Interplate coupling and relative plate motion in the Tokai district, central Japan, deduced from geodetic data inversion using ABIC

whys. J. Int. (1993) 113,607-621 Interplate coupling and relative plate motion in the Tokai district, central Japan, deduced from geodetic data inversion using ABIC Shoichi Yoshioka,l* Tetsuichiro Yabuki? Takeshi Sagiya? Takashi Tada3 and Mitsuhiro Matsu'ura' 'Department of Earth and Planetary Physics, University of Tokyo, Tokyo 113, Japan 'Hydrographic Department, Maritime Safety Agency, Tokyo 104, Japan Geographical Sutvey Institute, Ibaraki 305, Japan Accepted 1992 October 12. Received 1992 September 28; in original form 1992 May 8 SUMMARY The spatial distribution of the strength of interplate coupling between the subducting Philippine Sea and overlying continental plates in the Tokai district, central Japan, was investigated in detail through the inversion analysis of geodetic data using Akaike's Bayesian Information Criterion (ABTC). The geodetic data used for the analysis are annual rates of level changes (1972-1984) and horizontal length changes (1977-1988), which presumably represent average crustal movements during the interseismic period. The result of the inversion analysis shows the existence of a strongly coupled region extending from 10 to 30 km in depth. The total seismic moment accumulated in this area since the last event (the 1854 Ansei earthquake) is roughly estimated to be 5.5 X Id7 dyne cm, which corresponds to M, = 7.8. The interplate coupling becomes weaker toward the shallower and deeper portions. This is consistent in general tendency with a rheological model inferred from petrological viewpoints. The strength of coupling also tends to decrease toward northeast over the west coast of Suruga Bay. The direction of plate convergence inferred from the inversion analysis is oriented N30"W. This is significantly different from the direction of relative plate motion between the Philippine Sea and Eurasian plates but concordant with that between the Philippine Sea and North American plates. Key words ABIC, Bayesian modelling, geodetic data inversion, interplate coupling, relative plate motion. 1 INTRODUCTION The Tokai district, central Japan, is located in a region attracting our interest in plate tectonics. The region is considered to be subject to interaction of three different plates: the Philippine Sea plate, the Eurasian plate, and the North American plate (Kobayashi 1983; Nakamura 1983). According to Sen0 (1977) and Minster & Jordan (1979), the oceanic Philippine Sea plate is subducting beneath the continental Eurasian and North American plates in the N W direction with a low dip angle at the Suruga and Sagami troughs (Fig. 1). At the northern tip of the Jzu peninsula, the Philippine Sea plate has been colliding with the 'Present address: Department of Theoretical Geophysics, University of Utrecht, Po Box 80.021, Budapestlaan 4, 3508 TA Utrecht, The Netherlands. continental plates since the Tertiary (Matsuda & Uyeda 1971; Sugimura 1972), leading to an active and complicated tectonic regime. In addition, volcanic activity is relatively high around the Izu peninsula, because the volcanic front related to the subduction of the oceanic Pacific plate beneath these three plates is passing through there with a strike of the N-S direction (Sugimura 1959). Historical documents show that large interplate earthquakes have repeatedly occurred along the Nankai trough with an average interval of about 120yr (e.g. Utsu 1974). The recent events which occurred in the Tokai and Kinki districts are the 1707 Hoei (M8.4), 1854 Ansei (M8.4), and 1944 Tonankai (M8.0) earthquakes. On the basis of the distributions of seismic intensity, co-seismic crustal movements, and the running height of excited tsunami waves, Ishibashi (1977, 1981) concluded that the faulting areas of

608 S. Yoshioka et al. regarded as a seismic gap, where tectonic stress to generate a large interplate earthquake has been accumulated since the 1854 Ansei earthquake. Since this urgent warning against the impending Tokai earthquake, spatially and temporally dense observations in various kinds, such as seismic activity, crustal movement, electrical resistivity, and hydrological and geochemical changes, have been conducted to detect premonitory phenomena of the Tokai earthquake, and further to predict its occurrence (e.g. Hamada 1992). Among the various kinds of observations geodetic data obtained through levelling, trilateration, and tidal observation would be useful to elucidate the process of stress accumulation for the occurrence of the Tokai earthquake in the complicated tectonic regime. Since the Suruga trough is located very close to the land area, there is a high possibility to detect the crustal movements related to the interplate coupling between the subducting Philippine Sea and overlying continental plates from these geodetic data. So far the strength of coupling at plate boundaries running along the Japanese islands has been estimated from geodetic data with a finite element method by many investigators (e.g. Bischke 1974; Shimazaki 1974; Smith 1974; Scholz & Kato 1978; Kato 1979; Sen0 1979; Miyashita 1987; Sat0 1988; Miura, Ishii & Takagi 1989; Yoshioka 1991). However, these previous studies are insufficient because of the 2-D and/or forward modelling. In the present study, we use a newly developed analytic inversion method (Yabuki & Matsu ura 1992) to tackle this problem, taking account of slip distribution on a 3-D realistic plate boundary. This enables us for the first time to elucidate the spatial distribution of the strength of interplate coupling and the direction of relative plate motion. Our present purpose is to estimate the strength of interplate coupling and the direction of relative plate motion in the Tokai district from geodetic data and to clarify their tectonic implications in central Japan. 0 Figure 1. Tectonic setting in and around Japan. (a) Map showing relative plate motions [modified from Kakimi (1991)l. EUR: Eurasian plate; NA: North American plate; PAC: Pacific plate; PHS: Philippine Sea plate. Relative plate motions are taken from Sen0 et al. (1987, 1989). The dashed lines indicate the hypothetical plate boundaries between EUR and NA (Kobayashi 1983; Nakaumura 1983). The tsunami genetic areas of the 1854 Ansei and 1944 Tonankai earthquakes are taken from Hatori (1974) and Omote (1948), respectively. (b) Detailed map of the Tokai, South Kanto district [the boxed region in (a)]. The shaded area indicates regions with height above loo0 m. the former two events covered the Nankai to Suruga troughs, while the faulting area of the last event did not reach the Suruga trough. Therefore, the area extending from off Omaezaki to the northern end of Suruga Bay can be 0 2 DATA AND THEIR TECTONIC IMPLICATIONS In order to grasp the spatial pattern of vertical crustal movements in the Tokai district, we compiled the first- and second-order levelling data during the period from 1972 to 1984, reported by Geographical Survey Institute of Japan (GSI). For the levelling data in each survey, we carried out readjustment so as to minimize the sum of observation errors for all closed loops, fixing a bench mark at Uchiura [Fig. 2(a)]. Comparing the compiled data at the same point for two different surveys, we obtain the level changes relative to Uchiura during the period. Since the time intervals of levelling are different route by route, we take the annual rates of level changes, assuming that the rates have been constant in time during the period. The calculated annual rates (Oi) at Uchiura, Yaizu, Omaezaki and Maisaka are given in the second column of Table 1. In order to obtain the absolute uplift rates at all bench marks, we link these data with tidal records. Kato & Tsumura (1979, 1983) have developed a method to evaluate absolute crustal movements from tidal records, and revealed long-term (1951-1982) vertical crustal movements at about 100 tide-gauge stations along the coastlines of the Japanese islands. In their analysis, although the effects of atmospheric

(a) o b s. c m/y r 0-1.0 x +1.0 f Interplate coupling from geodetic data inversion 609 Table 1. Annual rates of level changes at Uchiura, Yaizu, Omaezaki, and Maisaka. Location Oi(cm/yr) T(cm/yr) D,(cm/yr) V;.(cm/yr) Uchiura 0.000 0.027-0.113-0.086 Yaizu -0.524-1.102 0.001-1.101 Omaezaki -0.744-1.226 0.080-1.146 Maisaka 0.076 0.114 0.105 0.219 Oj: relative uplift rates at bench marks deduced from levelling data (Uchiura is fixed). T: absolute uplift rates at tide-gauge stations deduced from tidal records. 4: uplift rates at bench marks relative to the corresponding tide-gauge stations, deduced from supplementary levelling data. 6 (=T + Di): absolute uplift rates at bench marks deduced from tidal records. Negative values indicate subsidence. 1972.73-1976.77 Omaezaki -5 Q 70 20 30km Figure 2. Vertical crustal movements in the Tokai district. (a) Annual rates of absolute vertical movements at all bench marks during the period from 1972 to 1984. The octagons and crosses represent subsidence and uplift, respectively. The size of each mark is in proportion to the annual rate. The solid stars indicate the locations of the four tide-gauge stations; Uchiura, Yaizu, Omaezaki and Maisaka. (b) Contour map of cumulative vertical movements for the period from 1900 to 1973 [modified from GSI (1978)l. The reference point Numazu is fixed. (c) Contour map of cumulative vertical movements for the period from 1972-1973 to 1976-1977 [modified from GSI (1978)l. The reference point Numazu is fixed. pressure, seasonality, and regional sea-level changes were corrected, the estimated crustal movements may still include some effect of eustatic sea-level changes. The average uplift rates (7;) over the period from 1976-77 to 1982 at Uchiura, Yaizu, Omaezaki and Maisaka tide-gauge stations are given in the third column of Table 1. In the present study we assume that these values represent nearly absolute crustal movements at the four stations. The uplift rates (Di) at the four bench marks relative to the corresponding tide gauge stations can be also estimated by using data of a supplementary levelling route (the fourth column of Table 1). Thus we can obtain the annual rates (v.) of absolute crustal movements at the four bench marks by adding Di to as shown in the fifth column of Table 1. Finally, in order to obtain the absolute crustal movements at all bench marks, we determine the correction C so as to minimize the following quantity in the least-squares sense. S(C) = 4 i=l [y - (Oi - C)]? The calculated correction C is 0.231 cm yr- ', which should be subtracted from the relative uplift rates at all bench marks. In Fig. 2(a) we show the annual rates of absolute vertical crustal movements at all bench marks obtained on the basis of the above method. The octagons and crosses represent subsidence and uplift, respectively. Since earthquakes large enough to affect crustal movements did not occur during this period, the observed crustal movements are regarded as ones related to the stress accumulation during the interseismic period of the Tokai earthquake. From Fig. 2(a) we can find that the region along the western coast of Suruga Bay has been continuously subsiding through the interseismic period. At the northern end of Suruga Bay and near Omaezaki, the subsidence rate reaches almost 1 cm yr-'. In particular, the subsidence rate increases along the three levelling routes toward Omaezaki. The overall pattern of the subsidence rate has a tendency to decrease gradually toward the west in proportion to the distance from the Suruga trough, and an upheaval region appears in the northeastern extension of Lake Hamana. This may be related to the uplift of the Akaishi mountain range, whose upheaval rate has been fastest in the Japanese islands or the recent several decades (Dambara 1971). Comparing the pattern of vertical crustal movements for the period from 1972 to 1984 with those for the previous two periods (GSI 1978) shown in Figs 2(b) and (c), where a bench mark at Numazu is fixed, we can see that the overall features mentioned above are similar among them. In other words, we could say that the same tectonic force has been exerting

610 S. Yoshioka et al. over this area since the beginning of this century. However, the subsidence rate appears to increase for the recent period. In addition to the data of vertical crustal movements, we can use trilateration data during the period from 1977 to 1988 as an indicator of horizontal surface deformation. In contrast to the horizontal displacement data obtained through triangulation measurements, trilateration data have the advantage that they do not include systematic errors caused by the movements of reference points. Taking an temporal average over the period, we obtain the annual rates of sidelength changes as shown in Fig. 3(a). The dashed and solid lines denote contraction and extension, respectively, and their thickness represents the rate of contraction or extension normalized by the sidelength of 10 km. Most of the data indicate contraction, but some of large extension are also found. This suggests complicated horizontal surface deformation in the Tokai district. obs. (a) cm/ (yr*lokmm) In order to understand dominant strain fields more clearly, we show the principal axes of strain changes during the period from 1974-1977 to 1986-1988 (GSI 1990) in Fig. 3(b). The dashed and solid lines denote contraction and extension, respectively, of each triangular area. Contraction in the N-S to NW-SE direction appears to be predominant for the western half of this district, while the directions of contraction distribute randomly for the eastern half. The domination of extension is also detectable near Shizuoka. This might be related to the existence of the Irozaki- Shizuoka tectonic line (Mogi 1977) or the Sunzu fault (Tsueneishi & Sugiyama 1978), and relatively high seismic activity in this region (Yamazaki & Ooida 1979; Yoshida 1983; Aoki 1985). We employ the levelling and trilateration data shown in Figs 2(a) and 3(a) for the present inversion analysis. Total numbers of the levelling and trilateration data used here are 198 and 137, respectively. -1. 2 - --I -0.9 --- -0. 6 - -0. 3 --- -0. 3-0. 0 0. 0-0. 3 Figure 3. Horizontal surface deformation in the Tokai district. (a) Annual rates of side-length changes during the period from 1977 to 1988. The dashed and solid lines denote contraction and extension, respectively. Thickness of the line represents the annual rate of contraction or extension normalized by the sidelength of 10km. (b) The cumulative principal strains during the period from 1974-1977 to 1986-1988 [modified from GSI (1990)) The dashed and solid lines denote respectively contraction and extension of each triangular area. The numerals indicate the maximum shear strains (X1OV6), and the bracketed numerals indicate the annual rates of the area of each triangular region (xlo-6).

Interplate coupling from geodetic data inversion 61 1 Fipe 3. (Continued) 3 THE MODEL AND METHOD FOR INVERSION Now we describe our model and method to analyse the geodetic data. We consider the stress accumulation caused by interaction between the subducting Philippine Sea and overlying continental plates. The situation is schematically illustrated in Fig. 4. During an interseismic period, a region at an intermediate depth remains locked, while the shallower and deeper portions are decoupled, and a steady slip proceeds there. Then, as a result of the steady slip at the shallower and deeper portions, the tectonic stress accumulates in the locked region. Such a situation can be expressed as the superposition of a uniform steady slip over the whole plate boundary and a back slip in the locked region. The crustal deformation produced by the uniform steady slip has a relatively long wavelength, and its rate is small compared with the deformation rate due to the back slip (Matsu ura & Sat0 1989). Hence, neglecting the deformation due to the uniform steady slip, we may regard the crustal deformation in the interseismic period as the effect of the back slip in the locked region. In this study, in order to estimate the spatial distribution of back slip from geodetic data, we employ the inversion method newly developed by Yabuki & Matsu ura (1992). This method enables us to extract unbiased information from insufficient and inaccurate data. Here, we briefly describe the outline of the method. First, we determine the geometry of a curved plate boundary (model surface) from the information of microearthquake distributions. Once the geometry of the model surface is given, representing the distribution of back slip by the superposition of basis functions (bi-cubic B-splines) defmed on the model surface, we can obtain a set of linear observation equations; di = Hijaj + e, (2) i where di are observed deformation rates, aj are coefficients of the superposition of basis functions, ej are random errors, and Hjj are elastic response to a unit back slip at observation points. The response function Hjj can be calculated on the basis of the representation theorem of elastodynamics (Yabuki & Matsu ura 1992). Our goal is to find the best estimates of model parameters aj and reconstruct the back-slip distribution on the model surface. By the way, we have another sort of information about the back-slip distribution; that is, the spatial variation of back slip must be smooth in some degree because of the finiteness of stress accumulation in the locked region. To incorporate this sort of prior information into the observation equations, we introduce a measure of the roughness of back-slip distribution. In our notation, with the

612 S. Yoshioka et al. Continental / plate decoupled Continental plate &coupled locked Philippine plate Sea % Philippine Sea plate + plate Figure 4. Schematic diagram showing the back-slip model. The effects of locking at an intermediate depth (left) can be represented by the superposition of the effects of a uniform steady slip over the whole plate boundary (right top) and a back slip at the intermediate depth (right bottom). This diagram shows a special case; the rate of back slip is equal to the rate of relative plate motion, and so the locked portion is completely coupled. model parameters a,, it may be written as where Rp, are the elements of a coefficient matrix, whose concrete expressions are given in Yabuki & Matsu ura (1992). Using this quantity, we define a prior probability density function (PDF) of the model parameters. We assume a Gaussian distribution, N(0, aze), for the data errors ei and define a likelihood function of the model parameters for given data di. Combining the prior PDF and the likelihood function by using Bayes theorem, we can constuct a posterior PDF of the model parameters, which is called a Bayesian model. It should be noted that the Bayesian model has a flexibility in the selection of the relative weight of the two sorts of information. Then, our problem is to find the best estimates of the relative weight and the model parameters from observed data so as to minimize the quantity 1 + -5 z aprp9a9 CL P.9 (3) (4) with C,, = (E-l),,. (5) Here, the parameters uz and p2, which are called hyperparameters, control the structure of the Bayesian model. For the selection of the most appropriate values of the hyperparameters, we use Akaike s Bayesian Information Criterion (ABIC) proposed by Akaike (1980) on the basis of entropy maximization principle. Once the values of hyperparameters are given, we can determine the best estimates of model parameters so as to minimize the quantity in e-q. (4) and evaluate the covariance of estimation errors by using Jackson-Matsu ura s formula (Jackson & Matsu ura 1985). The model source region and the iso-depth contours of the upper boundary of the Philippine Sea plate, which has been obtained from the distribution of microearthquakes by Ishida (1992a), are shown in Fig. 5. Unlike the case of co-seismic faulting, where the source region can be determined from aftershock distributions, there is no a priori information to specify the coupled (back slip) region on the plate boundary. Hence, we take a sufficiently large model source region to avoid the artificial effect produced by limiting it. In the present analysis the outside of the model source region is assumed to be completely decoupled.

Interplate coupling from geodetic data inversion 613 36" N 35" N 36" N 137" E 138" E Figure 5. Iso-depth contours (in km) of the upper boundary of the Philippine Sea plate [modified from Ishida (1992a)l. The rectangle indicates the model source region. The shaded area indicates the area where the upper boundary of the Philippine Sea plate was determined from hypocentral distributions or high-velocity zones. The dashed lines and light shaded area denote uncertain results because of the sparse distribution of earthquakes. The thick broken lines and solid circles indicate respectively the volcanic front and main Quaternary volcanoes associated with the subduction of the Pacific plate. The large solid circles indicate volcanoes for which historical documents of eruptions exist. The eastern rim of the model source region is taken along the strike of the Suruga trough. We divide the model source region into 11 X 8 subsections and distribute 14 X 11 bi-cubic B-splines so that they cover homogeneously the whole region; the distribution of each component of back slip on the model surface is represented by the superposition of 14 X 11 bi-cubic B-splines with various amplitudes. Then our problem is to determine the two hyperparameters and the 308 model parameters from the 335 observed levelling and trilateration data. This is equivalent to determine the spatial distribution of back-slip vectors on the model surface. 4 RESULTS AND DISCUSSION 4.1 The inverted back-slip distribution and its tectonic implications Figure 6 shows the distribution of the back-slip motion of the overlying continental plate relative to the subducting oceanic plate, inverted from the annual rates of crustal movements. The areas with estimation errors larger than the estimated back-slip rates are shaded. The strongly coupled region with the back slip rate of about 4 cm yr-' is identified beneath Kakegawa to Omaezaki. Considering the convergence rate, 3.2 cm yr-' (Seno 1977) - 5.2 cm yr-' (Minster & Jordan 1979), between the Philippine Sea and Eurasian plates at the Suruga trough, we can say that the interplate coupling is very strong, indicating an effective strian build up for the forthcoming Tokai earthquake there. Incidentally, assuming that the back-slip rate has been constant in time since the 1854 Ansei earthquake, we can roughly estimate the total seismic moment accumulated in this region by the present. The seismic moment M, is generally defined by M, = pds (6) where p is the rigidity of the medium, and D is the fault slip averaged over a source area S. As the source area of the forthcoming Tokai earthquake we take the area with back slip rates greater than 3.0cmyr-I. Then the total seismic moment M, accumulated in this area is estimated as 5.5 X loz7 dyne cm-' with p = 3.0 X 10" dyne cm2, = 3.4 (cm yr-') X 139 (yr) = 473 cm, and S = 3.9 X cm'. The expected surface wave magnitude M, of the earthquake becomes 7.8, following the empirical relation (Aki 1972) log,, M, = lsm, + 16.0 (M, > 7). (7) Another feature is that the estimated back-slip rates tend to decrease towards the northeast over the west coast of Suruga Bay. This may be related to deceleration of the NW oriented convergence of the Philippine Sea plate due to the collision of the Izu peninsula with continental plates. Now we check the effect of uncertainty in the sea-level trends at the tide gauge stations on the result of inversion analysis. As is seem from Table 1, the differences, Oi - v, between the relative and absolute uplift rates at the four bench marks are not consistent with each other. Among them the absolute uplift rate at Uchiura is relatively small, probably due to its geographical condition. Hence, we may suppose that the tidal record at Uchiura is less contaminated by various oceanographic or meterological noises. Assuming the absolute uplift rate at Uchiura we recalculated the annual rates of vertical crustal movements and estimated the back-slip distribution by using them. The result shows a very similar pattern to that in Fig. 6, except that the back-slip rate is reduced by about 10 per cent as a whole. In addition, we checked the effect of difference in the configuration of the plate boundary. For the configuration of the upper boundary of the Philippine sea plate in the Tokai district, Yamazaki, Ooida & Aoki (1989) have proposed a somewhat different model. We estimated the back-slip distribution for this plate boundary model and obtained a similar pattern to that in Fig. 6, but the back-slip rate is reduced by about 30 per cent as a whole. These results indicate that the overall pattern of back-slip motion is not so affected by the uncertainty in the sea-level trends and the difference in the configuration of the plate boundary. Figure 7(a) shows change in the back-slip rates with distance along the plate boundary at the cross section A-B (Fig. 6). The error bars indicate the standard deviations of estimation errors. Although the estimation errors tend to increase in the shallower and deeper portions, we can find a

614 S. Yoshioka et al. Figure 6. The spatial distribution of back-slip vectors on the plate boundary, inverted from the annual rates of crustal movements. The back-slip motion of the overlying continental plate relative to the subducting oceanic plate is shown. The areas with estimation errors larger than the estimated back-slip rates are shaded. significant depth dependence of the strength of interplate coupling. The strongly coupled region extends from 10 to 30km in depth, and the strength of coupling tends to decrease toward the shallower and deeper portions. This would be the first case to succeed in revealing the depth dependence of interplate coupling from geodetic data. According to Shimamoto (1990), the plate boundary in the Tohoku district, northeast Japan, is divided into three different zones from petrological viewpoints: (1) a shallow decoupled zone down to the depth of about 30 km, (2) an intermediate seismogenic zone extending from about 30 to 60km in depth, and (3) a deeper aseismic slip zone [Fig. 7(b)]. The shallow zone (1) is weak and aseismic because of the constant supply on an enormous amount of H,O due to progressive metamorphism. On the other hand, the aseismic slip in the deeper zone (3) is related to the ductile property of rocks due to the high temperature there. Our result obtained from the geodetic data inversion is consistent in general tendency with this rheological model, but completely different in the depth extent of each zone. This discrepancy might be due to a difference in the age of subducting plate and thermal structure between the Tohoku and Tokai districts. In the Tokai district the young and hot Philippine Sea plate is subducting. In addition, the volcanic front with a strike of the N-S direction is passing through the eastern rim of the model region. Because of the heat supply from the subducting plate itself and the possible upwelling of diapir, the lower bound of the seismogenic zone in the Tokai district might be much shallower than that in the Tohoku district, where the low temperature associated with the subduction of the cold Pacific plate is expected.

Interplate coupling from geodetic data inversion 615 TOHOKU, JAPAN plsuc 7. The depth dependence of the strength of interplate coupling. (a) Change in back-slip rates with distance along the plate boundary at the cross section A-B in Fig. 6. The thick solid curve drawn from the point B toward the left bottom corner indicates the vertical cross-section of the upper boundary of the subducting Philippine Sea plate. (b) Schematic diagram showing the strength of interplate coupling in the Tohoku district, northeast Japan, inferred from petrological viewpoints [modified from Shimamoto (1990)l. T Japan trench; VF: volcanic front; AF wismic front; M: mechanical boundary zone. An interplate seismogenic zone extends from A to B (SSF: seismic-slip front). 4.2 Surface deformation rates calculated from the inverted back-slip model We show the annual rates of vertical movements calculated from the inverted back-slip model (Fig. 6) in Fig. 8(a) and the residuals obtained by subtracting them from the observed data [Fig. 2(a)] in Fig. 8(b). The observed data are fairly well explained by the inverted back-slip model except for some data in the westernmost and easternmost regions. Figures 9(a) and (b) show the annual rates of sidelength changes calculated from the inverted back-slip model and the residuals obtained by subtracting them from the observed data [Fig. 3(a)], respectively. Note that the thickness of lines in Fig. 9(a) does not correspond to that in

616 S. Yoshioka et al. (4 cal. c m/y r 0-1.0 x +l. 0 (4 cal. cm/ (yr*10km) --- -0. 4 - -0. 3 --- -0. 3 - -0. 2 - -0. 2 - -0. 1. _ - -0. 1-3. 0 0.0-0.1 c m/y r 0-1.0 x +l. 0 (b) obs. -cal. cm/ (yr*lokm) --- -1. 2 - -0. g --- -0. 9 - -0. 6 --- -0. 6 - -0. 3 --_ -0. 3-0. 0 0.0-0.3 Figure 8. Annual rates of vertical crustal movements. (a) Calculations from the inverted back-slip model in Fig. 6. (b) The residuals obtained by subtracting the calculations from the observations in Fig. 2(a). Figs 3(a) and 9(b). This is for better understanding of the overall feature of the calculated deformation field. The inverted model appears to trace the relatively strong NE-SW oriented contraction and NW-SE oriented extension at the easternmost region. The discrepancy in the rates of vertical movements at the easternmost region might be caused by this apparent fitness to the trilateration data' Another feature to be noticed is the relatively strong N-S to NW-SE oriented contraction in the northern half of the region. This is probably due to the effect of strong coupling at the depth of around 20 km [Fig. 7(a)]. In contrast, in the southern half, the magnitude of contraction is relatively Figure 9- Annual rates of sidelength changes. (a) Calculations from the inverted back-slip model in Fig. 6 (b) The residuals obtained by subtracting the calculations from the observations in ~ i 3(a). ~, small, reflecting the weaker coupling in shallower portion. On the whole the calculated horizontal deformation field is characterized by weak contraction. The complicated pattern

Interplate coupling from geodetic data inversion 617 of the observed horizontal deformation field is not well explained by the inverted back-slip model. This may be due to the complicated tectonic setting in the Tokai district. 4.3 The direction of back slip and its relation to platemotion models In addition to the magnitude of back slip, the present method of geodetic data inversion enables us to extract another important information, namely, the direction of back slip. In our model (Fig. 4) the opposite direction of back-slip motion represents the direction of relative plate motion in a steady state. Unlike the conventional methods to estimate relative plate motions, the present method is straightforward because of the use of geodetic data just above the plate boundary during an interseismic period. It should also be noted that the present analysis uses the data completely independent of those used in the former investigations. The result obtained through the present analysis is shown in Fig. 6. The direction of the back-slip vectors, which represents the direction of the motion of the subducting Philippine Sea plate relative to the overlying continental plate, is oriented N30"W f 9" on average over the region with back-slip rates greater than 3.0 cm yr-l. Comparing this result with the directions expected from the former plate motion models, namely, N54"W by Sen0 (1977) and N44"W by Minster & Jordan (1979), we can find a significant discrepancy among them. The direction of the back-slip vectors obtained for another plate boundary model (Yamazaki el al. 1989) mentioned in Section 4.1 is oriented N36"W f 3" on average over the region with back-slip rates greater than 2.5 cm yr-', indicating that the discrepancy is still significant. In Fig. lo(a) and (b) we show the fault-plane solutions of subcrustal earthquakes that occurred in the Tokai district during the period from 1978 to 1981 and the superposition of their P- and T-axes, respectively (Ukawa 1982). As can be seen from Fig. lo(a), strike-slip type events are dominant in this region. The distribution of T-axes in Fig. 10(b) indicates that the ENE-WSW oriented tension is dominant. Although the P-axes are scattered in dip, we can also recognize the NWN-SES oriented horizontal compression. The direction or horizontal compression deduced from the fault-plane solutions is significantly different from the direction of relative motion between the Pacific and Eurasian plates or the Philippine Sea and Eurasian plates, expected from the global plate motion model [Fig. 10(b)]. The direction (N30"W) of relative plate motion obtained from the present inversion analysis seems to be more suitable to explain the alignment of P-axes in the NWN-SES direction. The direction is also in good agreement with the average direction (N27"W) of the horizontal movements of most triangulation points in the Kanto-Tokai district (Fujii & Nakane 1982). Now we briefly describe the tectonic setting in central Japan in terms of relative plate motion. So far the oceanic Philippine Sea plate has been considered to be subducting beneath the continental Eurasian plate at the Nankai, Suruga and Sagami troughs in the NW direction (Seno 1977; Minster & Jordan 1979). On the contrary, the fault-slip motion of the 1923 Kanto earthquake (M7.Y) deduced from geodetic data inversion (Matsu'ura et al. 1980) indicates that the preferable direction of plate motion at the Sagami trough is N29"W. Kobayashi (1983) and Nakamura (1983) proposed a new hypothesis that northeast Japan, which has been considered to be a part of the Eurasian plate, belongs to the North American plate. The southwestern boundary between the Eurasian and North American plates is conjectured to be the Itoigawa-Shizuoka tectonic line (ISTL), which is a Quaternary active fault system located along the Fossa magna, the N-S oriented main graben structure. As shown in Fig. ll(a), if we take account of a relative motion between the Eurasian and North American plates at the ISTL, the contradiction for the relative plate motions at the Nankai, Suruga and Sagami troughs appears to be worked out. However, it is still controversial whether or not northeast Japan belongs to the North American plate (e.g. Ishibashi 1984, 1986; Sen0 1985; Ishida 1992b), because of no reliable information about relative plate motion at the ISTL. If the relative plate motions illustrated in Fig. ll(a) are correct, the direction of N30"W at the Suruga trough deduced from the present inversion analysis appears to be contradictory. Recently, Yoshioka et al. (1993) have investigated the interplate coupling at the Sagami trough by using the same inversion method and obtained nearly the same direction (N33"W f 8") of relative plate motion there. A natural interpretation of this coincidence is that the Philippine Sea plate is subducting beneath the same continental plate at both the Suruga and Sagami troughs. Judging from the direction of plate convergence, the North American plate would be preferable as the overlying continental plate. The assumption that the overlying continental plate is the North American plate leads to the conclusion that there is no relative plate motion at the ISTL. In fact, the directions of P-axes of fault-plane solutions do not necessarily support the existence of the relative plate motion at the ISTL (e.g. Tsukahara & Kobayashi 1991; Ishida 1992b). If this is the case, it is naturally conjectured that the plate boundary between the Eurasian and North American plates must be located somewhere on the western side of the ISTL. On the other hand, considering the fact that the fault-slip directions at the time of the 1944 Tonankai (M8.0) and 1946 Nankaido (M8.1) earthquakes (e.g. Kanamori 1972; Ando 1975; Yabuki & Matsu'ura 1992), and the direction of interplate coupling inferred from 3-D finite element analysis using geodetic data during an interseismic period (Yoshioka 1991) coincide with the direction of relative plate motion estimated by Sen0 (1977), the boundary between the Eurasian and North American plates must be located somewhere on the eastern side of the eastern rim of the fault region of the Tonankai earthquake. From these considerations we may conclude that our results obtained from the inversion analysis of geodetic data are consistent with the idea that the boundary between the Eurasian and North American plates is located along the Fukui- Neodani-Ise Bay Line (Iio 1989) or that the relative plate motion is consumed by slip motion along many faults located within the broad region between the Tsurugawan- Isewan Tectonic Line (TITL) and the ISTL (Seno 1985; Okada 1986) [Fig. ll(b)].

618 S. Yoshioka et al. (a) 3 5 O I 139'E (b):-:.:f+..* Range of the strike of subcrustal seismic zone N p-axis T-axis Subcrustal Earthquakes Figure 10. Tectonic stress field in the Tokai district, central Japan, inferred from the focal mechanisms of subcrustal events. (a) Focal mechanisms of subcrustal events plotted on the lower hemisphere by equal area projection [after Ukawa (1982)) (b) P- and T-axes of the subcrustal events plotted on the lower hemisphere by equal area projection [modified from Ukawa (1982)) The open and solid circles indicate the P- and T-axes, respectively. The two stippled arrows show the directions of motion of the Philippine Sea plate (PH) and the Pacific plate (PC) relative to the Eurasian plate (EU). The solid arrow indicates the direction of plate convergence deduced from the geodetic data inversion. The azimuthal range of the strike of the subcrustal seismic events is also indicated. 5 CONCLUSIONS We have investigated the spatial distribution of the strength of interplate coupling and the direction of relative plate motion in the Tokai district through the inversion analysis of geodetic data using ABIC. Significant results obtained here are as follows: (1) a strongly coupled region extending from 10 to 30 km in depth is identified. The maximum back slip rate reaches 4.0 cm yr-' beneath Kakegawa to Omaezaki, indicating an effective strain build up for the forthcoming

Interplate coupling from geodetic data inversion 61 9 Tokai earthquake there. The total seismic moment accumulated in this region since the 1854 event is roughly estimated to be 5.5 X loz7 dyne cm, which corresponds to M, = 7.8. The strength of coupling tends to decrease toward the shallower and deeper portions. This is consistent in general tendency with the interplate coupling model proposed from petrological viewpoints. The strength of coupling also appears to decrease toward northeast over the west coast of Suruga Bay. (2) The results of the inversion analysis show that the direction of plate convergence at the Suruga trough is N30"W. This may indicate that the continental plate overlying the Philippine Sea plate at the Suruga trough is not the Eurasian plate but the North American plate. km ACKNOWLEDGMENTS 3'7' (bl N 136' E 131' E 138' E I I F / Legend Halo 'Tect;: Actlve fault lofrrred Block Bouodar We are grateful to Drs Katsuhiko Ishibashi, Takao Eguchi, Takashi Miyatake and Yoshihisa Iio for their valuable comments. We also thank two anonymous reviewers and Prof. Brian Kennett for their helpful suggestions. We used HITAC S-820/80 and HITAC M-680H computer systems at the Computer Center of Tokyo University and the Earthquake Prediction Data Center of the Earthquake Research Institute, University of Tokyo. This research was supported by grants for the Japanese Ministry of Education, Science and Culture (No. 02952101). 36' N 35' N 5 Figure 11. Tectonic setting in central Japan. (a) Relative plate motions in and around the south Kanto-Tokai district [modified from Ishibashi (1984)l. EUR: Eurasian plate; NAM: North American plate; PHS: Philippine Sea plate. The open arrows indicate the directions of relative plate motions calculated from the global plate motion model proposed by Minster & Jordan (1978, 1979). The numerals indicate the relative velocity in cmyr-'. The solid arrows indicate the relative plate motion at the Suruga trough (this study) and the Sagami trough (Yoshioka et al. 1993), deduced from the geodetic data inversion. (b) Distributions of active faults, tectonic lines, and inferred block boundaries in central Japan [modified from Yamada, Teraoka & Hata (1982); Sangawa, Sugiyama & Kinugasa (1983); Kato & Sugiyama (1985); and Kanaori, Kawakami & Yairi (1992)). TITL: Tsurugawan-Isewan Tectonic Line; FNBB: Fukui-Neodani Block Boundary; MABB: Miboro-Atera Block Boundary; NSBB: Nekomata-Sakaitoge Block Boundary. MTL and ISTL indicate the Median Tectonic Line and the Itoigawa-Shizuoka Tectonic Line, respectively. [I REFERENCES Akaike, H., 1980. Likelihood and the Bayes procedure, in Bayesian Statistics, pp. 143-166, eds. Bernardo, J. M., DeGroot, M. H., Lindley, D. V. & Smith, A. F. M., University Press, Valencia, Spain. Aki, K., 1972. Scaling law of earthquake source time-function, Geophys. J. R. astr. Soc., 31, 3-25. Ando, M., 1975. Source mechanisms and tectonic significance of historical earthquakes along the Nankai trough, Japan, Tecronophysics, 27, 119-140. Aoki, H., 1985. Seismic activity and tectonics in the Tokai district, Earth Mon. 7, 159-166 (in Japanese). Bischke, R. E., 1974. A model of convergent plate margins based on the recent tectonics of Shikoku, Japan, J. geophys. Res., 79, 4845-4857. Dambara, T., 1971. Synthetic vertical movements in Japan during the recent 70 years, J. Geod. Soc. Japan, 17, 100-108 (in Japanese with English abstract). Fujii, Y. & Nakane, K., 1982. Horizontal crustal movement in Kanto-Tokai district (IV)(V)-Damage of triangulation station mark and result of calculated displacement vectors, J. Geod. Soc. Japan, 28, 29-40 (in Japanese with English abstract). Geographical Survey Institute of Japan, 1978. Crustal movements in the Tokai district, Rep. Coord. Comm. Earthq. Pred., 19,%-99 (in Japanese). Geographical Survey Institute of Japan, 1990. Crustal movements in the Tokai district, Rep. Coord. Comm. Earthq. Pred., 44, 240-249 (in Japanese). Hamada, K., 1992. Present state of earthquake prediction system in Japan, in Earthquake Prediction, pp. 33-69, eds Dragoni, M. & Boschi, E. Hatori, T., 1974. Sources of large tsunamis in southwest Japan, &in, 27,lO-24 (in Japanese). Iio, Y., 1989. The plate boundary between southwest Japan and northeast Japan, and the Fukui earthquake, Earth Mon. 11, 109-119 (in Japanese),

620 S. Yoshioka et al. Ishibashi, K., 1977. Re-examination of a great earthquake expected in the Tokai district, central Japan-Possibility of the Suruga Bay earthquake, Rep. Coord. Comm. Earthq. Pred., 17, 126-132 (in Japanese). Ishibashi, K., 1981. Specification of a soon-to-occur seismic faulting in the Tokai district, central Japan, based upon seismotectonics, in Earthquake Prediction, Maurice Ewing Ser., 4, 297-332, eds Simpson, D. W. & Richards, P. G., Am. Geophys. Un., Washington, DC. Ishibashi, K., 1984. The plate movements in and around the southern part of the Fossa Magna, Earth Mon. 6, 61-67 (in Japanese). Ishibashi, K., 1986. Theorem that the northeast Japan is a part of the North American plate and that the southwest Japan is moving toward the east, Earth Mon. 8,762-767 (in Japanese). Ishida, M., 1992a. Geometry and relative motion of the Philippine Sea plate and Pacific plate beneath the Kanto-Tokai district, Japan, J. geophys. Res., 97,489-513. Ishida, M., 1992b. Seismic activity in the Kanto-Tokai district, Earth Mon. (Special Issue) 4, 128-133 (in Japanese). Jackson, D. D. & Matsu ura, M., 1985. A Bayesian approach to nonlinear inversion, J. geophys. Res., 90,581-591. Kakimi, T., 1991. Earthquakes in and around the Japanese Islands, Chapter 5, pp. 145-175, ed. Hagiwara, T., Kashima Publisher (in Japanese). Kanamori, H. 1972. Tectonic implications of the 1944 Tonankai and the 1946 Nankaido earthquakes, Phys. Earth planet. Interiors, 5, 129-139. Kanaroi, Y., Kawakami, S. & Yairi, K., 1992. The block structure and Quaternary strike-slip block rotation of central Japan, Tectonics, 11, 47-56. Kato, H. & Sugiyama, Y., 1985. Kanazawa Neotectonic Map Ser., Sheet 10, Geological Survey of Japan, Tsukuba. Kato, T., 1979. Crustal movements in the Tohoku district, Japan, during the period 1900-1975, and their tectonic implications, Tectonophysics, 60, 141-168. Kato, T. & Tsumura, K., 1979. Vertical crustal movements in Japan as deduced from tidal records (1951-1978), Bull. Earthq. Res. Inst., Tokyo Univ., 54, 559-628 (in Japanese with English abstract). Kato, T. & Tsumura, K., 1983. Vertical crustal movements in Japan as deduced from tidal records (1951-August, 1982), Rep. Coord. Comm. Earthq. Pred., 29, 368-380 (in Japanese). Kobayashi, Y., 1983. Incipient of subduction of a plate, Earth Mon. 5,510-514 (in Japanese). Matsuda, T. & Uyeda, S., 1971. On the Pacific-type orogeny and its model-extension of the paired belts concept and possible origin of marginal seas, Tectonophysics, 11, 5-27. Matsu ura, M., Iwasaki, T., Suzuki, Y. & Sato, R., 1980. Statistical and dynamical study on faulting mechanisms of the 1923 Kanto earthquake, J. Phys. Earth, 28, 119-143. Matsu ura, M. & Sato, T., 1989. A dislocation model for the earthquake cycle at convergent plate boundaries, Geophys. J. Int., %, 23-32. Minster, J. B. & Jordan, T. H., 1978. Present-day plate motions, J. Geophys. Res., 83, 5331-5354. Minster, J. B. & Jordan, T. H., 1979. Rotation vectors for the Philippine Sea and Rivera plates (abstract), EOS Trans. Am. Geophys. Un., 60, 958. Miura, S., Ishii, H. & Takagi, A., 1989. Migration of vertical deformations and coupling of island arc plate and subducting plate, in Slow deformation and Transmission of Stress in the Earth, pp. 125-138, eds Cohen, S. C. & Vanikk, P., Geophys. Monogr., Ser., Vol. 49. Miyashita, K., 1987. A model of plate convergence in southwest Japan, inferred from levelling data associated with the 1946 Nankaido earthquake, J. Phys. Earth, 35, 449-467. Mogi, K., 1977. An interpretation of the recent tectonic activity in the Izu-Tokai District, Bull. Earthq. Res. Inst., Tokyo Univ., 52, 315-331 (in Japanese with English abstract). Nakamura, K., 1983. Possible nascent trench along the eastern Japan Sea as the convergent boundary between Eurasian and North American plates, Bull. Earthq. Res. Inst., 58, 711-722 (in Japanese with English abstract). Okada, A., 1986. Active faults in central Japan and the problem of the plate boundary, Earth Mon. 8, 756-761 (in Japanese). Omote, S., 1948. On the central area of seismic sea waves, Bull. Earthq. Res. Inst., Tokyo Univ., 25, 15-19. Sangawa, A., Sugiyama, Y. & Kinugasa, Y., 1983. Kyoto Neotectonic Map Ser., Sheet 11, Geological Survey of Japan, Tsukuba. Sato, K., 1988. Stress and displacement fields in the northern Japan island arc as evaluated with three-dimensional finite element method and their tectonic interpretations, Tohoku, Geophys. J., 31, 57-99. Scholz, C. H. & Kato, T., 1978. The behavior of a convergent plate boundary: crustal deformation in the South Kanto district, Japan, J. geophys. Rex, 83,783-797. Seno, T., 1977. The instantaneous rotation vector of the Philippine Sea plate relative to the Eurasian plate, Tectonophysics, 42, 209-226. Seno, T., 1979. Intraplate seismicity in Tohoku and Hokkaido and large interplate earthquakes: a possibility of a large interplate earthquake off the southern Sanriku coast, northern Japan, J. Phys. Earth, 27, 21-51. Seno, T., 1985. Is northern Honshu a microplate? Tectonophysics, 115, 177-196. Seno, T., Moriyama, T., Stein, S. Woods, D. F., Demets, C. R., Argus, D. & Gordon, R., 1987. Redetermination of the Philippine Sea plate motion (abstract), EOS Trans. Am. Geophys. Un. 68, 1474. Seno, T., Moriyama, T., Stein, S. Woods, D. F. & Demets, C. R., 1989. Redetermination of the Philippine Sea plate motion based on the final result of NUVELl- (abstract), Abstr., Seism. SOC. Japan, 1,50 (in Japanese). Shimamoto, T., 1990. Deformation mechanisms and rheological properties of fault rocks in the strength-peak regime, Extended Abstr., International Symposium on Earthquake Source Physics and Earthquake Precursors, 28-31. Shimazaki, K., 1974. Pre-seismic crustal deformation caused by an underthrusting oceanic plate, in eastern Hokkaido, Japan, Phys. Earth planet. Interiors, 8, 148-157. Smith, A. T., 1974. Time-dependent strain accumulation and release at island arcs: implications for the 1946 Nankaido earthquakes, PhD thesis, Massachusetts Institute of Technology, Cambridge. Sugimura, A., 1959. Geographische verteilung der characterstendenzen des magmas in Japan, Kazan, 4, 77-103 (in Japanese with German abstract). Sugimura, A., 1972. The plate boundary in and around the Japanese islands, Kagaku, 42,192-202 (in Japanese). Tsukahara, H. & Kobayashi, Y., 1991. Crustal stress in the central and western parts of Honshu, Japan, Zisin, 44, 221-231 (in Japanese with English abstract). Tsuneishi, Y. & Sugiyama, Y., 1978. Sunzu fault across the Suruga bay, Rep. Coord. Comm. Earthq. Pred., 20, 138-141 (in Japanese). Ukawa, M., 1982. Lateral stretching of the Philippine Sea plate subducting along the Nankai-Suruga trough, Tectonics, 1, 543-571. Utsu, T., 1974. Space-time pattern of large earthquakes occurring off the Pacific coast of the Japanese islands, J. Phys. Earth, 22, 325-342. Yabuki, T. & Matsu ura, M., 1992. Geodetic data inversion using a Bayesian information criterion for spatial distribution of fault slip, Geophys. J. Int., 109, 363-375. Yamada, N., Teraoka, Y. & Hata, M. M. (chief eds), 1982.