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J. Phys. Earth, 37, 101-131, 1989 CRUSTAL MOVEMENTS IN THE INNER ZONE OF SOUTHWEST JAPAN ASSOCIATED WITH STRESS RELAXATION AFTER MAJOR EARTHQUAKES Takao TABEI* Geophysical Institute, Kyoto University, Kyoto, Japan (Received May 30, 1988; Revised April 7, 1989) Transient deformation resulting from postseismic stress relaxation in underlying viscoelastic layers is examined. The main purpose of the present study is to understand spatial and temporal modes of postseismic deformation especially due to strike-slip faulting with a realistic geometry. The fault size as well as the viscoelastic structure of the earth proved to have large effects on the amount of postseismic deformation. Therefore, it should be taken into serious consideration in modeling the faulting. It is noteworthy that the concentration of shear strain into the near field continues long after the faulting. This strain concentration is similar to the preseismic strain accumulation and is contrary to the coseismic strain release. The viscoelastic structure of the earth, however, is hard to determine solely by the surface measurements performed at long time intervals. Crustal movements in the Inner Zone of Southwest Japan, in particular, those associated with the 1927 Tango earthquake of M=7.5, are then investigated in connection with postseismic stress relaxation. The discrepancies between the observed and calculated postseismic deformations can be reduced if the effect of tectonic stress is added to the calculated deformation field. 1. Introduction It is widely accepted that the basic model to explain the physical behavior of the earth's crust and upper mantle generally consists of three layers with different rheological properties; namely, the uppermost elastic and brittle lithosphere, the intervenient ductile asthenosphere with low viscosity, and the substratum with relatively high viscosity. In addition, it is also recognized that there exist considerable regional heterogeneities in both thicknesses and properties of the layered structure of the earth. These heterogeneities probably characterize the mode of accumulation and release of tectonic stress in the region, and this mode is reflected in the crustal movements and seismic activity peculiar to the region. * Present address:Department of Physics, Faculty of Science,Kochi University,Kochi, Japan. 101 102 T. TABEI With the recent advance in accuracy in the determination of hypocenters of earthquakes, it has become clear that there is a sharp cut-off depth for seismic activities in tectonically active inland regions (e.g., KOBAYASHI, 1976; OIKE, 1977; SIBSON,1982; MEISSNER and STREHLAU, 1982; CHENand MOLNAR,1983; MIKUMOet al., 1988; ITO, 1988). It seems that most earthquakes that occur inland sufficiently far from the subduction zone are restricted to the upper crust, in other words, a seismic-aseismic transition occurs at the mid-crustal depth. The thermal dependence of fracture strength of rock has been discussed to interpret the lower limit of focal depth in Central and Southwest Japan (e.g., KOBAYASHI, 1976; MIKUMOet al., 1988; ITO, 1988). Based on laboratory data on rock deformations, SIBSON(1982) assumed frictional failure and quasi-plastic flow in the upper and lower crusts, respectively, and clarified the depth-dependence of shear resistance of the continental crust in the Western United States. These studies suggest that an anelastic treatment is indispensable not only for the upper mantle but for the lower crust when the failure and deformation of the crust in tectonically active inland regions are discussed. Transient crustal movements following an elastic rebound at the time of a large earthquake are interesting phenomena in understanding the anelastic properties of the earth's crust and upper mantle and also in comprehending the mode of accumulation and release of tectonic stress. NUR and MAVKO(1974) first obtained analytical expressions of the postseismic displacement fields due to a dislocation in an elastic layer overlying a viscoelastic half-space. In recent years, further studies have been carried out on quasi-static surface deformation resulting from postseismic stress relaxation in underlying viscoelastic layers. Crustal movements due to major underthrust earthquakes occurring repeatedly at the subduction zone are characterized by large vertical displacements whose patterns significantly change with time. They have mostly been modeled in connection with a steady plate subduction and asthenospheric stress relaxation (e.g., THATCHERand RUNDLE,1979; THATCHERet al., 1980; MIYASHITA,1983; THATCHER and RUNDLE,1984; MIYASHITA, 1987) and a relatively simple two- or three-layered structure model seems to explain appropriately the transient crustal movements observed. Similar modelings have also been made for slow and steady deformation along a strike-slip fault (RUNDLEand JACKSON, 1977; SAVAGE and PRESCOTT, 1978; YANG and TOKS_??_Z, 1981). These modelings, however, have mainly been made for a highly idealized long fault that exists in an elastic layer overlying a viscoelastic substratum. Thus, it is questionable whether the model results are immediately applicable to crustal movements due to moderate-size faulting. For example, an earthquake with a magnitude larger than 7.0 that occurs in the Inner Zone (the Japan Sea side) of Southwest Japan is mainly represented by strike-slip faulting with a length of about 30 to 40 km. However, quantitative consideration has not yet been given for postseismic deformations caused by stress relaxation after such faulting. In the present study, the effects of fault size and viscoelastic structure of the earth's crust and upper mantle on the postseismic deformations are examined Crustal Movements in Southwest Japan after Major Earthquakes 103 through a three-dimensional numerical simulation in which viscoelastic treatments are introduced for the lower crust and the upper mantle on the basis of the vertical distribution of microearthquakes. The spatial pattern, amount, and timedependence of the deformation are then estimated for faulting with a realistic geometry. The deformation due to postseismic stress relaxation is formulated according to MATSU'URA et al. (1981) and IWASAKI(1985). In their formulations, quasi-static deformations caused by faulting with arbitrary orientation and slipvector in a multi-layered half-space can be treated. Furthermore, crustal movements observed during several decades after the 1927 Tango earthquake of M=7.5, that occurred in the Inner Zone of Southwest Japan, are investigated especially in connection with the relation between the postseismic stress relaxation in underlying viscoelastic layers and the tectonic stress. These investigations will give us a new insight into crustal movements related to the mode of accumulation and release of tectonic stress. 2. Modelingof PostseismicDeformation 2.1 Tectonicsetting of the Inner Zone of SouthwestJapan Figure 1 shows the distribution of the main active faults and tectonic lines in and around Southwest Japan (THERESEARCH GROUPFORACTIVEFAULTS,1980). The Median Tectonic Line separates Southwest Japan into two tectonic regions, namely, the Inner Zone (the Japan Sea side) and the Outer Zone (the Pacific side). Tectonics in the Outer Zone is characterized by an interaction between the Philippine Sea and Eurasian plates. The former is considered to be subducting northwestward beneath Southwest Japan from the Nankai trough (Fig. 1). Along this trough, great earthquakes have repeatedly occurred accompanied by large crustal movements in the coastal regions (ANDO,1975). Studies of the focal mechanisms of these earthquakes and their aftershocks show that these are the earthquakes of low-anglethrust type (ICHIKAWA, 1971;KANAMORI, 1972a; SHIONO, 1977). The tectonic setting is rather complicated in the Inner Zone. The regular arrangement of reverse faults and conjugate strike-slip faults shown in Fig. 1 suggests that they have been formed by a horizontal tectonic compression in a nearly E-W direction (HUZITA et al., 1973). Similarly, studies of focal mechanisms of shallow earthquakes in this region have revealed that pressure axes lie in a horizontal E-W to ESE-WNW direction (ICHIKAWA, 1971;NISHIDA,1973;SHIONO, 1977),some examples of which are shown in Fig. 2. Moreover, long-term crustal movements detected by geodetic measurements indicate a nearly E-W contraction (GEOGRAPHICAL SURVEY INSTITUTE, 1987). It is therefore considered that the tectonic stress acting in the Inner Zone is dominantly the horizontal compression in the almost E-W direction and the movement of the Philippine Sea plate is not a governing factor (e.g., HASHIMOTO, 1982).The detailed mechanism causing such an E-W compression, however,has not been clarified yet and is under livelydiscussion. 104 T. TABEI Fig. 1. A map showing the distribution of the main active faults and tectonic lines in and around Southwest Japan (compiled from THE RESEARCH GROUP FOR ACTIVEFAULTS,1980). M.T.L. and I.S.T.L. represent the Median Tectonic Line and the Itoigawa-Shizuoka Tectonic Line, respectively. Three large earthquakes in the Inner Zone, namely, the 1927 Tango (M= 7.5), the 1943 Tottori (M= 7.4), and the 1948 Fukui (M= 7.3) earthquakes, were accompanied by remarkable crustal movements showing typical strike-slip faulting (TSUBOI,1932; NASU,1950; SATO, 1973). Their focal mechanisms are indicated in Fig. 2 by symbols Ta, To, and Fu, respectively. KANAMORI (1972 b, 1973) calculated the synthetic seismograms for the three earthquakes on the basis of the distribution of P-wave first motions, the aftershock distributions, and the triangulation data. He determined fault parameters from the best-fit synthetic seismograms. The results obtained are listed in Table 1. The three earthquakes are very similar in scale and type of faulting and can be regarded as representing typical patterns of the release of tectonic stress that has been accumulated in this region. Shallow microseismicities in the Inner Zone are considerably active along the active faults, as shown in Fig. 3(a) (OIKE, 1977). The vertical distribution of Crustal Movements in Southwest Japan after Major Earthquakes Fig. 105 2. Distribution of P-axes and focal mechanisms of major crustal earthquakes in Southwest Japan (after SHIONO,1977). All diagrams are projected on the lower hemisphere. Shaded and open quadrants of the diagrams indicate the compressional region of P-wave first motion and the dilatational one, respectively. Symbols Ta, To, and Fu represent the 1927 Tango (M= 7.5), the 1943 Tottori (M=7.4), and the 1948 Fukui (M=7.3) earthquakes, respectively. Table 1. Fault parameters of the three large earthquakes in the Inner Zone of Southwest Japan (after KANAMORI,1972b, 1973). accurately determined hypocenters of microearthquakes indicates a sharp concentration of focal depths into the upper crust and an abrupt disappearance in and below the lower crust, as shown in Fig. 3(b). These results as well as the distribution of active faults give important clues for understanding the nature of the crust of the tectonically active inland region. For example, we can consider that strain buildup caused by accumulation of tectonic stress and strain release through brittle fractures alternately take place in the elastic upper crust, while an acting stress is continuously consumed by an anelastic flow in or below the lower crust, and consequently, stress is not accumulated there. 106 T. TABEJ (a) (b) 3. Distribution of microearthquakes that occurred during the period from July 1965 to June 1976 (after DIKE,1977). (a) Epicentral distribution of shallow microearthquakes whose depths are less than 40 km. (b) Representative crustal structure and vertical distribution of hypocenters in the same region as that shown in (a). Fig. 2.2 Mathematical Transient viscoelastic (1981) layers and Figure overlying are and formulation deformation as IWASAKI 4(a) to shows be a Maxwell The respectively. When by postseismic according a layered (the to stress the relaxation formulations Coordinates source layer), (behaving substance of half-space (n + 1)-th viscoelastic viscosities the induced modeled in by underlying MATSU'URA et al. (1985). substratum assumed elastic. is the and time for stress n-th layer fault function that where as the an the geometry can and layer solid the shown represented for n and layers are denoted in Fig. by parallel the layers substratum confining other substratum are be of n-th elastic deviation) and consists pressure are perfectly by ƒÅ' and ƒÅ, 4(b). the Heaviside step Crustal Movements in Southwest Japan after Major Earthquakes (a) Fig. 4. of Definition layers and Fault the n-th length; angle; the and layer, one; and (modified interfaces. ƒÅ and ƒÅ' respectively. (b) W, fault U0, amount foot (b) of parameters their 107 width; of final D, Geometry depth dislocation; ƒÉ, ur(_??_,z),displacement from denote to the IWASAKI, the 1985). viscosities (a) Numbering of the substratum of the finite-dimensional lower margin slip-angle components of of the in cylindrical the hanging fault. fault; ƒÂ, wall L,. dip against coordinates. function H(t), total displacement fields at the surface are written in the cylindrical coordinates as (1) where ur(_??_ ,z) represents the coseismic elastic displacement and vr(_??_,z) the postseismic viscoelastic one that is dependent on the elapsed time after faulting. When a point dislocation is given in the m-th layer, the radial component vr of the viscoelastic displacements is expressed in the integral representation as (2) with (3) 108 T. TABEI where m U0 is the the geometrical and amount Lam_??_s functions of expressed in the effect is are MATSU'URA be integrations of fault with integrations lated. carried of grid have degree non-uniform of of a dip-angle are structure and the fault (ƒÂ) vz, and using 1982). with the time gravitational The a technique integrals to source The MATSU'URA, referred of the geometry. points been W grid kernel developed respect to to ƒÌ by in Eq. is, without of a as dislocation of the any a of (2) 84 the at on can the In (12 and near of field, a the interpolation the fault source the surface be the a is by calcu- to study, length however, and width more to it the has case the the grid Though time, as two- bi-cubic reduced present 7 in plane as interpolation. applicable fault over study, represented computational modification, out present on and double carried point position accuracy long the selected functions. taken numerical be two-dimensional integration calculation rather In interpolated bi-cubic enhance requires 4(b)). are at been must location double the fault, source of points the are usually For and method Taking analytical has distribution (Fig. displacement the selected a point a new Consequently, of finite-dimensional for displacements integration accuracy to First, valuable, respectively). method (2), layered to semi-infinite using sources. integration directions, Eq. time-dependence the width functions. point functions. number and out discrete numerical in the functions obtained L calculated B-spline the due solutions length of Then both analytical so that fields the B-spline location dimensional points (1981) Ll ƒÊ the v_??_, and represent (IWASAKI by the and and components, Vr,j, in V_??_,j the integrals related them Kl (_??_) and displacement order l, ƒÉm and (2). They not of layer, azimuth two Eq. function m-th evaluated. are bi-cubic the in Bessel station included by are displacement plane are approximated numerically For to affected they et al. the other functions. incorporated functions by is However, on The which the source-existing similar kernel which function. can Vz,j, Jl(ƒÌr) the fault. forms viscoelastic deformation, the the and as dislocation, of depending slip-angle(ƒÉ) are of constants this a high of the plane. 2.3 Structure model of the earth's crust and upper mantle The postseismic viscoelastic deformation at the surface is, dependent on the layered structure of the earth's crust and upper mantle. On the basis of the delay in arrival time of long-traveled seismic waves, the upper mantle beneath the Japanese Islands has been thought to have the characteristics of low velocity and large attenuation (KANAMORI,1970). The threedimensional attenuation structure of Northeast Japan, which was estimated by the inversion of seismic intensity data, shows that the low-Q zones are dominant in the crust and upper mantle on the backarc side and are in contrast with the high-Q zones on the Pacific side (HASHIDAand SHIMAZAKI, 1987). Moreover, a numerical modeling of tectonic flow induced by a subducted slab has indicated high temperature and low viscosity beneath island arcs and marginal basins (ANDREWS and SLEEP,1974). Therefore, the idea that the asthenosphere beneath the Japanese Crustal Movements in Southwest Japan after Major Earthquakes Table Islands has structure et In we the and upper et present 2 ratios and by ƒÑ has is A Fig. of the the the an with of In the basis the the elastic the with of of upper and asthenosphere modeling of present viscosity, treatment a finite-element on Therefore, high as viscosity asthenosphere. consists viscoelastic low substratum crust 3(b). relatively recognized with of lower Japan its similar in the in Southwest with made material constants thicknesses and explosion densities mainly after from faulting the structure velocities the low lower crust Northeast Japan employed in SATO are et in layers et al., (1981). The al. varying units represents the (YOSHII executed is measured where ƒÊ3 model of observations deformation mantle, ƒÅ/ƒÊ3, of P-wave seismic are time model employed possibly result additional (MIZOUE, 1976) NAKANISHI (1980) Shikoku of its Philippine time, aseismic has ScS to Sea however, dead that plate he are the mostly 1974). Maxwell's rigidity. Poisson's of viscosity time- ratio ƒÅ'/ƒÅ. relaxation The ƒÅ/ƒÊ3 the derived The calculations the slab this that had heterogeneities of will is subducted plane of time be denoted ScSp phases regions (Fig. dipping interface reached another intermittently 2), is the the were the velocity is were interpreted in upper mantle. the beneath possibility descended the boundary Chugoku that this in the structure of not at several which upper stations He pointed subducted At is related subduction in converted has the region. the uniform. as of interface past induce earthquakes configuration subduction observed structure. and subcrustal that and the slab seismic indicate complex of a long seismic Japan interface had indicated lateral three-dimensional that the that has The plate reported P at the presence Southwest Chugoku possibility the large-scale Sea and from the the beneath Philippine ignores from deformation. and 1981) subducted waves here mainly surface (HIRAHARA, out by observation here. These the of which been the of upper supported seismic effect that into shown crust thickness. the with treatment Zone lower postseismic The an Inner mantle), The elapsed the the lists result dependent is also (1981). study. the idea explosion asthenosphere and compared microearthquakes sufficient al. Table of for mantle SATO from of (upper and the a thick Japan, a viscoelastic viscoelastic viscosity This from that Southwest is negligible introduce substratum founded. derived assume of viscosity model crust, we crust distribution structure The study, high addition, is well velocity Japan. 1974). inland relatively model for the Inner Zone of Southwest developed P-wave present the vertical of al., the underlies by highly model (YOSHII its been Structure 2. 109 the same to the process 110 T. TABEI because no subcrustal earthquake occurs beneath the Chugoku region. The absence of subcrustal seismicity implies that at present the interaction between the subducted Philippine Sea plate and the continental Eurasian plate is not so strong beneath the Chugoku region. As a first approximation, therefore, ignoring the effects of subducted slab may be justified for modeling the deformations in the Inner Zone of Southwest Japan. The effect of the superficial layer of the crust on the surface deformation is not taken into account in the present model because it is exceedingly hard to quantify. TANAKA(1981)has concluded that some of the postseismic deformations detected by strainmeters or tiltmeters, which were represented by exponential functions with time constants of a few years, may be caused by an earthquake-induced viscoelastic relaxation of stress within rocks around the observation vault. We recognize that the local crustal movements are sometimes largely affected by heterogeneities within rocks, transient movement of underground water, instabilities of alluvial layers, and so forth. However, it is uncertain whether the superficial layer of the crust has a governing factor in long-term regional crustal movements. 3. Model Results 3.1 Effect In of studies dimensional size the problem treatment simplification. major fault of such However, factors evaluate effect deformations. that we governing the of the of the are fault coseismic fault an infinite the idealized is often size both in the be Table 2 and is for one fields. elastic two- adopted may deformation on presented an length fault postseismic length model coupling, that and of structure has convinced variation The elastic-viscoelastic of the Here we viscoelastic employed in the evaluation. Holding fixed, different along fault The 30 km In general, in the strike-slip faulting displacement 5 strike of to of fault profiles 30•‹, as and fixed respectively. The of the the amount at 15 km. fault, the for in strike-slip a dip-slip on calculated changes center by for the vertical the is slip-vector are shows is normalized width profiles fault. The fault at Figure profiles the viscosity ratio ƒÅ'/ƒÅ are in taken surface. shows the width are with horizontal The dislocation 6 the plane cases of of coseismic where fault several and on the changes in both dip-angle Figs. are 5 and 6 is 10. the than postseismic after to and taken deformation dip-angle, displacements Figure amplitude tentatively width, perpendicular displacement at fault lengths. line plane. vertical the viscoelastic parallel the displacement than the and fault displacement fixed that elastic variation the faulting, deformation is twice in elastic fault one, as the is from Figs. panels in not time clearly of a more left relaxation are has this seen (lower profiles length and larger 5 and Figs. the effect remarkable 6. 5 and At the 6, where asthenosphere), distinguishable on the in dip-slip early viscoelastic faulting stage the elapsed differences because of of the time among their small 111 Crustal Movements in Southwest Japan after Major Earthquakes ELASTIC VISCOELASTIC Fig. 5. slip Changes fault. parallel in The to normalized plane. The pendicularly mation the fault by U0 profiles to (lower horizontal fault the two PART displacement is vertical and strike that are center figures), is are the taken profiles its plotted, along of the width the fault. viscosity is with of length fixed where amount PART at the scale coseismic the line In the of a pure on postseismic is strike- Displacements displacement dislocation extending ratio ƒÅ'/ƒÅ of 15 km. on the is the surface viscoelastic assumed to fault perdefor- be 10. amplitudes. On the other hand, the effect of variation in fault length becomes more remarkable gradually with time (lower right panels in Figs. 5 and 6). Therefore, we conclude that the fault length should be taken into serious consideration in modeling the long-term postseismic viscoelastic deformation. 3.2 Spatial patterns of displacement and strain fields To understand the time-dependent deformation due to moderate-size strikeslip faulting, displacement and strain fields are calculated at several elapsed times after faulting. The model fault is assumed to be vertical and have a length of 34 km and a width of 13km. The upper margin of the fault must be located underground because singular points appear if a source is located at the surface. Thus the depth to the lower margin of the model fault is tentatively taken as 13.13 km; that is 1% larger than the fault width. The fault geometry is nearly equivalent to those of the 1927 Tango, the 1943 Tottori, and the 1948 Fukui earthquakes. 112 T. TABEI ELASTIC PART VISCOELASTIC Fig. 6. Changes fault. The The profiles to and As are to shown generally however, region in are is in in the The at (a) are the same with fixed line left-lateral plane. as length at 30 in Fig. are represented be 10 Fig. km 5. of a pure and 30•‹, The viscosity dip-slip respectively. ratio is by and and at the of in the Figs. t= been 7, 8, and 9, viscoelastic Here, time has displace- postseismic respectively. elapsed 1 m vertical shown and figure, those as in time of the horizontal coseismic Fig. in are the the displaced where each (b), sense different the calculated deformations in component displacements, the 10ƒÑ. The viscoelastic viscosity ratio ƒÅ . 7(a) same (b) strike-slip Horizontal elastic and displacements positions pure fault strains remarkably displacements postseismic a the quite profiles dip-angle along coseismic shown deformations '/ƒÅ is assumed are on The are taken horizontal respectively. displacement and 10. with given ments, ones be dislocation uniformly vertical width are assumed A in fault PART 7(a) order faulting. not particularly maximum postseismic displacement The of ones. and to (b). It amounts seems compensate However, that for the the cumulative vectors displacements, the surrounding relatively small amounts of large. vertical displacement appears do not Crustal Movements in Southwest Japan after Major Earthquakes 113 (a) (b) Fig. 7. fault Horizontal plane. displacement The respectively. the given ments The fault width. on at the the due length and depth of A fault elapsed uniform plane. width the strike-slip fault margin Coseismic t= pure the dislocation (a) time lower to of 10-ƒÑ. The are of with the faulting assumed fault (b) ratio with a 34 and be is taken a left-lateral displacements. viscosity to is 1% vertical 13 larger km, than component of Postseismic displace- assumed to be 1 m is 10. coincide in Fig. 8(a) and (b). These figures show the turnover from coseismic upheavals to postseismic subsidences and the reverse case from coseismic subsidences to postseismic upheavals. These turnovers may be caused by the slow reaction of the underlying viscoelastic layers against the sudden change in stress fields and by the compensation for the undulation of the boundary between the elastic and viscoelastic layers. The gravitational effect has been considered in calculation of postseismic deformations, although it proves not dominant in this case. The most noteworthy result is obtained from the pattern of the strain field. As shown in Fig. 9(a) and (b), the postseismic strains in the near field of the fault are generally accumulated in the reverse sense to those of the coseismic strain releases. In other words, the pattern of postseismic strains is roughly similar to the distribution of shear strains that were accumulated in the near field before strike-slip faulting. The postseismic strain accumulation implies a concentration of shear stress in the vicinity of the main fault plane. This stress concentration is induced by the postseismic anelastic flow in the underlying viscoelastic layers (YANG and TOKS_??_Z, 1981) and will promote a long-term aftershock activity in the hypocentral region or creep-like secondary faulting in the near future. 114 T. TABEI (a) (b) Fig. 8. Contour maps of (a) coseismic and (b) postseismic vertical displacements. See the caption of Fig. 7. (a) (b) Fig. 9. (a) Coseismic and (b) Fig. 7. postseismic horizontal strains . See the caption of Crustal Movements in Southwest Japan after Major Earthquakes 3.3 Effect To calculated at viscosity line this five ratios. figure, Figure to from the in the lower at fault. different the as addition, of in Fig. relaxation example, t =10ƒÑ is in it is the case has ratio times largely viscoelastic 10, we near that the on determine even of ƒÅ'/ƒÅ=•‡ and if a is plane. As in on the to that the each certain shown of of the 10 to ratios that upper 40 km among structure model, ratio. surface deformation the displacement difference obtained the means about amplitude in along amplitudes which simultaneously the that taken displacement field viscosity different of smaller, the the structure recognize effect changed by to fault approaches in little cannot time ƒÑ, difficult a large noteworthy are the are with are amount becomes and affected models profiles the on appears it is the and ratio displacements structure dislocation decreases elapsed effect shown the For at crust itself fault viscosity deformation In amplitude ratio ƒÅ'/ƒÅand Fig. the remarkable of horizontal three in which the viscosity the for results, of amount As structure, times the the profiles. Though obtained center variation remarkable obtained. shows the profiles while 10 the is the of viscoelastic elapsed U0 that more away of by viscosity mantle, structure effects different displacement the the viscoelastic the perpendicular normalized the of estimate 115 profile between at t= is viscosity 6ƒÑ in the the is profile case 10. Changes in horizontal displacement profiles with time for three structure models with different viscosity ratios. The profiles are taken along the line extending on the surface perpendicularly to the center of the fault. The scale of displacement is normalized by U0. Parameters denoting the fault geometry are fixed at those in Figs. 7, 8, and 9. of 116 T. TABEI ƒÅ '/ƒÅ =10 . Therefore, intervals is not viscoelastic of long-term kinds discussed of in measurement powerful structure mation, other the a the monitoring with the and of are deformation establishing crust investigations connection postseismic for earth's detailed field of method a upper the The value For time-dependence of is of long model mantle. deformation required. at unique time for further the infor- indispensable the and viscosity deformation itself in the is next subsection. 3.4 Time-dependence of deformation Temporal variations in postseismic horizontal strains at selected positions are shown in Fig. 11. In this figure, changes in maximum shear strain due to pure strikeslip faulting with a dislocation of 3 m are plotted against the normalized elapsed time. The positions used for calculations are located perpendicular to the center of the fault. Viscosity ratio is assumed to be 10 as a representative value, which gives the deformation with moderate amplitude as shown in Fig. 10. Figure 11 shows the continuation of viscoelastic deformation over a long time after faulting, being driven by the anelastic flow due to stress relaxation in the underlying viscoelastic layers. The apparent relaxation times at the surface are much longer than the rheological relaxation times of the underlying viscoelastic layers. This result is most likely due to a coupling of the elastic and viscoelastic Fig. 11. Time changes dislocation of pendicular to are fixed at 10. Two broken in the Inner the maximum The center those in Zone two lines figure are drawn Southwest of and of the 7, 8, lines Southwest the under Japan shear positions Figs. straight These beneath in 3 m. elapsed an strain used fault. and The the Japan which times represented 5•~10 19P. strike-slip faulting are denoting viscosity approximate that to calculations Parameters 9. assumption is due for are stationary years viscosity fault is tectonic estimated in the the ratio ƒÅ'/ƒÅ by with located a per- geometry assumed to strain NAKANE be rates (1973). at the bottom of the asthenosphere of this Crustal Movements in Southwest Japan after Major Earthquakes layers and The is quite viscoelastic elapsed time displacement deformation. the Of fault Two rates size the by the of (1973). It in strain viscoelastic nearly final of not medium final state 4% depends 11 steady into that only approximate Southwest dominant postseismic in about value in Fig. of NAKANE is strain the the the of on at the displacement, the the alone. state the coseismic elastic structure model but faulting. lines Zone of reaches to final mode straight relaxation treatment the this and Inner triangulation stress the amounts course, broken in that from deformation t_??_40ƒÑ. Converting maximum on different transient 117 field the Japan, can be the early is gradually as seen from stage of tectonic from this that the taken stationary estimated figure the the postseismic over by strain first-order strain due to deformation the tectonic and strain with time. The rigidity relaxation of the deformation of have two at the viscosity occur been the seems appropriate earthquake of words, estimate of must of that the the the however, we Zone Nankai however, viscosity we have from or of no available beneath viscosity Japan and time-dependence asthenosphere assume Southwest the the other studies region the lies thickness in the about of 110 time considered If viscosity the For upper we of of model of viscosity to have tectonically 500 on km. adopt mantle viscosity of asthenosphere is about and 2.44 yr. of the has (1984). estimated asthenowhich been lithosphere Japanese and is made with however, viscosity at model, thickness, which the the as regions, low a finite- RUNDLE the stable 5•~10 19P, beneath in of estimation inland with of recently, earthquakes structure a tectonically active More thickness This Kanto thickness asthenosphere the viscosity 1923 asthenosphere THATCHER the this underthrust of a 30-km-thick the 1983). low periodically 1) if the 10 21 P because asthenosphere the in after layered of 10 19 to and (1984) that (Fig. the by the depends from 100 developed expected. of of RUNDLE Moreover, caused the uplifts range km. viscosity of and IWASAKI, and the between a highly the of (1973), postglacial are the configuration those wide that and for viscosity This faulting trough and the in 18Pa•Es). observed Sagami deformations plate thrust movements at the that earthquakes asthenosphere. represented (5•~10 THATCHER modeled vertical 20P from of They (MATSU'URA WALCOTT in the regions are limit occurred is somewhere of lithosphere that different is unknown, thickness the The analysis and shield explain cyclic by times assumption underthrust to 2•~10 an elapsed is 5•~10 19P a study 1). the the under major viscoelastic 60 km and Islands from by 11 drawn Japanese derived used to are the Fig. a trough. are sphere figure in (Fig. of According lines trough (1987) modeling relaxation Outer other to viscosity overlying is MIYASHITA lower of Thus caused M=7.9 lithosphere element the mainly Nankai lithosphere for of beneath deformation at from the in evaluated unfavorable, value straight bottom elastic the for broken has cyclic the is Japan. made asthenosphere the the be Islands. The years asthenosphere, It Southwest been Japanese the the must concerning Zone that of quantitatively. information Inner time asthenosphere, a a thin sufficient possibly the Islands, the 118 T. TABEI On mation the cumulative the be fault; this noted and in the 4. that strain. vicinity continuously postseismic time strain because Observations these be the after the postseismic of the fault the the by plane about geodetic strain same strain similarities of field the two same become kinds of as that the of it should as that of expected before distinction gradually strain sense be the vicinity Here, can stress However, of the measurements. in the defor- maximum 15•~10-6 in tectonic will viscoelastic the concentration question. whole and Model to the and is accumulated if the in that faulting surface strain region conclude amounts a remarkable the from years state verified Therefore, of we 100 final easily on assumptions, about until can again tectonic with of for strain the acts basis continues more on faulting of the difficult accumulation. Calculations The model of postseismic deformation due to stress relaxation is applied to the interpretation of crustal movements associated with a major earthquake in the Inner Zone of Southwest Japan. Fig. 12. Horizontal displacements at the triangulation points associated with the 1927 Tango earthquake of M=7.5. The data observed during the period from 1884-1889 to 1927, which were compiled by TSUBOI(1932), are employed. Numerals attached to the leveling route indicate the identity numbers of bench marks. Crustal Movements in Southwest Japan after Major Earthquakes 119 4.1 The 1927 Tango earthquake The 1927 Tango earthquake of. M= 7.5 is probably one of the best geodetically documented earthquakes in the Inner Zone and most appropriate for examining the deformation due to postseismic stress relaxation. The epicenter and mechanism diagram are shown in Fig. 2. The 1943 Tottori and 1948 Fukui earthquakes seem less appropriate in examining the postseismic deformation than the Tango earthquake. The revision survey for the Tottori earthquake was carried out about 14 years after the earthquake (SATO, 1973). This seems too long to distinguish coseismic and postseismic deformations from the measurements. Moreover, it is uncertain how much the thick alluvial layer in the Fukui region (NASU, 1950) affected the surface deformation. And more unfortunately, the resurveyed regions after these two earthquakes are smaller than in the case of the Tango earthquake. Two remarkable seismic faults (the Gomura and Yamada faults), which are conjugate to each other, appeared at the time of the Tango earthquake. Detailed investigations of crustal movements associated with this earthquake were made by TSUBOI(1930 a, b, 1931, 1932). Figure 12 shows the horizontal displacements at the 137 triangulation points during the period from 1884-1889 to 1927. The pattern of the displacements reveals large left-lateral strike-slip movements along the Gomura fault and slightly right-lateral ones across the Yamada fault. Vertical displacements during the period from 1888 to 1927 along the first-order leveling route, which is shown in Fig. 12, are plotted in Fig. 13. A large dip-slip movement of over 1 m is seen across the Yamada fault while the movement across the Gomura Fig. 13. Changes in relative heights of bench marks along the first-order leveling route. The solid and broken lines indicate the observed and calculated vertical displacements, respectively. Bench mark 1366 is assumed to be a datum point. The observed data were compiled by TSUBOI(1930 a). Fault models adopted for the calculation are given in Table 3 and the locations of bench marks are shown in Fig. 12. 120 T. TABEI fault is about The of the and 0.7 (or Studies at to interpret the WALSH, 1969; and the observed the Gomura parameters): km, geodetic and are generally as 30-35 though discuss is the temporal 9-20 90•‹. the the 20 km Gomura Yamada fault for been 1957; to CHINNERY, 1982). by the made On varying Gomura 1961; the other fault fault para- that best fits of km, of studies, (see Fig. U0 = 3.0-3.7 strike-slip. m, The discrepancies the the 4(b) of the fault and ƒÉ m, ƒÉ_??_120•‹ takes plane the models are of a small is generally (reverse parameters definitions fault among Yamada fault for value considered about as faulting the follows: with dip L= a right- and ƒÂ=40-60•‹. a simple fault the of postseismic model main fault in into the present have the but study the been fault listed in dip-angle obtained of after on study is comprehend The are dislocation present to deformation. consideration, parameters a uniform of parameters transient adopted with purpose spatial Table some 3. to and parameters the the not of Taking the the Gomura fault modification of is the models. Coseismic Table displacements 2 and in Fig. observed profile. observed ones, sufficiently As Most than have IWASAKI, seismological a few variations Other pre-existing shown data seismograms follows 10-19 because distribution at and model U0 = 1.3-1.8 study, earthquake fixed km, adopted spatial aftershock are component), modes Tango (1935). that while (KASAHARA, left-lateral parameters present plane W= there fault W= the km, predominantly strike-slip In concluded geodetic synthetic these The fault from a seismological to vertical 10-15 NASU shallower 50•‹. observed fault L= a lateral by are seismogram. indicating direction. shock He MATSU'URA calculated established main traces. models 1977; one. in detail southwestward) about movements (1973) has According nearly fault MATSU'URA, the fault of strike-slip investigated inclined angle establish KANAMORI meters the steeply an crustal the was along vertical northwestward than following distributed is nearly hand, is smaller aftershocks immediately generally dips that of aftershocks fault in m distribution the 14 Table 3. models and vertical The in have been in Table ones calculated indicating effective shown fault as Figs. first 12 Fault parameters are crustal that a calculated a simple approximation and 14, using 3. Horizontal small plotted in movements structure Fig. 13 generally model to the model displacements with interpret discrepancies of the 1927 Tango earthquake a superposed agree well uniform the between adopted listed calculated are with the with the dislocation mode of the is faulting. observed for the calculations. and Crustal Movements in Southwest Japan after Major Earthquakes Fig. 14. Calculated lations coseismic coincide are the same horizontal displacements. with the triangulation as those employed points in Fig. Points shown 121 selected in Fig. for calcu- 12. Fault models 13. calculated crustal movements are recognized in the southwestern part of the region and also in the head region of the Tango Peninsula. In the former case, the effects of the 1925 Tajima earthquake of M= 7.0, which occurred at about 25 km west of and about 21 months before the Tango earthquake, may be present. In the latter case, however, the cause of discrepancy is not known. There might be systematic errors due to movements of reference points which are not considered here. Nevertheless, we consider that these discrepancies are small and negligible compared with the general agreement of the calculated crustal movements with the observed ones. 4.2 Postseismic In reality, laborious is too tasks, long to and grasp strike-slip faulting. following the The has probably to progress Tango 15 to that the with been caused crustal the earthquake generally direction of shows stress surveys it is unfortunate Figure is due geodetic the 1927 deformation ESE-WNW deformation repeated not horizontal interval between movements horizontal strains (GEOGRAPHICAL characterized a strain relaxation detect by rate only of by about the in deformations consecutive detail in produced in cases the 52 INSTITUTE, an 0.2-0.3•~10-6/yr. postseismic surveys most in SURVEY a contraction are viscoelastic almost This of years 1987). E-W strain deformation to field 122 T. TABEI 1979 15. Horizontal strains in Tango district produced in the 52 years following the 1927 Tango earthquake (compiled from GEOGRAPHICAL SURVEY INSTITUTE, 1987). Fig. associated with which is to positions of with discrepancies Tango the 19P derived for from 3. The Therefore, about a the of the the the the is and of the ratio ƒÅ'/ƒÅ. the the noteworthy regional comparable calculated stress, The because latter those are coseismic also at in is somewhat there is strains to Peninsula because tectonic direction. former nearly Tango upper viscoelastic mantle. the out of quantitative displacements in deformation as from derived survey earthquake. We shown On tentatively deformation, This postseismic latest the the postseismic time ƒÑ, of are in and the the by same the 14). of of also the than faults field observed 12 viscosity 21ƒÑ after viscosity contribution This calculations time in strain others. studies but from The (Figs. the earthquake compression larger relaxation the about a apart fault. between For Tango by make Peninsula 5•~10 time 1927 sufficiently field harmony Sec. the characterized considered near -1927 in the value of in the the Japan, above we viscosity as Fig. 15 corresponds there is little = 10, a value assume ƒÅ'/ƒÅ> been discussed viscosity, contrary, assume has to in is 2.44 an elapsed yr. information which gives Crustal Movements in Southwest Japan after Major Earthquakes 123 the deformation with a moderate amplitude, as shown in Fig. 10, but can be modified later. Here, it should be noted that varying the viscosity ratio affects the amplitude of deformation but has little effect on the deformation pattern. The postseismic viscoelastic deformation during the period corresponding to that shown in Fig. 15 is calculated for 132 mesh points at intervals of 4 km. The contributions from the Gomura and Yamada faults are superposed, though, because of its size, the effect of the Yamada fault is comparatively small. The horizontal displacement field is quite similar to the model result shown in Fig. 7(b), that is considered to directly reflect the pattern of tectonic flow induced in the underlying viscoelastic layers. In contrast, the vertical displacement field, not shown here, indicates a pattern which is quite different from that shown in Fig. 8(b). This is chiefly because of the dip-slip component of the Gomura fault and partly because of the existence of the Yamada fault. Though the general features of the calculated horizontal strain field shown in Fig. 16 are in harmony with the observed ones shown in Fig. 15, there are a few discrepancies. The calculated strains are smaller than those observed. The distribution of extension is comparable with that of contraction in the calculated strain field, while extension is hardly observed except in the Tango Peninsula. Moreover, a Fig. 16. Calculated earthquake. the time =10. postseismic Calculation of the latest horizontal has survey been shown strains made at in Fig. associated t=21ƒÑ, 15, that with almost assuming ƒÅ'/ƒÅ=5•~10 the 1927 Tango corresponds to 19P and ƒÅ'/ƒÅ T. TABEI 124 strain concentration near the faults is seen in the calculated strain field but not in the observed one. Quantitative discrepancies between the observed and calculated strain fields can be reduced to some extent if we decrease the viscosity of the lower crust and make it approach to that of the upper mantle, or if we adopt a smaller value for the viscosity of the upper mantle keeping the viscosity ratio fixed. However, the discrepancy between deformation patterns remains mostly unchanged. Thus it is supposed that the observed strain field shown in Fig. 15 is most likely due to the effect of superposition of the postseismic viscoelastic deformation associated with the 1927 Tango earthquake and the tectonic stress acting on the region after the earthquake. 5. Discussion Figure 17 shows coseismic and postseismic changes in relative height between two adjacent bench marks with a distance of about 2 km across the Gomura and Yamada faults (KANAMORI,1973). The movement across the Gomura fault is relatively small and its rate decayed rapidly within a few years after the earthquake. In contrast, the movement across the Yamada fault has shown a gradual progress that can be fitted by an exponential function with a time constant of about 3.0 yr. As seen in Fig. 8(b), postseismic vertical displacement is hardly detectable by geodetic measurements in the short distance across the vertical strike-slip fault. In the case of the Gomura fault, which has a coseismic dip-slip component of about 0.8 m, calculated postseismic relative displacement between the bench marks above is, at most, smaller than a few millimeters. Moreover, it is in the reverse sense to that of the observed movement shown in Fig. 17 and has a much longer time constant. On the other hand, the pattern of postseismic deformation around the inclined dipslip fault is largely dependent on the dip angle and width of the fault plane Fig. 17. Coseismic and postseismic changes in relative height between two adjacent bench marks with a distance of about 2 km across the Gomura and Yamada faults (after KANAMORI, 1973). The postseismic change until 1930 was first pointed out by TSUBOI(1931). Crustal Movements in Southwest Japan after Major Earthquakes (THATCHER shows et al., a better the relative this creep-like caused is noticed in the under that centration the around in the after the such creep-like region probably in an of is part in the same that a still new remains has crustal as caused a stress stress regional sense were there tectonic of and final con- continued movements creep fault plane amount even frictional Fig. 17 motions on motion were strengths (1979). plane. underwent of While functions, fault in the of exponential the shown the parts MIYATAKE by motion Both enough the same on the there There the long-term is no infor- is a possibility consist of the Andreas San a series as to that from concentration the that of episodic fault (SMITH reverse that of of the the fault will the of and the be information the coseismic of Fig. somewhat 9(a) with Fig. elastic taken part of In the deformation into the at in model and that be other of location is noticed will strain the accumu- words, in accumulation: 9(b). by the size it Therefore, the a the time-dependence. release; reduced and though the deformation strain plane case, elastic However, viscoelastic be fault of the probably deformation this about additional postseismic the patterns those occurred. of on in cannot no though additional slip The to amount is part comparison near the additional, This gradual neglected. motion elastic an fault. time-dependent similar there creep-like sense sense the deformation since the be in the are quite except the to to are induce of parts additional in will responding small where strain reverse the This the additional strain strain in sense. Considering strains the contribution into the 0.16•~10-6/yr in 0.04•~10-6/yr on the rate of tectonic to part. this plane regional and surroundings deformation, horizontal the the infer deformation movements Though the the on curves the elastic study, inferred after we viscoelastic these distribution behavior earthquake, postseismic is fault However, decades caused that duration represented deformation time in the earthquake which the creep-like in part nearly three Therefore, stress. dominating MIKUMO similar viscoelastic additional lated Yamada fault. 1968). of the the non-uniform by are manner viscoelastic of the displacement the transient present tectonic determine short-term deformation the not that expected and out postseismic consists the on the WYSS, slight, is However, pointed cumulative The in progressed implies of it concerned movements about and were movements regional unfortunately, as creep-like creeps the faults, motions. plane, the even the Gomura movement. 17 This occurrence dependent mation for the earthquake. e cannot, W fault Fig. creep-like to the 1 cm observed in for relaxation. these similar than exceed the movements. state possibility not shown that calculated observation than stress coseismic stress acting smaller postseismic It displacement the does is far movements by that Relative with displacement earthquake; the 1980). agreement 125 strain the of postseismic about of tectonic strain ESE-WNW basis regional field. direction the 0.2•~10-6/yr three Here, and following in maximum stress, we we assume introduce contraction of extension of perpendicular observations: shear uniform the (NAKANE, stationary 1973), the T. TABEI 1 26 Fig. 18. Calculated strain superposed. a rate of of postseismic The 0.16•~10-6/yr 0.04•~10-6/yr horizontal regional in in the the strain ESE-WNW perpendicular strains is assumed with to direction direction the consist and to that uniform regional of contraction extension of the with with a rate contraction. strain observed at the positions sufficiently apart from the fault as shown in Fig. 15, and the strikes of the Gomura and Yamada faults. Figure 18 shows the calculated postseismic strain field, where the uniform regional strains are superposed on the postseismic viscoelastic ones shown in Fig. 16. The additional deformation due to a postseismic creep-like motion is not considered. This figure shows a better agreement with the observed results shown in Fig. 15, though the discrepancy in the Tango Peninsula remains little improved. Figure 18 also indicates the difficulties in understanding and distinguishing the effects of the deformation caused by postseismic stress relaxation from the strain fields observed. This is because the pattern of the postseismic viscoelastic strain fields is quite similar to that of the regional tectonic strain. To remove the ambiguity resulting from the similarities and to distinguish between these two types of deformations, a long-term detailed monitoring of postseismic crustal movements is indispensable in the region extending to about 100km from the fault. This is because remarkable postseismic displacement will appear in the near field about 15 to 40 km away from the fault, as shown in Fig. 10. Unfortunately, such monitoring has not yet been accomplished, mainly because of the shortage of measurements Crustal Movements in Southwest Japan after Major Earthquakes 127 resulting from the laborious tasks involved in repeated geodetic surveys and partly because of a lack of accuracy. However, we are convinced that these problems will be overcome in the near future by employing a new and more accurate method with a simpler management; for example, by three-dimensional relative positionings using the Global Positioning System (GPS) engaged in advanced space techniques. According to YAMAUCHI (1975), the apparent relaxation times of the postseismic deformations detected by continuous observations of crustal movements or geodetic measurements range from about 20 min to about 8 yr, though not all of the deformations accompanied earthquakes of strike-slip fault type. The remarkable postseismic deformation with its small relaxation time, that is often detected by continuous observations with strainmeters or tiltmeters, cannot be explained by stress relaxation in the underlying viscoelastic layers. Therefore, another deformation mechanism should be considered. TANAKA(1981) has concluded that some of the deformation with a time constant of a few years may be caused by viscoelastic stress relaxation within rocks around the observation vault. Moreover, it is supposed that the earthquake-induced transient movements of underground water sometimes have large effects on local surface deformations during the period immediately after an earthquake (TABEI,1987). The mechanism of the postseismic deformation that originates from the superficial layer of the crust, however, has not been considered in the present study. To understand the nature of the crust, more details of the mechanism of postseismic deformation should be investigated. 6. Concluding Remarks Transient deformation caused by postseismic stress relaxation in underlying viscoelastic layers is examined through a three-dimensional numerical simulation mainly for strike-slip faulting in the Inner Zone of Southwest Japan. In the present model, viscoelastic treatments are introduced to the upper mantle and also to the lower crust on the basis of the depth distribution of hypocenters of microearthquakes in the region concerned. It is made clear that the fault size as well as the viscoelastic structure of the earth's crust and upper mantle has a large effect on the amount of postseismic deformation. Thus the fault size should be taken into serious consideration in modeling the faulting. The most noteworthy result in the model calculations is the distribution patterns of the postseismic strain field. A large shear strain, which is similar to the preseismic strain accumulation and is contrary to the coseismic strain release, is induced for a long time after faulting in the near field of the fault zone. The viscoelastic structure of the earth's crust and upper mantle, however, is hard to determine solely on the basis of geodetic measurements executed at long time intervals. Therefore, a long-term detailed monitoring of the deformation is indispensable and other kinds of field investigations are required to obtain further information about the viscoelastic structure. 128 T. TABEI Crustal movements associated with the 1927 Tango earthquake of M= 7.5 are examined for both the coseismic elastic rebound and the postseismic viscoelastic transient deformation caused by stress relaxation after faulting. The coseismic movements can be fitted by a simple conjugate fault system in which a uniform dislocation on the fault plane is assumed. The discrepancies between the observed and calculated postseismic movements are most likely due to the effect of tectonic stress. The tectonic stress is considered to have continued acting and dominating the regional crustal movements even after the earthquake. The ambiguity resulting from the similarities between the deformation due to postseismic stress relaxation and the regional tectonic movements remains unsolved. But we are convinced that it will be overcome by long-term detailed monitoring of the movements employing a new technique with a higher accuracy and a simpler management; for example, by three-dimensional relative positionings using the Global Positioning System, in the near future. I would like to thank Professor Ichiro Nakagawa for giving helpful advice throughout the course of this study and critically reading the manuscript. I wish also to acknowledge the valuable discussions with Professor Norihiko Sumitomo, Mr. Yutaka Tanaka, Mr. Kunio Fujimori, and the members of our laboratory. My thanks are also due to Professors Yoshimichi Kishimoto, Takeshi Mikumo, Torao Tanaka, and Kazuo Oike, who kindly offered helpful comments for the revision of the manuscript. The numerical calculations were executed with the computer system at the Data Processing Center of Kyoto University. 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