A MODEL OF PLATE CONVERGENCE IN SOUTHWEST JAPAN, INFERRED FROM LEVELING DATA ASSOCIATED WITH THE 1946 NANKAIDO EARTHQUAKE

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1 J. Ph_vs. Earth, 35, , 1987 A MODEL OF PLATE CONVERGENCE IN SOUTHWEST JAPAN, INFERRED FROM LEVELING DATA ASSOCIATED WITH THE 1946 NANKAIDO EARTHQUAKE Kaoru MIYASHITA Department of Earth Sciences, Ibaraki University, Mito, Japan (Received March 12, 1987; Revised February 8, 1988) We propose a kinematic model of plate convergence at the Nankai trough, a convergent boundary between the Philippine Sea and Asian plates. By using a twodimensional finite element technique, we take account of some structural inhomogeneities of the crust and upper mantle; the Philippine Sea plate is subducting into the asthenosphere underlying the anomalously thin Asian plate, where the plate boundary is coupled tightly in the shallower portion but loosely in the deeper. The model is inferred from preseismic, coseismic, and postseismic changes in surface elevation associated with the 1946 Nankaido earthquake (M=8.2). These changes are precisely estimated from the first-order leveling data ( ) by using an epoch reduction method. The preseismic seaward tilt can be interpreted by a steady state subduction of the Philippine Sea plate with a convergence rate of 4.5 cm/yr. The coseismic surface elevation change is well explained by a low-angle thrust faulting with an average shear stress drop of 2.0 MPa; although the faulting propagates along a lower portion of the plate boundary, it extends upward to the earth's surface branching away from the boundary at a depth of 22 km. The postseismic surface movements are interpreted by superposition of the viscoelastic response to the coseismic faulting and the effect of the steady state subduction of the Philippine Sea plate. In particular, the viscoelastic response of the loosely coupled part of the plate boundary is the underlying mechanism of the postseismic uplift localized in the coseismically subsided region. If the steady state subduction of the Philippine Sea plate continues for 150 yr, the shear stress averaged over the fault plane is found to amount to 2.0 MPa, which is sufficiently high to cause a major subduction earthquake. Hence, we can predict that the cyclic process of stress accumulation and release at the Nankai trough can be repeated every 150 yr. 1. Introduction The 1946 Nankaido earthquake (M=8.2) is one of the largest earthquakes which occurred in southwest Japan (Fig. 1). Several fault models of this earthquake 449

2 450 K. MIYASHITA Fig. 1. Location map of the Shikoku district, southwest Japan. Inset shows the tectonic setting around Japan. Solid triangles in line represent the axis of the Nankai trough. Rectangles and a mechanism diagram indicate the surface projection of the fault plane of the 1946 Nankaido earthquake (ANDO, 1982), and the P-wave nodal plane solution of the earthquake (KANAMORI, 1972), respectively. have been proposed to explain seismological and/or geodetic data (FITCH and SeHoLz, 1971; KANAMORI, 1972; ANDO, 1975, 1982). As pointed out by these authors, the 1946 Nankaido earthquake can be interpreted in terms of the low-angle thrust faulting at the Nankai trough, a convergent boundary between the Philippine Sea and Asian plates. We can well interpret the surface deformation at the time of a major earthquake at the convergent plate boundary by using elastic dislocation theory. However, we have not yet well understood the mechanisms responsible for the surface deformations before and after it. Undoubtedly, it is necessary to clarify such mechanisms not only for understanding of the plate convergence process but also for prediction of the occurrence of major earthquakes at the plate boundary. The 1946 Nankaido earthquake is probably the best example for studing the mechanisms stated above. For this earthquake, we can use a geodetic data set about preseismic, coseismic, and postseismic leveling changes. The data set has been obtained by the repetition of first-order leveling surveys since the 1890's by the Military Land Survey Department and the Geographical Survey Institute of Japan. Using the geodetic data covering such a long term, we can investigate quantitatively

3 A Model of Plate Convergence in Southwest Japan 451 the mechanisms of preseismic, coseismic, and postseismic changes in surface elevation. The models of mechanism for the time-dependent surface movement after a major underthrust earthquake can be classified into two groups: (1) aseismic slip on a lower part of the coseismic fault plane and/or on its downward extension (FITCH and SCHOLZ, 1971; KASAHARA, 1975; BROWN et al., 1977; SCHOLZ and KATO, 1978), and (2) stress relaxation in the asthenosphere following an earthquake occurrence (NUR and MAVKO, 1974; MELOSH, 1976; THATCHER and RUNDLE, 1979; MATSU'URA et al., 1981; COHEN, 1982; MATSU'URA and IWASAKI, 1983). The present study will adopt a model which is based on stress relaxation not only in the asthenosphere but also in another viscoelastic region. Generally, the viscoelastic response to earthquake faulting depends on a rheological structure model of the crust and upper mantle as well as a fault model. Now, the fault model can be well determined from seismological and geodetic data on the basis of elastic dislocation theory. Unfortunately, there have remained many problems unsolved on the rheological structure of the crust and upper mantle. Most of the studies on such problems have assumed simplified structural models, for example, an elastic plate overlying a viscoelastic half space (NUR and MAVKO, 1974; RUNDLE and JACKSON, 1977; THATCHER and RUNDLE, 1979, 1984), and a multilayered elastic medium with an intervening viscoelastic layer (MATSU'URA et al., 1981; COHEN, 1982; MATSU'URA and IWASAKI, 1983). However, these layered structure models are inadequate for dealing with the viscoelastic deformation near the convergent plate boundary. This is because structural inhomogeneities of the crust and upper mantle are very remarkable in such a region. MIYASHITA (1983) has shown that" the patterns of viscoelastic displacement fields are significantly affected by the horizontal structural inhomogeneities: the presence of an oceanic slab subducting into the asthenosphere, and the difference in thickness between the oceanic and continental plates. In this study, first, we will show surface elevation changes before, at, and after the 1946 Nankaido earthquake, which are obtained from the first-order leveling data during the period of with the help of an epoch reduction method. Secondly, we will present a mechanical model to interpret the observed elevation changes at the preseismic, coseismic, and postseismic stages of the 1946 Nankaido earthquake. The surface displacements due to the model are computed by using the two-dimensional finite element technique (MIYASHITA, 1981, 1983). 2, Observed Data 2.1 An epoch reduction method In order to estimate the surface elevation changes at the preseismic, coseismic, and postseismic stages of the 1946 Nankaido earthquake (Fig. 1), we apply an epoch reduction method (MIYABE, 1955; HAYASHI, 1969) to the first-order leveling data during the period of In Japan, it has generally taken several years

4 452 K. MIYASHITA or more to survey completely the first-order leveling network covering the area deformed by a major earthquake. Hence, it would often be found that the time interval between successive surveys differs with each leveling route, and its difference becomes very large between the leveling routes which are separated far away in the network. We cannot neglect the effect of such a difference in observation time interval when discussing surface elevation changes during certain time intervals. By using an epoch reduction method, HAYASHI (1969) has estimated the vertical surface movements in Japan during the standardized periods of and , respectively. In the following, we will outline the epoch reduction method used in this study. We consider the change in height difference between a pair of adjoining bench marks with time. Let y_i(i=0,1,...,m) be the height difference at the time t_i(i= 0, 1,., m). We suppose that the height difference varies linearly with time during each time interval. Then, a reduced height difference Y_j at an arbitrary standard epoch T_i(t_<i-1><T_j<t_i) can be estimated as where v_i= (y_i y_<i-1>)/(t_i y_<t-1>). However, the present study assumes that the reduced height differences just before and after the earthquake are obtained by extrapolating the observed preseismic and postseismic height differences, y_k and yk+1, with the height difference rates, v_k and v_<k+2>, respectively. In Fig. 2, a schematic diagram for estimating the reduced height differences from observations is shown. Figure 2 also shows how to estimate the height difference which could not be determined because of re-installation of a bench mark at a certain time, e.g., t_6 in the figure. In the case of Fig. 2, the height difference, y_6, is assumed to have changed linearly with time during the period between t_5 and t_6 at an average rate of those before and after the period, i.e., v_6=(v_5+v_7)/2. Next, we adjust the reduced change in height difference during a standardized period on the basis of the conventional net adjustment calculation. Let h_i and z_i(i= 1,...,l) be an adjusted and an original value of the reduced change in height difference, respectively, for i-th pair of adjoining bench marks along a leveling route between junction bench marks, p and q. We have where H_k (k =p, q) is an adjusted value of the change in height difference between k-th junction bench mark and a reference point in the net adjustment calculation, s_i denotes a distance between i-th pair of adjoining bench marks, and S is a distance between the junction bench marks. 2.2 Preseismic, coseismic, and postseismic elevation changes Applying the epoch reduction method, we evaluate the change in surface elevation associated with the 1946 Nankaido earthquake for each standardized time interval of (preseismic), (coseismic), (early

5 A Model of Plate Convergence in Southwest Japan 453 Fig. 2. Schematic diagram for estimating a reduced change in height difference during a standardized period from observations. Surface elevation changes during standardized preseismic (t=t_2-t_1), coseismic (t=t_3-t_2), and postseismic (t = T_4-T_3;T_5-T_4) time intervals are defined as Yi-Y_<i-1> (i= 2, 3, 4, and 5), respectively. postseismic), and (late postseismic). Figure 3 shows the first-order leveling network consisting of three circuits and four junction bench marks in the Shikoku district. The junction bench mark at Zentsuji (1) is tentatively fixed to be a reference point in the net adjustment calculations. The surface elevation changes at the other three junction bench marks (2, 3, and 4) relative to the reference point of Zentsuji are summarized in Table 1. The surface elevation changes along the leveling routes, A, B, C, and D in Fig. 3 are shown in Figs. 4 to 7, where they are projected on the vertical planes along the corresponding profiles A, B, C, and D in Fig. 3. These profiles are taken to be perpendicular to the fault strike, N70 E of the 1946 Nankaido earthquake, which is nearly parallel to the Nankai trough axis (Fig. 1). The preseismic ( ) surface elevation changes (Figs. 4(a), 5(a), 6(a), and 7(a)) are characterized by trenchward tilting, which is remarkable within a distance of about 200 km from the Nankai trough. This result indicates that Muroto subsided at an average rate of 8.1 mm/yr with respect to Zentsuji during the preseismic period (Figs. 4(a) and 5(a)). The coseismic surface elevation changes in the eastern part of Shikoku (Figs. 4(b) and 5(b)) show some typical features of the coseismic surface deformation due to low-angle thrust faulting, such as localized uplift on a hanging wall side and

6 454 K. MIYASHITA Fig. 3. First-order leveling network in the Shikoku district, consisting of three circuits and four junction bench marks (numbers with solid circles). In Fig. 4-7, elevation changes along the four leveling routes, A, B, C, and D (dashed or solid heavy lines) are projected onto the corresponding profiles, A, B, C, and D, respectively, each of which is perpendicular to the fault strike of N70 E. Hatched rectangle (RAN2) indicates the surface projection of the western part of the fault plane, dimensions of which are 150 ~70 km2 (ANno, 1982). Table 1. Surface elevation changes at the junction bench marks. subsidence behind the uplift region. The observed uplift takes a maximum at Muroto, where the uplift amounts to 1,066 mm with respect to Zentsuji. However, the maximum uplift due to the earthquake faulting may be quite larger than that at Muroto, because Muroto is located about 20 km apart from the upper margin of the coseismic fault plane (Fig. 3). On the other hand, the maximum subsidence, whose location coincides with that of the onset of the preseismic trenchward tilting, amounts to about 600 mm with respect to Zentsuji (Figs. 5(b) and 6(b)). These

7 A Model of Plate Convergence in Southwest Japan 455 features have been explained approximately by the compound fault model shown in Fig. 1 (ANDO, 1982), where a western part of the fault dips 20 toward the northwest and has a reverse and right-lateral slip of 6 m. The most notable feature of the postseismic surface elevation changes is the uplift localized in the coseismically subsided region. This uplift is remarkable in the early postseismic period ( ) (Figs. 4(c), 5(c), and 6(c)). The uplift takes a maximum value near the position of the maximum coseismic subsidence. The maximum rate of the uplift amounts to about mm/yr with respect to Zentsuji, and is about three times as large as that of the preseismic subsidence (8.1 mm/yr at Muroto). This evidence suggests that the mechanism responsible for the postseismic uplift must closely be related with the coseismic faulting. Surface elevation changes in the late postseismic period ( ) in the eastern part of Shikoku (Figs. 4(d) and 5(d)) show that the uplift in the coseismically subsided region continued during this period. However, the maximum rate of the uplift (about 10 mm/yr) becomes less than a half of that in the early postseismic period. On the other hand, the late postseismic elevation change in the western part of Shikoku (Fig. 6(d)) indicates a pattern similar to the preseismic elevation change rather than the early postseismic one. This elevation change suggests that there may be some differences in the mechanism of postseismic elevation change between the eastern and the western part of Shikoku. Such a regional difference as stated above is also suggested by the one-month aftershock distribution (Moo', 1968); the aftershock area did not extend beyond the eastern part of Shikoku. Taking account of the regional difference in the mechanism of stress accumulation and release, we need at least two different models for interpreting the time-dependent surface elevation changes in the eastern and western parts of Shikoku. In the numerical simulations in the following section, however, our concern is restricted to the surface elevation changes in the estern part of Shikoku, especially those along the profile B (Fig. 3). Characteristics of the changes along the profile B are summarized in Fig. 8, where the average rates of preseismic, early postseismic, and late postseismic elevation changes are compared. 3. A Numerical Model of Plate Convergence 3.1 A structural model of the crust and upper mantle Figure 9 shows a two-dimensional structural model of the crust and upper mantle along the profile B, perpendicular to the Nankai trough axis. We use this structural model to compute the surface displacements associated with the process of stress accumulation, release, and relaxation at the convergent plate boundary by applying the two-dimensional finite element method (MIYASHITA, 1981, 1983). The investigations on explosion seismic observations, gravity anomalies, heat flow, and dispersion of surface waves (YosHII et al., 1974; YosHil, 1979; KAMINUMA, 1966) suggest that the Asian plate in southwest Japan is quite thinner than the lithospheric plate with an ordinary thickness of about 70 km. In this study, the Asian plate is

8 Fig. 4. Surface elevation changes, plotted against distances from the Nankai trough along the profile A in Fig. 3: (a) preseismic ( ), (b) coseismic ( ), (c) early postseismic ( ), and (d) late postseismic ( ) changes. Fig. 5. Surface elevation changes along the profile B in Fig. 3.

9 A Model of Plate Convergence in Southwest Japan 457 Fig. 6. Surface elevation changes along the profile C in Fig. 3. Fig. 7. Surface elevation changes along the profile D in Fig. 3.

10 458 K. MIYASHITA Fig. 8. Average rates of the surface elevation changes during the preseismic (solid triangles), early postseismic (open squares), and late postseismic (solid squares) periods, plotted against distances from the Nankai trough along the profile B in Fig. 3 (upper frame). Coseismic change in surface elevation along the profile B (lower frame). determined to have a thickness of 32 km. On the other hand, the configuration of the Philippine Sea plate subducting into the asthenosphere is determined on the basis of the studies on seismic velocity structure (HIRAHARA, 1981), distribution of earthquake hypocenters (MIZOUE, 1976), and earthquake mechanisms (SHIONO, 1977; ANDO, 1975, 1982). The Philippine Sea plate with a thickness of 55 km starts to subduct at a very shallow angle at the Nankai trough. At a distance of 200 km from the Nankai trough, the upper surface of the oceanic plate reaches the bottom of the continental plate of 32 kni thick, and descends further into the asthenosphere at a dip angle of 26 It has been shown that in the Japanese Islands most of the crustal earthquakes with a compression axis normal to the trench'axis have occurred at depths shallower than the Conrad depth (ICHIKAWA, 1971; YosHi, 1979). This suggests that the intact elastic coupling is applicable only to the upper part of the entire boundary between the continental and oceanic plates. The present study assumes that the lower part of the plate boundary is coupled very loosely. The loosely coupled part of the plate

11 A Model of Plate Convergence in Southwest Japan 459 Fig. 9. Two-dimensional structural model of the crust and upper mantle along the profile B, perpendicular to the Nankai trough in southwest Japan (Fig. 3). Hatched region represents the loosely coupled part of the plate boundary, which is modeled by a viscoelastic thin layer of low rigidity and low viscosity. Heavy solid line with double arrows shows the two-dimensional view of the fault plane of the 1946 Nankaido earthquake. A series of line segments with arrowheads indicates a velocity distribution relating to the steady state subduction of the Philippine Sea plate. boundary is modeled by a thin layer of low rigidity and low viscosity (hatched area in Fig. 9). The thickness of the thin boundary layer is taken to be 500 m, the rigidity about 1/10 of that of the surrounding elastic plate, and the viscosity 7.0 ~10^<17> Pa Es. The asthenosphere underlying the oceanic and continental elastic plates has a viscosity of 2.0 ~10^<19> Pa s, and extends to a depth of 260 km. In this study, rheological properties of the viscoelastic materials are assumed to be elastic for confining pressure, and Maxwell fluid for stress deviation. Material properties of the structural model used here are summarized in Table Preseismic model The preseismic surface elevation change in Fig. 8 can be explained in terms of a steady state subduction of the Philippine Sea plate, accompanied with downward dragging of the oceanic side of the Asian plate. This subduction process can be considered as the underlying process of stress accumulation at the convergent plate boundary. The steady state subduction of the Philippine Sea plate is modeled as follows: the motion of the Philippine Sea plate relative to the remote boundaries

12 460 K. MIYASHITA Table 2. Material properties of the structural model of the crust and upper mantle. with zero-displacement is given by assigning a distribution of subduction velocity along its leading edge and lower boundary surface (Fig. 9). The direction of the velocity varies gradually with depth although its magnitude (convergence rate) is kept constant; its dip-angle is uniformly zero on the oceanward of the Nankai trough axis, and increases to 26 at the leading edge. Through this steady state subduction, the boundaries between the elastic and viscoelastic bodies are treated as decoupled ones. This means here that there is no increase in elastic shear stress along the elastic-viscoelastic boundaries. The loosely coupled part of the plate boundary is also treated as a decoupled boundary. Hence, this part is subjected to a steady state aseismic deformation, resulting in stress concentrations at the lower edge of the elastically coupled part of the plate boundary. The depth of this edge corresponds to that of the hypocenter of the 1946 event. The pattern of the surface deformation computed depends not only on the distribution of subduction velocity along the Philippine Sea plate, but also on the depth of this edge. As shown in Fig. 10 (a), the observed preseismic surface elevation change can be interpreted by the steady state subduction of the Philippine Sea plate with a convergence rate of 45 mm/yr. This convergence rate is close enough to the value of 40 mm/yr, estimated on the basis of seismic data (SENO, 1977). 3.3 Coseismic model The coseismic surface movement due to the 1946 Nankaido earthquake has been explained adequately in terms of low-angle thrust faulting (FrTCH and SCHOLZ, 1971; ANDO, 1975, 1982). The coseismic surface elevation change in Fig. 8 can well be interpreted in terms of sudden shear stress release, i.e., a two-dimensional lowangle thrust fault (Fig. 9). The location of the present fault segment is determined on referring to the fault model by ANDO (1982). The fault segment runs along the plate boundary in the depth interval km, branches away at a depth of 22 km, and extends upward to the earth's surface on the oceanic side of the Asian plate. The dip angle of the fault segment is about 20 in the depth interval km, and increases gradually to 27 at the earth's surface. Along the fault segment, we assume a shear stress drop distribution shown in the 'upper right-hand corner of Fig. 10 (b); an average shear stress drop of 2.0 MPa on the elastically coupled part, and zero shear stress drop on the loosely coupled part. For this shear stress drop distribution, we obtain a good agreement between the observed and computed surface elevation changes (Fig. 10 (b)). In Fig. 10 (b), the absolute change of the reference point

13 A Model of Plate Convergence in Southwest Japan 461 Fig. 10. Observed and computed (solid curves) surface elevation changes, plotted against distances from the Nankai trough along the profile B in Fig. 3: (a) preseismic (top), (b) coseismic (middle), and (c) postseismic (bottom) changes. Inset in Fig. 10 (b) indicates the stress drop and fault offset distributions along the fault segment shown by the heavy solid line in Fig. 9. Fault blocks (No. 1,..,14) correspond to the elastically coupled part of the fault segment, and the remaining blocks (No. 15,...,18) the loosely coupled part. (Zentsuji) is taken to be +100 mm to obtain a satisfactory fit between the observed and computed changes. The steady state subduction of the Philippine Sea plate increases the average shear stress on the elastically coupled part of the fault segment at a rate of 1.34 ~10^<-2> MPa/yr. Hence, it takes about 150 yr until the average shear stress amounts to 2.0 MPa. On the other hand, the average recurrence time of the Nankaido earthquakes has been estimated to be 176 yr from the time sequence analysis for historical events (ANDO, 1975). Considering the accuracy of the estimations, the value of 150 }50 yr seems to be a proper approximation for the earthquake recurrence time.

14 462 K. MIYASHITA 3.4 Postseisinic model In this section, we try to interpret the postseismic surface elevation changes in Fig. 8 by superposition of the effects of stress relaxation and accumulation. The former is the response of the viscoelastic regions to the coseismic faulting, and the latter is the surface deformation due to the steady state subduction of the Philippine Sea plate. It is widely recognized that there exist various structural inhomogeneities of the crust and upper mantle in the region involving a subduction zone; the presence of a descending slab in the asthenosphere and the difference in thickness between continental and oceanic plates. MIYASHITA (1983) has shown that the viscoelastic surface deformation due to thrust faulting is strongly affected by such horizontal structural inhomogeneities. A structural model with a descending slab in the asthenosphere would produce quite smaller amplitude of the viscoelastic vertical surface displacement than a simplified layered structural model. MIYASHITA (1983) has also shown that if the thrust faulting extends to the bottom of the elastic plate, the viscoelastic vertical surface displacement profile would have a maximum on the hanging wall side. On the other hand, it would have only a minimum in the corresponding region, if the faulting is stopped within the plate. It can be seen from the computational result in Fig. 10(a) that during the time interval less than one-third of the preseismic one, the steady state subduction of the Philippine Sea plate has a secondary role in the postseismic surface elevation changes. It produces trenchward tilting in the seaward region within a distance of about 200 km from the Nankai trough, and slight uplift in the farther inland region; in the postseismic period of ( ), Muroto subsides 106 (122) mm, and the maximum uplift amounts to 33 (38) mm. Hence, we expect that the remarkable uplift localized in the coseismically subsided region can be accounted for by the viscoelastic response to the coseismic faulting. In the preceding section, we indicated the vertical surface displacement profile due to the coseismic faulting, accompanied with the average shear stress drop of 2.0 MPa on the elastically coupled part of the fault segment, and with the zero shear stress drop on the loosely coupled part. The induced fault offset distribution is shown in the upper right-hand corner of Fig. 10(b), together with the shear stress drop distribution. It is noted that the fault offset on the loosely coupled part is not negligible in spite of the zero shear stress drop. This part of the fault segment is included in the viscoelastic thin layer, by which the loose coupling is modeled. It is assumed here that just after the coseismic faulting the viscoelastic thin layer receives the simple shear strain, equivalent to twice the fault offset divided by its thickness, and then the corresponding shear stress is relaxed. Figure 11 shows viscoelastic vertical displacement profiles due to the coseismic faulting during ten successive time intervals, together with the coseismic vertical displacement profile. Each time interval is taken to be the asthenospheric relaxation

15 A Model of Plate Convergence in Southwest Japan 463 Fig. 11. Viscoelastic vertical surface displacements during ten successive time intervals, each of which is equal to the asthenospheric relaxation time (t1 = 9.63 yr). Upper frame shows the coseismic elevation change, which is the same as in Fig. 10 (b). time (t_1 = 9.63 yr). Localized uplift is clearly noticed near the coseismically subsided region. We can also see that predominant uplift continues during the period of the first three time intervals (0 < t/t_1 < 3), which is 8.4 times as long as the relaxation time of the viscoelastic thin layer (t_2 = 3.43 yr). Hence, it can be said that most part of the predominant uplift is caused by the shear stress relaxation in the viscoelastic thin layer. Figure 10(c) shows comparison of the observed elevation change profiles with

16 464 K. MIYASHITA the computed vertical displacement profiles; the computed profile is the superposition of the effects of the viscoelastic response to the coseismic faulting and the steady state subduction of the Philippine Sea plate. The observed profiles are well explained if the reference point of Zentsuji subsided about 100 mm during and about 50 mm during , respectively. The absolute level changes at Zentsuji during these periods are not clear from observations, and require further investigation. 4. Discussion and Conclusion In the present study, first, we evaluated the precise changes in surface elevation before, at, and after the 1946 Nankaido earthquake by applying an epoch reduction method to the first-order leveling data since the 1890's. Next, we interpreted these surface elevation changes in terms of the steady state subduction of the Philippine Sea plate, the earthquake faulting, and superposition of the viscoelastic response to the faulting and the steady state subduction of the Philippine Sea plate, respectively. THATCHER and RUNDLE (1984) have also interpreted the surface deformation associated with the 1946 Nankaido earthquake in terms of the cyclic deformation due to periodically repeated earthquakes at subduction zones. Their interpretation was based on the lithosphere-asthenosphere coupling model, in which the crust and upper mantle structure was modeled by the simple layered structure of an elastic plate overlying a viscoelastic half space. However, such a simple structural model would be inadequate for dealing with the viscoelastic deformation due to the coseismic faulting at subduction zones. It is because the viscoelastic deformation is strongly affected by the structural inhomogeneities of the crust and upper mantle, especially by whether the descending oceanic plate in the asthenosphere is taken into account or not (MIYASHITA, 1983). Concerning the interseismic (preseismic) deformation, they reproduced it indirectly by assuming that the total deformation during the period of one seismic cycle damps perfectly, i.e., by assuming that there is no permanent deformation. However, this assumption is doubtful because a series of marine terraces (YOSHIKAWA et al., 1964) suggests that a permanent component of the cyclic deformation cannot be neglected. Unfortunately, the mechanism of the permanent deformation has been unsolved. Hence, it is satisfactory to consider the physical mechanism of the preseismic deformation directly as shown in our model. Surface deformations due to our model were strongly dependent on the structural inhomogeneities of the crust and upper mantle: the loose coupling in the lowest part of the convergent plate boundary, the Philippine Sea plate subducting into the asthenosphere, and the thin Asian plate causing the coseismic faulting to extend through the entire depth interval of the plate. The following are the results obtained in the present study. The preseismic surface elevation change was characterized by the seaward tilt, indicating that Muroto subsides at a rate of 8.1 mm/yr with respect to Zentsuji. This change was explained by the steady state subduction of the Philippine Sea plate,

17 A Model of Plate Convergence in Southwest Japan 465 which is subducting steadily at a convergence rate of 4.5 cm/yr into the asthenosphere, exerting a downward pull of the oceanic side of the Asian plate. The coseismic surface movement was explained by the following low-angle thrust faulting; it was accompanied with an average shear stress drop of 2.0 MPa along most parts of the fault plane, and zero shear stress drop along the remaining part corresponding to the loosely coupled part of the convergent plate boundary. Concerning the fault plane, only its lower part coincides with the convergent plate boundary, and its upper part extends to the free surface of the Asian plate, branching away from the plate boundary at a depth of 22 km. The postseismic surface elevation changes were interpreted by superposition of the viscoelastic response to the coseismic faulting and the steady state subduction of the Philippine Sea plate. However, their distinct feature of the localized uplift in the coseismically subsided region could be explained by the viscoelastic response alone. In particular, the response of the viscoelastic thin layer along the loosely coupled part of the convergent plate boundary played an important role in its explanation. Finally, we summarize the model of plate convergence at the Nankai trough, fundamentally consisting of the two phases of stress accumulation and release in the source region of the Nankaido earthquake. The steady state subduction of the Philippine Sea plate with the convergence rate of 4.5 cm/yr increases the average shear stress over the earthquake fault plane at the accumulation rate of 1.34 ~10^<-2> MPa/yr. Hence, we can predict that if the subduction process continues for about 150 yr just after one Nankaido earthquake, it can be interrupted by the next Nankaido earthquake with the average shear stress drop of 2.0 MPa. We would like to express our sincere appreciation to Dr. M. Matsu'ura, Geophysical Institute, Faculty of Science, the University of Tokyo for his critical reading of the manuscript and helpful suggestions. REFERENCES ANDO, M., Source mechanisms and tectonic significance of historical earthquakes along the Nankai trough, Japan, Tectonophysics, 27, , ANDO, M., A fault model of the 1946 Nankaido earthquake derived from tsunami data, Phys. Earth Planet. Inter., 28, , BROWN, L. D., R. E. REILINGER, S. D. HOLDAHL, and E. I. BALAZS, Postseismic crustal uplift near Anchorage, Alaska, J. Geophys. Res., 82, , COHEN, S. C., A multilayer model of time dependent deformation following an earthquake on a strike-slip fault, J. Geophys. Res., 87, , FITCH, T. J. and C. H. SCHOLZ, Mechanism of underthrusting in southwest Japan; A model of convergent plate interactions, J. Geophys. Res., 76, , HAYASHI, T., A study on the vertical movements of the earth's crust by means of the precise leveling, Bull. Geogr. Surv. Inst., 15, 1-67, HIRAHARA, K., Three-dimensional seismic structure beneath southwest Japan: the subducting Philippine Sea plate Tectonophysics,

18 466 K. MIYASHITA ICHIKAWA, M., Reanalyses of mechanism of earthquakes which occurred in and near Japan, and statistical studies on the nodal plane solutions obtained, , Geophys. Mag., 35, , KAMINUMA, K., The crust and upper mantle structure in Japan, Part 2. Crustal structure in Japan from the phase velocity of Rayleigh waves, Bull. Earthq. Res. Inst., Univ. Tokyo, 44, , KANAMORI, H., Tectonic implications of the 1944 Tonankai and the 1946 Nankaido earthquakes, Phys. Earth Planet. Inter., 5, , KASAHARA, K., Aseismic faulting following the 1973 Nemuro-oki earthquake, Hokkaido, Japan (a possibility), Pure App!. Geophys., 113, , MATSU'URA, M. and T. IWASAKI, Study on coseismic and postseismic crustal movements associated with the 1923 Kanto earthquake, Tectonophysics, 97, , MATSU'URA, M., T. TANIMOTO, and T. IwAsAxt, Quasi-static displacements due to faulting in a layered half-space With an intervenient viscoelastic layer, J. Phys. Earth, 29, 23-54, MELOSH, H. J., Nonlinear stress propagation in the earth's upper mantle, J. Geophys. Res., 81, , MIYABE, N., Vertical earth movement in Nankai district, Bull. Geogr. Surv. Inst., 4, 1-14, MIYASHITA, K., Finite element modeling of a preseismic fault slip process for long-term anomalous surface deformations, J. Phys. Earth, 29, 55-76, MIYASHITA, K., Surface displacement patterns associated with asthenospheric stress relaxation following major underthrust earthquakes, J. Seismol. Soc. Jpn., 36, , 1983 (in Japanese). MIZOUE, M., Some remarks on the characteristics of subcrustal earthquake activities, Proc. Earthy. Predict. Res. Symp., Tokyo, , 1976 (in Japanese). MOGI, K., Development of aftershock areas of great earthquakes, Bull. Earthq. Res. Inst., Univ. Tokyo, 46, , NUR, A. and G. MAVKO, Postseismic viscoelastic rebound, Science, 183, , RUNDLE, J. B. and D. D. JACKSON, A kinematic viscoelastic model of the San Francisco earthquake of 1906, Geophys. J. R. Astron. Soc., 50, , SCHOLZ, C. H. and T. KATO, The behaviour of a convergent plate boundary: Crustal deformation in the South Kanto district, Japan, J. Geophys. Res., 83, , SENO, T., Instantaneous rotation vector of Philippine Sea plate relative to the Eurasian plate, Tectonophysics, 42, , SHIONO, K., Focal mechanisms of major earthquakes in southwest Japan and their tectonic significance, J. Phys. Earth, 25, 1-26, THATCHER, W. and J. B. RUNDLE, A model for the earthquake cycle in underthrust zones, J. Geophys. Res,, 84, , THATCHER, W. and J. B. RUNDLE, A viscoelastic coupling model for the cyclic deformation due to periodically repeated earthquakes at subduction zones, J. Geophys. Res., 89, , YOSHII, K., Crustal Structure in Japan, UP Earth Science, the University of Tokyo Press, Tokyo, 1979 (in Japanese).

19 A Model of Plate Convergence in Southwest Japan 467 YOSHII, K., Y. SASAKI, T. TADA, H. OKADA, S. ASANO, I. MURAMATU, M. HASHIZUME, and T. MORIYA, The third Kurayosi explosion and the crustal structure in the western part of Japan, J. Phys. Earth, 22, , YOSHIKAWA, T., S. KAIZUKA, and Y. Om, Crustal movement in the Late Quaternary revealed with coastal terraces on the southeast coast of Shikoku, southwestern Japan, J. Geod. Soc. Jpn., 10, H6-122, 1964.

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