 1.47 14.23 0.50 2.47 0.38 plastic transition zone, nor even to estimate the locking 950415 34.097 134.352 À6.57 0.87 11.65 0.62 2.75 0.38 depth because the deformation due to the deep MTL slip is 950416 34.060 134.560 À10.78 0.75 7.79 0.74 5.42 0.29 expected to be too small to explore these details. 950417 34.052 134.049 À7.94 0.81 11.04 0.64 6.20 0.31 950418 34.038 134.230 À9.08 0.74 11.22 0.62 4.29 0.32 950419 33.937 133.681 À8.35 0.68 14.46 0.47 5.12 0.33 4. Method 950420 33.879 133.389 À11.65 0.50 14.02 0.50 1.98 0.43 4.1. Mathematical Formulation 950421 33.878 134.058 À7.00 0.60 19.40 0.28 3.92 0.39 950422 33.830 134.668 À14.83 0.37 11.41 0.60 5.11 0.33 [13] We inverted the depth variation of both the downdip 950423 33.725 134.533 À17.78 0.16 12.37 0.58 1.60 0.46 and along-strike component of interplate coupling from 950424 33.619 134.372 À18.10 0.12 19.05 0.28 4.36 0.33 three-dimensional velocities along the line in Figure 1. 950425 34.472 134.314 À3.59 1.30 3.88 0.90 1.91 0.42 Velocities of GPS stations located less than 50 km from 950426 34.255 134.242 À4.40 1.18 7.34 0.78 4.31 0.31 950427 34.217 133.715 À3.19 1.17 9.64 0.69 5.29 0.30 the line are taken in the analysis. We also assumed that 950428 34.068 133.648 À6.10 0.89 12.15 0.58 4.77 0.30 we could not derive lateral variation of the slip rate of 950429 34.164 133.926 À4.66 1.09 9.95 0.67 5.73 0.30 the MTL because dense GPS observations are conducted 950439 33.654 133.805 À14.98 0.10 20.10 0.24 4.77 0.33 only at a portion of the MTL in eastern Shikoku (Figure 1). 950440 33.604 134.107 À16.85 0.10 21.01 0.21 4.07 0.35 950441 33.528 134.281 À23.20 0.36 17.23 0.37 À1.78 0.60 Note that the deep slip rate at the MTL, as well as the along- 950442 33.506 133.904 À20.52 0.33 21.76 0.17 1.98 0.40 strike component of the SWJ rigid plate motion with respect 950444 33.428 134.007 À22.08 0.53 24.54 0.08 0.02 0.51 to the Eurasian plate were estimated simultaneously with 960654 35.436 133.340 À0.06 2.03 À1.29 1.33 À2.09 0.88 the interplate coupling when along-strike velocities are 960655 35.361 134.325 À1.89 1.89 0.57 1.26 0.80 0.66 inverted. 960660 35.170 133.564 À1.95 1.86 À0.75 1.33 0.01 0.68 960661 35.178 134.050 À2.84 1.92 À2.85 1.40 0.93 0.63 [14] The observation equation is given by 960673 34.172 134.605 À8.48 1.10 6.45 0.98 3.17 0.49 960674 34.040 133.875 À6.77 0.87 15.30 0.54 2.97 0.50 E 960675 33.790 134.302 À15.72 0.37 12.47 0.72 3.67 0.72 d ¼ Gm þ ð1Þ 960676 34.446 133.999 À7.02 1.53 À0.21 1.34 0.45 0.62 960677 34.383 133.781 À1.78 1.69 4.30 1.08 À0.09 0.67 where the data d and the model m parameters are related by 960765 34.810 134.176 À2.25 1.83 0.67 1.29 2.37 0.53 the data kernel G [Mansinha and Smylie, 1971; Rani and 960766 34.580 133.757 À1.04 1.75 4.06 1.08 À3.45 0.89 E 970827 34.218 134.393 À6.09 1.59 6.14 1.28 2.54 0.97 Singh, 1992], and is the error in the data which is assumed 97S025 34.135 134.384 À9.13 1.19 6.56 1.08 2.07 0.73 to have a Gaussian distribution with zero mean and 97S026 34.109 134.326 À8.75 1.14 8.40 0.98 5.53 0.70 covariance Æ. 97S027 34.104 134.262 À8.53 1.18 8.15 1.00 3.05 0.70 [15] The model parameter m was estimated by the 97S028 34.123 134.337 À4.14 1.49 8.83 0.99 0.66 0.81 97S029 34.111 134.172 À8.35 1.13 9.94 0.91 3.46 0.75 damped least squares method [e.g., Menke, 1989] which 97S030 34.089 134.171 À6.45 1.18 12.17 0.77 4.61 0.64 minimizes the cost function E given by 97S037 34.089 134.040 À6.09 1.33 11.14 0.91 5.54 0.98 97S038 34.081 134.004 À6.48 1.32 11.85 0.92 3.36 0.98 T T 97S039 34.059 133.969 À1.60 1.52 16.61 0.61 4.19 1.03 E ¼ ðÞd À Gm À1ðÞþd À Gm l2ðÞDm ðÞDm ð2Þ 97S040 34.062 134.113 À7.63 1.25 10.81 0.94 6.27 0.91 a Ve, Vn, and Vu are east-west, north-south, and vertical components of subject to the constraint that the interplate coupling velocities, and se, sn, and su correspond to the associated standard deviations. coefficient should be between 0 and 1. The interplate coupling coefficient a is defined as a = vb/vp, where vb and vp are the back-slip velocity [Savage, 1983] and the relative ETG 5 - 4 AOKI AND SCHOLZ: DEFORMATION IN SW JAPAN

optimal damping parameter is the one that minimizes CVSS. 4.3. Error in the Solution [17] Because the solution is constrained so that the seismic coupling be between 0 and 1, the error for the solution is not readily obtained from a linear manipulation. The uncertainty in the solution is to be assessed by Bootstrap resampling [Efron and Tibshirani, 1993]. Once the best fitting model parameter, mest is obtained, the Figure 2. Model of strain accumulation at the Nankai 0 0 residual vector r is given by r = rd À G mest. The residuals Trough subduction zone and the Median Tectonic Line are randomly resampled with replacement allowing multiple (MTL). In this case, the plate subducting from left (south) to picks to form the resampled residual vector r*, which has right (north) corresponds to the Philippine Sea Plate, and the the same dimension as r. For example, if r =[r1r2r3r4r5], overriding plate corresponds to southwest Japan. The then r* could be r*=[r r r r r ]. The model parameters are interplate coupling is 1 when the overriding plate is down 3 2 1 3 5 then estimated from the resampled data vector d*=Gmest + dragged by the subducting plate at the same speed as the r* for many, say, 1000, times. The 95% confidence bound subducting plate and 0 when the overriding and subducting of the model parameters is defined by removing the 2.5% plates are completely decoupled. In MTL, the shallower part lowest and highest model parameters. is locked in the interseismic period while the deeper part is slipping. We evaluated the slip rate for a vertical fault and a 4.4. Combining Results From Multiple Components fault dipping 35 to the north. Although there should exist a [18] The downdip component of interplate coupling will brittle-plastic transition zone and it is important to constrain be calculated from both vertical and horizontal deformation its the depth range, we chose the simpler model in which data, while the along-strike component of interplate cou- the locking depth is fixed to be 15 km without a BPTZ pling will be calculated only from horizontal deformation because the slip rate at the MTL is likely to be too small to data. The downdip component of the interplate coupling is explore the details. Also we need to note that the thus precisely obtained by combining the results from two deformation due to the MTL deformation will be masked components of deformation data. The error analysis de- by the deformation due to the subduction because of the scribed previously estimates the probability distribution of proximity of the Nankai Trough and the MTL. We also the possible interplate coupling as a function of depth. Two show the depths where deeper extension of the MTL distributions are combined by the idea of the conditional reaches to the plate interface; these are 38 km for the probability as vertical MTL and 49 km for the dipping MTL. P ðÞm P ðÞm PðÞ¼m R v h ð5Þ P m P m dm plate motion between the PHS and EUR [Seno et al., 1993], vðÞhðÞ respectively, D is the finite approximation of the second- order differentiation for the spatial smoothness of the where Pv(m), Ph(m), and P(m) represent the probability solution. l is a damping parameter, the larger value of distribution of the interplate coupling obtained from the which gives a smoother solution but less spatial resolution. vertical, horizontal, and combined deformation field. The problem described in equations (1) and (2) are simplified to minimize the cost function E0 given by (see Appendix A) 5. Results 5.1. Interseismic Coupling E0 ¼ ðÞd0 À G0m T ðÞd0 À G0m ð3Þ [19] Figure 3 shows the inversion result obtained from vertical velocities only, indicating that interplate coupling decreasesfrom1to0between25and40kmdepth 4.2. Optimal Damping Parameter (Figure 3a). The existence of this wide brittle-plastic tran- 2 [16] The damping parameter l controls the relative sition zone (BPTZ) is required to explain the plateau of importance of minimizing the residual versus minimizing vertical velocities between 180 km and 240 km as a the spatial roughness of the solution, as mentioned above. function of distance from the trench (Figure 3b), as pointed The appropriate value of l2 is given from the cross- out by Aoki and Scholz [2003]. If the BPTZ is narrow, that validation (CV) method [Wahba, 1990]. The CV method is, the interplate coupling decreases abruptly from 1 to 0, the is based on the idea that a good model well predicts unused vertical velocity profile would have a sharp peak. Note that from used data. The cross-validation sum of squares we do not see a steady decrease of the seismic coupling in (CVSS) is thus given by the BPTZ, but it has an area where reduction rate of interplate coupling is lower between 32 and 38 km depth. XN The resolution analysis shows that the spatial resolution of 1 0 CVSS l2 ¼ d0 À d~ ð4Þ the interplate coupling at 30–35 km is good enough to N k k k¼1 believe that this plateau exists in reality (Figure 3e). [20] The plate interface at a subduction zone is expected 0 ~0 where N is the number of data, d k is the unused data, and d k to be decoupled at shallower depth due to elevated pore is the predicted data from the rest of N À 1 data. The pressure within the accretionary prism [Byrne et al., 1988]. AOKI AND SCHOLZ: DEFORMATION IN SW JAPAN ETG 5 - 5

Figure 3. Results of the inversion analysis from vertical velocities only. (a) Depth distribution of interplate coupling coefficient, with the solid line for the expected distribution and dashed lines for upper and lower 95% confidence limits. (b) Comparison between observed data with the 2s uncertainty (dots) and calculated values (solid line). (c) Configuration of the plate interface. (d) Cross-validation sum of squares (CVSS; see text for derivation) as a function of the damping parameter l2. The star indicates the minimum of the CVSS and the corresponding value of l2 is employed as the damping parameter in the analysis. (e) Resolution kernels at various depths. If the resolution is perfect, the shape of the kernel will look like a delta function, that is, with a narrower peak, with better resolution of the interplate coupling. The results indicate that the interplate coupling shallower than 20 km is not well resolved.

The inversion result obtained from vertical velocities sug- analysis also shows the plateau that was defined by the gests that the shallower part could be decoupled (Figure 3a), vertical data alone. The combination failed for the shal- but it is not resolved well (Figure 3e). It is fair to state that lower part because the distributions of interplate coupling we cannot constrain the state of interplate coupling at given from the two components are inconsistent. Figure 7 shallower depths from vertical velocities alone. Because also shows that the vertical velocities are much more of that, the horizontal velocities were also inverted to see sensitive to the interplate coupling at depth than MTL- whether they have a sharper resolving power to constrain normal velocities. the interplate coupling at shallower depths. [21] Figure 4 shows the inversion result obtained from the 5.2. MTL Slip Rate MTL-normal velocities, indicating that the plate interface [23] Although the MTL-parallel velocities were not found looks completely coupled up to 10 km depth (Figure 4a), to work well to constrain interplate coupling on the sub- but the resolution is poor at all depths (Figure 4e). This duction interface, they could be capable of constraining the result also shows that the MTL-normal velocities are not as deep right-lateral slip rate at the MTL and the MTL-parallel sensitive as vertical velocities to seismic coupling at depth component of the rigid plate motion, as shown in Figure 8. (Figure 4a). Unfortunately, the MTL-parallel velocities do The result shows the MTL slip rate within 95% confidence not constrain the interplate coupling very well, either bounds is between 0 and 5.50 mm/yr if we assume a vertical (Figures 5 and 6). fault and 0 and 3.88 mm/yr if we assume a north dipping [22] The vertical and MTL-normal velocities both help fault, respectively. These values are lower than the geolog- constrain the downdip component of interplate coupling. ically estimated value of 4–9 mm/yr [Tsutsumi and Okada, Combining them thus might give the depth distribution of 1996] for either a vertical or dipping MTL, and the value interplate coupling with more resolution. We combined obtained by dense campaign GPS measurements by Tabei et them by the method described in equation (5), to yield the al. [2002] (5 mm/yr), although the 95% confidence depth distribution of the interplate coupling shown in interval of our estimate is rather broad. The model also Figure 7. The results show that interplate coupling is well indicates that the MTL slip rate is rather independent of the resolved at depths greater than 18 km. The combined assumed dip angle of the MTL. ETG 5 - 6 AOKI AND SCHOLZ: DEFORMATION IN SW JAPAN

Figure 4. Similar to Figure 3 except that the results are obtained from the MTL-normal component of the horizontal velocities, indicating that the interplate coupling is generally less resolved than with the vertical component.

Figure 5. Similar to Figures 3 and 4 except that the result is obtained from the MTL-parallel component of the horizontal velocities and thus corresponds to the along-strike component of the interplate coupling, indicating that the resolution is poorer than the vertical component. Note that we assumed the vertical MTL for this analysis. AOKI AND SCHOLZ: DEFORMATION IN SW JAPAN ETG 5 - 7

Figure 6. Same as Figure 5 except that we assumed a north dipping MTL, indicating that the dip angle of the MTL is almost independent of the estimation of interplate coupling.

5.3. Rigid Plate Motion earthquake [Sagiya and Thatcher, 1999] which ruptured [24] We also estimated the rigid plate motion in the area down to 35 km, the middle of the BPTZ. with respect to the stable Eurasian craton [Steblov et al., [26] What does our result imply for an interseismic strain 2003] simultaneously with the depth distribution of the accumulation model? There have been debates as to how seismic coupling and the MTL slip rate (for the MTL- the schizosphere and plastosphere behave to accumulate parallel component) from horizontal velocities, the result of strain during the interseismic period. There are three basic which is shown in Figure 9. Note that the MTL-parallel models: the viscoelastic coupling model [e.g., Nur and component is close to the east-west component and the Mavko, 1974] in which a viscous plastosphere is overlain MTL-normal component is close to the north-south com- by a brittle schizosphere, the strong plastosphere model ponent. The result indicates that western Japan is likely to [e.g., Bourne et al., 1998] in which deformation is governed be moving slowly toward northwest west-northwest with by a strong plastosphere overlain by a weak schizosphere, respect to the stable Eurasian craton. The result also shows and the deep slip model [Savage and Prescott, 1978] in that the rigid plate motion is much smaller than the general which the fault extends from a seismogenic schizosphere notion that western Japan is moving eastward by 10 mm/yr relative to the Eurasian stable craton [Miyazaki and Heki, 2001]. The rigid plate motion is not large enough to hypothesize the existence of a separate plate, such as an Amurian plate.

6. Discussion 6.1. Interplate Coupling [25] The inversion result (Figures 3a and 7) shows a gradual reduction of interplate coupling from 1 to 0 between Figure 7. Depth distribution in downdip component of the 27 and 40 km depth. This depth range is basically consistent interplate coupling from both vertical and horizontal data with the estimation of the brittle-plastic transition zone (solid lines), from vertical velocities only (dashed lines), (BPTZ) from heat flow modeling [Hyndman et al., 1995]. and MTL-normal horizontal velocities (dotted lines). Two The simulation of seismic cycles from a rock friction law lines for each component correspond to lower and upper indicates that coseismic rupture should penetrate well into bound within the 95% confidence interval of the solution. the BPTZ [Tse and Rice, 1986; Stuart, 1988; Scholz, 1998]. The combined depth distribution is only at 18 km depth or This is consistent with our estimated BPTZ depth rage and below because the interplate coupling at the shallower part the depth of coseismic rupture during the 1946 Nankaido is not expected to be well resolvable. ETG 5 - 8 AOKI AND SCHOLZ: DEFORMATION IN SW JAPAN

Figure 8. Probability distribution of the MTL slip rate with upper bound of the 95% confidence limit assuming (a) a vertical and (b) a north dipping MTL. through a plastic plastosphere. Among the three, the deep [29] The shallow part of the plate interface may not be slip model is supported by the geological interpretation that fully coupled, but it was found to be hard to constrain the mylonite belts represent ductile shear zones in the plasto- coupling status at the shallow depth only from geodetic sphere [Scholz, 1988, 2002], results from seismic reflection data. Vertical velocities and MTL-parallel velocities favor studies that a fault extends into the lower crust [Henstock et low coupling of the top 15 km (Figure 3 and 5), but MTL- al., 1997; Parsons, 1998], and geodetic data [Gilbert et al., normal velocities favor higher coupling near the surface 1994]. Our inversion result clearly endorse the likeliness of (Figure 4). Geodetic data indicate the rupture in the 1946 the deep slip model. Savage [1995] pointed out that the Nankaido earthquake is not likely to have reached the viscoelastic coupling model is inconsistent with the tide surface [Sagiya and Thatcher, 1999]. Byrne et al. [1988] gage data for the Nankai Trough region. In the case of also pointed out that the top 10 km of plate interface may subduction, the strong plastosphere model can be ruled out be decoupled due to the elevated pore pressure within the because the loading is driven by the downgoing plate rather accretionary prism. Recent seismic reflection survey shows than the lower crust. Geodetic data cannot resolve the depth a strong reflector in the Nankai accretionary prism above distribution of the seismic coupling for a vertical strike-slip 9kmdepth[Park et al., 2002]. This suggests weak fault like the San Andreas fault [Mavko, 1981] nor distin- interplate coupling at that depth range due to the elevated guish the three models shown above [e.g., Savage et al., pore pressure. 1999], but vertical deformation with GPS stations directly above a shallow dipping fault, as in the present case, are 6.2. MTL Slip Rate capable of resolving slip at depth sufficient to distinguish [30] Our estimation of the MTL slip rate within 95% between the models. confidence bounds is between 0.00 and 5.50 mm/yr if we [27] If interplate coupling is seen in terms of the relative assume a vertical MTL and 0.00 and 3.88 mm/yr if we velocity of the plate motion, we find that the BPTZ is acting assume a north dipping MTL, respectively (Figure 8). Our like a deeply buried crack in which a crack tip is at the top maximum values are at the low end of the geological of the BPTZ. The linear reduction of seismic coupling near estimate of 4–9 mm/yr [Tsutsumi and Okada, 1996], and the top of the BPTZ (Figure 7) suggests that the BPTZ acts the value estimated from densely occupied campaign GPS as a plastic rather than elastic crack. This is similar to the measurements [Tabei et al., 2002]. If we combine these, the linear reduction of slip as a fault tip is approached [e.g., slip rate of the MTL is probably about 4–5 mm/yr. Dawers et al., 1993]. [31] Tsutsumi and Okada [1996] trenched the MTL and [28] Interplate coupling does not decrease monotonically found that the last earthquake in the studied area occurred with depth, but it decreases to a plateau region at 32–38 km, between the thirteenth and sixteenth centuries. They also after which it decreases rapidly to zero (Figure 7). As speculated that the last earthquake was likely in 1596 by mentioned above, a resolution test shows that the plateau is likely to exist. The existence of the plateau cannot be expected from a seismic cycle model assuming frictional behavior from top to bottom, where interplate coupling is expected to decrease smoothly with depth [Tse and Rice, 1986; Stuart, 1988]. If instead the BPTZ is assumed to be flowing plastically, we would expect interplate coupling to decrease exponentially with depth, as in a Brace and Kohlstedt [1980] type model. The existence of the plateau at about 32–35 km suggest that there is either a change in Figure 9. Estimated rigid plate motion in southwest Japan mechanism (say, from frictional to plastic) or material, or with respect to the stable Eurasian craton with 1s error both, at that depth. ellipses assuming a vertical and a north dipping MTL. AOKI AND SCHOLZ: DEFORMATION IN SW JAPAN ETG 5 - 9 combining their result with old Japanese literature. If [36] We also estimated the deep slip rate of the MTL these assumptions are valid, this portion of the MTL has motion. Results show that the slip rate is not sensitive to already accumulated at least 4 mm/yr 400 years 1.6 m the MTL dip angle, which is ambiguous, and that the slip of slip. rate is likely to be between 0 and 5 mm/yr. If this result [32] Our result also shows that our data have no resolving is combined with the geological estimate (4–9 mm/yr) power to constrain the dip angle of the MTL, even with the and geodetic estimate obtained by dense campaign GPS dense distribution of GPS sites. Constraining the fault measurements (5 mm/yr), the MTL slip rate may be near geometry of the MTL from geodetic data alone is inherently the upper bound of our estimate, that is, 4–5 mm/yr. difficult no matter how dense the site distribution, because Considering the paleoseismological evidence that the last the MTL motion is so small compared with the relative plate earthquake should have occurred between the thirteenth and motion between EUR and PHS that the deformation signal sixteenth centuries, most likely in 1596, at least 1.6 m of from the MTL slip is masked by that from the interplate slip must have been accumulated since the last earthquake. coupling. This suggests that this part of MTL is capable of causing an earthquake as large as the Kobe (1995, M = 6.9) earthquake 6.3. Rigid Plate Motion that occurred just 100 km to the north. [33] Figure 9 shows the residual rigid plate motion of [37] Our results also show that southwestern Japan is western Japan. It indicates that western Japan is moving likely to be on the Eurasian plate, not on a separate plate 0.5 mm/yr toward the west-northwest. Although the like the Amurian plate. uncertainty is large, it precludes the idea that western Japan is on an Amurian plate [e.g., Heki et al., 1999; Miyazaki and Heki, 2001], a separate plate moving eastward by 10 mm/ Appendix A: Simplification of the Observation yr relative to EUR [Zonenshain and Savostin, 1981]. The Equation discrepancy is due to the difference of the reference frame [38] The inverse problem in this study estimates model between previous studies and our study; previous studies are parameters which minimize E in equation (2). Because the based on the reference frame of Heki [1996], while ours second term in the observation equation (1) is a reflection used Steblov et al. [2003]. As Heki [1996] acknowledged, for a priori information that the solution should be spatially his reference frame has large uncertainties because of a lack smooth, equation (1) is modified by [Jackson, 1979] of data across Russia, while Steblov et al. [2003] added data in Russia to obtain a more reliable reference frame. Our d G result indicates that western Japan is on the EUR plate in the ¼ m þ E2 ðA1Þ reference frame of Steblov et al. [2003]. Note that our 0 D analysis does not deny the existence of the AMR, that is, E the AMR may exist with a different plate boundary geom- where 2 represents the error which has the Gaussian etry than proposed by Zonenshain and Savostin [1981] or distribution given by Heki et al. [1999]. E [34] Is this residual motion explained by intraplate 2 NðÞ0; 2 ðA2Þ deformation in this region? Wesnousky et al. [1982] estimated intraplate strain rate from active faults data. Their 0 ¼ ðA3Þ results show that western Japan north of the MTL exhibits 2 01=l2 I WNW compression of 0.1–0.7 mm/yr. Subtracting this rate from our estimate of rigid plate motion with respect to the In order for the data covariance to be unity, the observation stable Eurasian craton gives a corrected rigid plate motion equation (A1) will be modified by near zero. This further confirms the hypothesis that western Japan is on the Eurasian plate, not on a separate d0 ¼ G0m þ e0 ðA4Þ microplate. where d d0 ¼ À1=2 ðA5Þ 7. Conclusion 2 0 [35] We derived the depth distribution of interplate coupling, the MTL slip rate, and rigid plate motion simul- G G0 ¼ À1=2 ðA6Þ taneously using the three-dimensional interseismic deforma- 2 D tion field obtained from GPS data. The results show that a BPTZ extends between 25 and 40 km depth at the plate interface. Interplate coupling does not steadily decrease E0 ¼ NðÞ0; I ðA7Þ within the BPTZ, but has an area where the reduction rate of interplate coupling is lower from 32 to 35 km depth. T À1 À1=2 À1=2 A8 This may suggest a three layer model, with a change in 2 ¼ 2 ¼ 2 ð Þ deformation mechanism or material there, in which the deeper region is more resistive to shear than the upper [39] Acknowledgments. We thank Bob King and Misha Kogan for a one. The results also show that vertical velocities are much horizontal velocity field with respect to a new reference frame, and the Geographical Survey Institute of Japan for data access. Reviews by John more sensitive to the interplate coupling than horizontal Beavan, Kosuke Heki, and an anonymous reviewer improved the manu- velocities. script. Some figures are created with the Generic Mapping Tools (GMT) ETG 5 - 10 AOKI AND SCHOLZ: DEFORMATION IN SW JAPAN

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