JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. B3, 2151, doi: /2002jb002067, 2003

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. B3, 2151, doi: /2002jb002067, 2003 Postseismic crustal deformation following the 1993 Hokkaido Nanseioki earthquake, northern Japan: Evidence for a low-viscosity zone in the uppermost mantle Hideki Ueda National Research Institute for Earth Science and Disaster Prevention, Tsukuba, Japan Masakazu Ohtake and Haruo Sato Department of Geophysics, Graduate School of Science, Tohoku University, Sendai, Japan Received 3 July 2002; revised 5 November 2002; accepted 19 November 2002; published 14 March [1] Postseismic crustal deformation following the 1993 Hokkaido Nansei-oki earthquake (M = 7.8), northern Japan, was observed by GPS, tide gauge, and leveling measurements in southwestern Hokkaido. As a result of comprehensively analyzing these three kinds of geodetic data, we found the chief cause of the postseismic deformation to be viscoelastic relaxation of the coseismic stress change in the uppermost mantle. Afterslip on the main shock fault and its extension, by contrast, cannot explain the deformation without unrealistic assumptions. The viscoelastic structure, which we estimated from the postseismic deformation, consists of three layers: an elastic first layer with thickness of 40 km, a viscoelastic second layer with thickness of 50 km and viscosity of Pa s, and an elastic half-space. This model suggests the presence of an anomalously lowviscosity zone in the uppermost mantle. The depth of the viscoelastic layer roughly agrees with that of the high-temperature portion and the low-v p zones of the mantle wedge beneath the coast of the Japan Sea in northern Honshu. These correlations suggest that the low-viscosity primarily results from high temperature of the mantle material combined with partial melt and the presence of H 2 O. These correlations also suggest that the lowviscosity zone in the uppermost mantle is widely distributed in the back arc side of the volcanic front and that postseismic deformation induced by viscoelastic relaxation may be frequently observed after large earthquakes in this area. INDEX TERMS: 1236 Geodesy and Gravity: Rheology of the lithosphere and mantle (8160); 1242 Geodesy and Gravity: Seismic deformations (7205); 7218 Seismology: Lithosphere and upper mantle; 8162 Tectonophysics: Evolution of the Earth: Rheology mantle; KEYWORDS: postseismic crustal deformation, 1993 Hokkaido Nansei-oki earthquake, viscoelastic relaxation, tide gauge, GPS, leveling Citation: Ueda, H., M. Ohtake, and H. Sato, Postseismic crustal deformation following the 1993 Hokkaido Nansei-oki earthquake, northern Japan: Evidence for a low-viscosity zone in the uppermost mantle, J. Geophys. Res., 108(B3), 2151, doi: /2002jb002067, Introduction [2] Following a large earthquake, postseismic crustal deformation has been observed by various kinds of geodetic measurements [e.g., Brown et al., 1977; Thatcher et al., 1980; Heki et al., 1997; Ueda et al., 2001]. Most of the deformations have been assumed to be due to one of two possible mechanisms: afterslip on the fault plane and its extension [e.g., Thatcher, 1975; Brown et al., 1977; Barrientos et al., 1992; Heki et al., 1997; Donnellan and Lyznga, 1998; Reilinger et al., 2000; Ueda et al., 2001], or viscoelastic relaxation of the coseismic stress change in the ductile lower crust and upper mantle [e.g., Thatcher and Rundle, 1979; Thatcher et al., 1980; Wahr and Wyss, 1980; Copyright 2003 by the American Geophysical Union /03/2002JB002067$09.00 Tabei, 1989; Pollitz and Sacks, 1992]. After the 1994 Sanriku-Haruka-oki earthquake (M = 7.5), GPS measurements revealed significant postseismic deformation, which was interpreted as being a large afterslip on the main shock fault [Heki et al., 1997; Heki and Tamura, 1997]. Nishimura et al. [2000] revealed that the afterslip further extended toward the south and toward the downdip direction of the plate interface. On the other hand, the postseismic elevation changes seen after the 1946 Nankaido earthquake (M = 8.2) were explained by viscoelastic relaxation in the upper mantle [Miyashita, 1987]. It is important to clarify the physical mechanism of postseismic deformation, since modeling of this type of deformation can provide important information on the constraints on the frictional properties of the fault [Marone et al., 1991] and on the viscoelastic structure of the medium [e.g., Thatcher et al., 1980; Pollitz et al., 2000, 2001]. ETG 6-1

2 ETG 6-2 UEDA ET AL.: POSTSEISMIC CRUSTAL DEFORMATION Figure 1. Map showing the aftershock area of the 1993 Hokkaido Nansei-oki earthquake (shaded area) and the tectonic environment of northeastern Japan. The rectangle indicates the study area shown in Figures 2, 4, 5, 9, and 10. Dashed and dotted curves indicate the plate boundary proposed by Nakamura [1983] and the volcanic front, respectively. A solid star and a circle show the epicenter of the 1896 Riku-u earthquake and the Wakkanai GPS station, respectively. AM, Amurian plate; EU, Eurasian plate; OK, Okhotsk plate; NA, North American plate. caused serious damage to the Japan Sea coastline. The eastern margin of the Japan Sea is characterized by the occurrence of large thrust earthquakes [e.g., Ohtake, 1995], and the Hokkaido Nansei-oki earthquake occurred between the focal regions of the 1940 Shakotan earthquake (M = 7.5) to the north and the 1983 Japan Sea earthquake (M = 7.7) to the south. Kobayashi [1983] and Nakamura [1983] proposed that a nascent trench (the dashed line in Figure 1) is present along the margin. This nascent trench is believed to be a plate boundary between the Amurian and the North American plates [Heki et al., 1999] or between the Eurasian and Okhotsk plates [Seno et al., 1996]. The Hokkaido Nansei-oki earthquake was a reverse-fault type, but the fault model obtained by Tanioka et al. [1995] (Figure 2) has a complex fault geometry. The fault, which is consistent with the aftershock distribution, consists of a northernmost subfault A with a shallow dip to the east, subfaults B and C with shallow dips to the west, and subfaults D and C with steep dips to the west. The slip, oriented approximately eastwest, amounted to 3.1 m on average. [5] The northeastern Japan arc, where the Pacific plate is subducting beneath the continental plate from the Japan and Kurile Trenches, is one of the most archetypal subduction zones in the world. Horizontal strain in the arc derived from geodetic observations is characterized by compressional strain in a roughly east-west direction [Shen-Tu and Holt, 1996; Mazzotti et al., 2000; Sagiya et al., 2000]. Mazzotti et [3] However, limitations on observations with respect to space, time and accuracy make it difficult to discriminate between the two possible causes. The postseismic crustal deformation following the 1992 Landers earthquake (M = 7.5) observed by GPS was initially interpreted as an afterslip on the downdip extension of the main shock fault [Shen et al., 1994; Savage and Svarc, 1997]. However, by reexamination using interferometric synthetic aperture radar (InSAR) data containing the vertical component of the postseismic deformation, it was confirmed that the postseismic deformation had been caused by viscoelastic relaxation of the medium [Deng et al., 1998; Pollitz et al., 2000]. In this paper, we carefully investigate the postseismic deformation following the 1993 Hokkaido Nansei-oki earthquake, and clarify its cause. 2. Hokkaido Nansei-Oki Earthquake [4] The M w = 7.8 Hokkaido Nansei-oki earthquake of 12 July 1993 occurred 50 km west of the coast of Hokkaido, northern Japan (Figure 1). The hypocenter was located by the Japan Meteorological Agency at E, N, 34 km deep. Large tsunamis generated by the earthquake Figure 2. Map showing the locations of GPS stations (triangles and diamonds), tide gauge stations (solid squares) and the leveling route (dotted curve). Star denotes the epicenter of the Hokkaido Nansei-oki earthquake. Shaded rectangles and thick arrows indicate the main shock fault consisting of subfaults A, B, C, D, and E, and their slip vectors of overriding blocks, respectively [after Tanioka et al., 1995]. Thick lines denote the upper boundary of the subfaults.

3 UEDA ET AL.: POSTSEISMIC CRUSTAL DEFORMATION ETG 6-3 al. [2000] explained the strain derived from GPS observation data by loading of the relative motion of the Pacific plate to the continental plate. After the Hokkaido Nansei-oki earthquake, a marked horizontal crustal deformation was observed by GPS in the Oshima Peninsula and Okushiri Island, southwestern Hokkaido (Figure 2). Mazzotti et al. [2000] pointed out that the relatively large velocities in the southwestern part of Hokkaido cannot be explained by elastic loading from the Japan and west Kurile Trenches. Ito et al. [2000] also interpreted the compressional strain in the northeastern Japan arc by loading of the relative motion of the Pacific plate to the continental plate. They pointed out that anomalous extensional deformation, which cannot be explained by their model, exists in the southwestern Hokkaido. These studies strongly suggest the occurrence of a postseismic crustal deformation following the Hokkaido Nansei-oki earthquake. However, details of the deformation and its mechanism have not yet been clarified. [6] Postseismic crustal deformations have been investigated for several large interplate earthquakes along the Japan Trench. All of them have been interpreted by large afterslips on the plate boundary [Miura et al., 1993; Kawasaki et al., 1995; Heki et al., 1997; Heki and Tamura, 1997; Nishimura et al., 2000; Ueda et al., 2001]. Although postseismic crustal deformations are also reported for the 1964 Niigata [Taguchi and Fujii, 1989] and the 1983 Japan Sea [Miura et al., 1990] earthquakes that occurred along the east margin of the Japan Sea, the characteristics of postseismic deformation in the region are as yet unknown. Using geodetic data obtained after the Hokkaido Nanseioki earthquake, we study its postseismic deformation and clarify the physical mechanism of the deformation on the basis of the assumption that it was generated by afterslip or viscoelastic relaxation. 3. Data [7] This study utilizes GPS data, tide gauge records and leveling data obtained by the Geographical Survey Institute of Japan (GSI) in the western part of Hokkaido. Figure 2 illustrates the locations of the observation stations and the leveling route. The GPS stations are part of the nationwide Global Positioning Network (GEONET) permanent array, established by the GSI in 1994 [Miyazaki et al., 1997]. The GPS data we use are site velocities estimated from the daily estimates of coordinates of the stations in the period from April 1996 to December 1999 (3.8 years) at 23 stations (triangles in Figure 2), and from June 1997 to December 1999 (2.6 years) at 9 stations (diamonds in Figure 2). We do not use data from before April 1996, since the number of stations was limited to only 7 in the area covered by Figure 2. Figure 3 shows the time series of movements at typical GPS stations: on Okushiri Island (Figures 3a, 3b, and 3c) and on the northwest coast of the Oshima Peninsula (Figures 3d, 3e, and 3f ). The horizontal and vertical components are movements relative to the Wakkanai station (solid circle in Figure 1) and (Oshoro), respectively. Linear curves indicate the average rate of deformation fitted to the data using the least squares method. Fitting is very good for the horizontal components, although less reliable for the vertical component. Figure 3. Time series of movement of GPS stations (a, b, and c) and (d, e, and f ) The horizontal and vertical movements are from the Wakkanai (Figure 1) and (Figure 2) GPS stations, respectively. The solid lines indicate the regression lines fitted to the data. [8] Zhang et al. [1997] and Mao et al. [1999] have suggested that errors in the GPS time series consist of white and colored noise caused by unmodeled effects including monument instabilities, uncertainty in satellite orbit parameters, atmospheric and local environmental effects. Since Mao et al. [1999] analyzed a 3-year time series and concluded that the noise characteristics of the coordinate time series can be modeled by a combination of white plus flicker noise, we take account of white noise and flicker noise in evaluating GPS velocity errors. They provide an approximate expression for the total velocity error (s r ): s r ¼ " # 1=2 12s2 w gt 3 þ as2 f g b T 2 ; ð1þ where g is number of measurements per year, T is the total time span in years, a and b are empirical constants (a = 1.78 and b = 0.22), and s w and s f are the magnitudes in millimeters of white and flicker noise, respectively (the random walk component is neglected here). We obtain a rough estimate of velocity errors by using the formula and mean values of the magnitude of white and flicker noise obtained by Mao et al. [1999] for stations located in regions other than North America, western Europe and the tropical regions [Mao et al., 1999, Table 8]. The velocity errors obtained for stations observed for 3.8 years are 1.7 mm/yr (east), 1.3 mm/yr (north), and 2.8 mm/yr (vertical), and for

4 ETG 6-4 UEDA ET AL.: POSTSEISMIC CRUSTAL DEFORMATION Figure 4. Observed horizontal velocities with confidence ellipses of 1s at GPS stations (solid arrows) averaged over the period from April 1996 to December 1999 for 23 stations (triangles in Figure 2), and the period from June 1997 to December 1999 for 9 stations (diamonds in Figure 2) relative to the Wakkanai station (Figure 1). Superimposed are theoretical velocities (open arrows) calculated from the best fit viscoelastic model. 2.6 years are 2.4 mm/yr (east), 1.9 mm/yr (north), and 4.1 mm/yr (vertical). Dixon et al. [2000] pointed out that errors given by Mao et al. [1999] may be values too large for modern analyses or different site locations. Since the velocities relative to Wakkanai and Oshoro stations must contain errors in velocities of the reference station, we conservatively use the estimation based on work by Mao et al. [1999] in this study. [9] Figure 4 shows the horizontal velocities (solid arrows) at the GPS stations relative to the Wakkanai station. Westward movement is seen at all stations with maximum velocity along the west coast of the Oshima Peninsula. Figure 5 shows the vertical velocities (solid arrows) of GPS stations relative to the station at Oshoro. Two GPS stations in Okushiri Island ( and ) indicate clear subsidence, in contrast to a small uplift in the northern part of the Oshima Peninsula. [10] The tide gauge stations we use are Okushiri and Oshoro (solid squares in Figure 2). In Figures 6a and 6b, we show daily mean tide records at the Oshoro and Okushiri stations, respectively. The tide records fluctuate strongly with amplitudes of up to 400 mm peak to peak due to oceanographic and atmospheric influences. By taking the difference of these two tide gauge records, we can minimize the fluctuations, and obtain the relative vertical deformation between the two tide gauge stations (Figure 6c). We further process the difference in tide records by using a median filter [e.g., Ueda et al., 2001] to remove high-frequency noise, and by using BAYSEA [Ishiguro, 1986] to remove seasonal fluctuations. Thus we obtained the final result shown in Figure 6d, which is expected to represent the relative vertical displacement between the two stations. The filtering procedure followed the method of Ueda et al. [2001]. The Oshoro tide gauge station, located relatively distant from the focal zone of the Hokkaido Nansei-oki earthquake, is reasonably stable, with a very small longterm rate of tide level change of 0.3 mm/yr for the period from 1958 to 2000 [Geographical Survey Institute, 2000]. Thus the difference in tide levels in Figure 6d is almost completely attributable to the subsidence of the Okushiri station. The velocity of subsidence is 13.3 ± 0.2 mm/yr in the period from January 1995 to September 2000, shown by a solid arrow in Figure 5. This velocity is anomalously high compared with other tide gauge stations in Japan registered at the Coastal Movements Data Center [Geographical Survey Institute, 2000]. The vertical velocity at the Okushiri tide gauge station is very close to that at the nearest GPS station , 12.2 mm/y r. This agreement shows that the vertical component of GPS data is useful in detecting crustal deformations in spite of a larger observational error than seen in the horizontal component. [11] The leveling route, extending 129 km from Oshoro to BM 24, is shown by a dotted curve in Figure 2. It contains 71 benchmarks with a spacing of 2 km. The GSI performed first-order leveling surveys along this route in August 1993, 1 month after the earthquake, and in August Figure 7 shows the height change between the two surveys. The results indicate uplift of BM 24 by 30 mm Figure 5. Observed vertical velocities at GPS and Okushiri tide gauge stations (solid arrows) relative to the Oshoro tide gauge station with confidence ellipses of 1s. Superimposed are theoretical vertical velocities calculated from the best fit viscoelastic relaxation model (open arrows).

5 UEDA ET AL.: POSTSEISMIC CRUSTAL DEFORMATION ETG 6-5 Figure 7. Elevation changes (solid squares) over 5 years after the Hokkaido Nansei-oki earthquake along the leveling route shown in Figure 2 relative to the Oshoro tide gauge station. The solid curve shows the theoretical vertical displacement calculated from the best fit viscoelastic relaxation model. Figure 6. Daily mean tide gauge records at the (a) Oshoro and (b) Okushiri stations. (c) The difference in the daily mean tide records between Figures 6a and 6b. (d) The difference of tide records processed by BAYSEA [Ishiguro, 1986] and a median filter [e.g., Ueda et al., 2001] to remove seasonal and short period fluctuations, respectively. The dashed curve in Figure 6d shows the theoretical vertical displacement calculated from the best fit viscoelastic relaxation model. The vertical line shows the occurrence time of the Hokkaido Nansei-oki earthquake. relative to Oshoro. The p error in first-order leveling is regulated to within 2:5 ffiffi s mm, where s is the length of leveling route in km, which predicts a maximum error of 28 mm over the leveling route. Since actual surveys are performed with higher accuracy than the regulation, the leveling data shows clear evidence of uplift along the leveling route. The leveling data are consistent with the GPS data showing the uplift of the northern part of the Oshima Peninsula. [12] Three independent sets of geodetic data show the presence of marked crustal deformation following the Hokkaido Nansei-oki earthquake. The postseismic deformation is characterized by the westerly movement of southwestern Hokkaido, the subsidence of Okushiri Island, and the uplift of the Oshima Peninsula. 4. Viscoelastic Relaxation Model 4.1. Method [13] In this section, we model the postseismic crustal deformation assuming viscoelastic relaxation of the coseismic stress change. For modeling the deformation, we consider a viscoelastic structure consisting of an elastic first layer with thickness H 1, a Maxwell body viscoelastic second layer with thickness H 2 and viscosity h, and an elastic half-space. Each layer respectively represents the crust, the upper mantle and the subducting Pacific plate. Seismic wave velocity and the density of each layer are set as shown in Table 1. The properties of the first and second layers are based on a reflection profile obtained by Okada et al. [1973] for the area west of the coast of the Shakotan Peninsula (see Figure 2 for location). For the third layer, the velocity is that in the Pacific plate beneath northeast Japan [Obara et al., 1986], and the density is that of the Preliminary Reference Earth Model [Dziewonski and Anderson, 1981] at a depth of 150 km. Unknown model parameters are H 1, H 2 and h. The viscoelastic deformation is synthesized using the method of Matsu ura et al. [1981] with the threelayered viscoelastic structure. The fault model of Tanioka et al. [1995] is used for the calculation. [14] We conducted a grid search to find the best fit values of the unknown model parameters H 1, H 2, and h that minimize the misfit: S ¼ XN w i s O i s C 2 i ; i¼1 where N is the total number of data items, w i is the weight coefficient for the ith data item, and s i O and s i C are the ith observed and calculated crustal deformations, respectively. The data we used are the horizontal and vertical velocities of the GPS stations, the vertical velocity of the Okushiri tide gauge station and the vertical displacement along the leveling route. The horizontal and vertical data are referred to the Wakkanai station and the Oshoro tide gauge station, respec- Table 1. Viscoelastic Structure Model Layer V p, km/s V s, km/s r, g/cm 3 Thickness, km Viscosity, Pa s H H 2 h ð2þ

6 ETG 6-6 UEDA ET AL.: POSTSEISMIC CRUSTAL DEFORMATION tively. For the horizontal velocities, s i O in equation (2) is replaced by s i O v S, where v S is an additional unknown vector that represents average crustal deformation due to the subduction of the Pacific plate. For GPS data, we assign w i the reciprocal of the square of the measurement error of corresponding data. The error in GPS velocity is mm/yr for the horizontal component, and mm/yr for the vertical component. For the tide and leveling data, we assign w i the reciprocal of the square of 2 mm/yr and 1 mm, respectively. [15] The search range is km for H 1, and km for H 2, both in steps of 5 km. For h, the range is Pa s to Pa s, where the step is Pa s for Pa s, and Pa s for Pa s Results [16] As a result of the analysis, we obtained the best fit model: H 1 = 40 km, H 2 = 50 km, and h = Pa s, and the corresponding average horizontal velocity v S is 8 mm/yr in the direction of N66 W. This velocity coincides with 6 9 mm/yr that is expected from the loading of Pacific plate [Mazzotti et al., 2000]. Figure 4 compares the observed and calculated horizontal velocities derived from the best fit model. The best fit model reproduces the basic feature of the westerly movements of GPS stations over the entire study area, although the residuals are somewhat large in the southern part of the Oshima Peninsula. The comparison of the vertical velocities at the GPS and tide gauge stations is shown in Figure 5. The best fit model also agrees with the basic feature of the long-wavelength postseismic deformation characterized by the subsidence of Okushiri Island and uplift of the Oshima Peninsula. For leveling data, the solid curve in Figure 7 shows the calculated vertical displacement. The vertical displacement derived from the best fit model closely reproduces the tilt to the northeast along the leveling route, although the best fit model is unable to reproduce some of the short-wavelength deformations. The time series of the synthetic deformation of the Okushiri tide gauge station is shown in Figure 6d by a dashed curve. This synthetic curve shows close agreement with the difference in tide gauge records. Thus the viscoelastic model matches the gross observational features in both space and time. Some discrepancies seen in Figure 4 and 5 may be attributable to other effects, including lateral variation in viscosity and the subduction of the Pacific plate. [17] The computation of postseismic deformation does not include the effect of gravity. Rundle [1982] showed that in relation to the Maxwell relaxation time, the effect of gravity is small over the short period following an earthquake. The viscosity we obtained corresponds to a Maxwell time of roughly 2 years. The time span of our data is about 3 relaxation times. The result obtained by Rundle [1982] shows that the effects of gravity are still not significant over such a short postseismic period. It is therefore reasonable to ignore the effect of gravity in this study. [18] We investigated a viscoelastic structure model other than the best fit model that adequately agrees with the postseismic crustal deformation. Since the model must show a good fit to all the data types simultaneously, we selected the model as acceptable using the following criteria. We divided all the data into three data subsets: the horizontal component of the GPS data ( j = 1), the vertical component Figure 8. The investigated model parameter space of the three-layered viscoelastic structure. The stars and crosses indicate the best fit model and acceptable models, respectively. of the GPS data and the tide gauge record ( j = 2), and the leveling data ( j = 3). We also divided S in equation (2) into S j ( j = 1, 2, 3) corresponding to the data subsets. We regard models that simultaneously satisfy the condition of S j /S j 0 <2 for each data subset as acceptable, where S j 0 is the misfit of each data subset to the best fit model. [19] In Figure 8, the best fit model and acceptable models are denoted by a star and crosses, respectively. The ranges

7 of the acceptable model parameters are H 1 = km, H 2 = km, and h = to Pa s, respectively. UEDA ET AL.: POSTSEISMIC CRUSTAL DEFORMATION ETG Afterslip Model [20] Afterslip of the fault plane is also one of the potential causes of postseismic crustal deformation, since afterslips following large earthquakes have been frequently reported for the plate boundary east of the Pacific coast of Honshu [Miura et al., 1993; Kawasaki et al., 1995; Heki et al., 1997; Heki and Tamura, 1997; Ueda et al., 2001]. We examined whether the postseismic deformation following the 1993 Hokkaido Nansei-oki earthquake can be interpreted using an afterslip model or not. [21] In our model, we assume that afterslips of different amounts occurred on the subfaults A, B, C, D, and E in Figure 2. We assume slips of constant rates, since the postseismic deformation shown in the horizontal component of the GPS data is almost linear from April 1996 to December 1999 (see Figure 3). Postseismic deformation is synthesized by the method of Okada [1992] with an elastic half-space. We evaluated the slip rates of the subfaults so as to minimize equation (2). In the estimation, we did not use the leveling data, since information on the time history of the deformation during the 5 years is not included in the data and we do not know the time history of the postseismic deformation before 1995 when tide level observations started at the Okushiri station. [22] The slip rates of each subfault of the best fit afterslip model are shown in Figure 9b, and the corresponding average horizontal velocity v S is 9.6 mm/yr to in direction of N78 W. Figure 9 shows the comparison between the observed (solid arrows) and calculated (open arrows) velocities derived from the best fit model for the horizontal (Figure 9a) and vertical (Figure 9b) components. The calculated vectors show fairly good agreement with those of GPS observation for the horizontal component, but disagree for the vertical component. In the northern part of the Oshima Peninsula, calculated vertical changes, showing small subsidence, contradict the large uplift observed by GPS and precise leveling. [23] We investigate another afterslip model for confirmation of the result. In the model, we assume that afterslips of different amounts occurred on the subfaults A, B, C, D, and E, with their downdip extensions having the same size as the main shock fault: subfaults A 0,B 0,C 0,D 0, and E 0 in Figure 10a. The slip rates of each subfault of the best fit afterslip model are shown in Figure 10b, and the corresponding average horizontal velocity v S is 10 mm/yr to in direction of N81 W. Figure 10 shows the comparison between the observed (solid arrows) and calculated (blank arrows) velocities derived from the best fit model for the horizontal (Figure 10a) and vertical (Figure 10b) components. The calculated vectors show fairly good agreement with those of GPS observation for the horizontal and vertical components. However, the slip rates are extremely high, exceeding 10 m/yr for some subfaults and amounting to 4 m/yr on average. Moreover, the best fit model requires a range of different slip directions and unlikely backslips for some subfaults. The afterslip model is too unrealistic judging from the slip directions and slip rates obtained; in usual cases, slip direction is nearly the same as Figure 9. Comparison of the observed velocities (solid arrows) with confidence ellipses of 1s at the GPS and Okushiri tide gauge stations with theoretical velocities (open arrows) calculated from the best fit afterslip model for (a) the horizontal and (b) vertical velocities. The best fit model was obtained by assuming that afterslip is limited to the main shock fault. Shaded rectangles and thick arrows show the subfaults of the Hokkaido Nansei-oki earthquake (A, B, C, D, and E), and slip rates of the overriding block for the afterslip model, respectively. The Wakkanai station and the Oshoro tide gauge station are fixed for the horizontal and vertical velocities, respectively.

8 ETG 6-8 UEDA ET AL.: POSTSEISMIC CRUSTAL DEFORMATION the coseismic slip direction and the slip rate is in the order of several hundred millimeters per year [e.g., Heki et al., 1997] except immediately after the earthquake [e.g., Heki and Tamura, 1997]. [24] An extremely high rate can be seen, especially for the downdip extensions of the main shock fault. A high slip rate is needed to explain the vertical component of the postseismic deformation, because the vertical component cannot be explained at all by the best fit model that is obtained by assuming that afterslip is limited to the main shock fault (Figure 9). This discrepancy is probably due to the fact that slippage of faults at shallow depths is unlikely to cause vertical crustal deformations in distant areas. Even if we were to use a more complicated afterslip model, we would probably need to adopt unrealistic assumptions, including an extremely high slip rate on the downdip extension of the main shock fault. For these reasons, we conclude that afterslip is not acceptable as the dominant mechanism of the postseismic crustal deformation of the 1993 Hokkaido Nansei-oki earthquake. Figure 10. Comparison of the observed velocities (solid arrows) with confidence ellipses of 1s at GPS and Okushiri tide gauge stations with theoretical velocities (open arrows) calculated from the best fit afterslip model for (a) the horizontal and (b) vertical velocities. The shaded rectangles show the subfaults of the Hokkaido Nansei-oki earthquake (A, B, C, D and E) and corresponding downdip extensions (A 0, B 0, C 0, D 0, and E 0 ). Thick arrows on the subfaults indicate slip rates of the overriding block for the afterslip model. The Wakkanai station and the Oshoro tide gauge station are fixed for the horizontal and vertical velocities, respectively. 6. Discussion 6.1. Comparison With Other Observations [25] We find that the postseismic crustal deformation following the Hokkaido Nansei-oki earthquake can be explained by the viscoelastic relaxation of the coseismic stress change in a simple three-layered structure. The afterslip model, by contrast, cannot explain the deformation without adopting unrealistic assumptions. This result indicates that viscoelastic relaxation was clearly the dominant mechanism of the postseismic deformation. [26] The modeling of the postseismic deformation provides a rough picture of the viscoelastic structure beneath southwestern Hokkaido. The depth range of the viscoelastic layer of the acceptable models extends from 30 to 120 km, and the range occupies a part of the uppermost mantle. However, it does not coincide with the whole wedge mantle, since the thickness of the crust is 30 km along the coastline of the Japan Sea in the northern part of Honshu [Zhao et al., 1990], and the depth of the upper double seismic plane is km in southwestern Hokkaido [Kosuga et al., 1996]. The most plausible reason for the disagreement is that the viscoelastic layer we revealed may present a zone of extremely low viscosity, which allows a short-term stress relaxation of only a few years. [27] In Figure 11, we compare the viscoelastic structure we obtained with the thermal structure (dotted curve) [after Peacock and Wang, 1999] and P wave velocity perturbation (dashed curve) [after Nakajima et al., 2001] beneath the coastline of the Japan Sea in northern Honshu. The profiles are for latitude 40 N for the temperature and the average in northern Honshu for velocity, respectively. The temperature of the uppermost mantle is one of the most important causes of low viscosity, since high temperature generally leads to lower viscosity. The back arc side of the volcanic front in northeastern Japan arc is characterized by high heat flow [e.g., Uyeda and Hôrai, 1964]. The high-temperature portion corresponds to the high heat flow present beneath the back arc side. The velocity structure can also provide us with information on the origin of low viscosity. The structure shows that a low-v p zone exists at the same depth

9 UEDA ET AL.: POSTSEISMIC CRUSTAL DEFORMATION ETG 6-9 Figure 11. Comparison of the viscoelastic structure (solid line) and the thermal structure (dotted curve) [after Peacock and Wang, 1999], and the distribution of the averaged V p perturbation (dashed curve) [after Nakajima et al., 2001] beneath the coastline of the Japan Sea in northern Honshu. Error bars represent the ranges of the acceptable model parameters of the viscoelastic structure. as the high-temperature portion. The depth of the hightemperature portion exceeding 800 C is km and the low-v p zone is situated km in depth. They roughly agree with the depth of the viscoelastic layer allowing the uncertainty of the best fit model. [28] Nakajima et al. [2001] inferred that the low-velocity zone in the mantle wedge represents the ascending flow of hot mantle material from depth, including partial melt. The V p structure beneath northern Honshu was also modeled by Iwamori and Zhao [2000] on a mineralogical basis. In their model, melting is initiated beneath the back arc side with the transportation of H 2 O from the descending slab. Their idea is supported by Wyss et al. [2001] by combing the tomographic image of Nakajima et al. [2001] with the frequency-magnitude distribution of earthquakes. Wyss et al. [2001] state that H 2 O is expressed from the descending slab at a depth of km beneath the back arc side and induces the partial melting of the mantle material in the mantle wedge. [29] The presence of partial melt and H 2 O lowers the viscosity of the mantle material [Cooper and Kohlstedt, 1984; Karato et al., 1986]. Therefore the correlation of the viscoelastic layer with the high-temperature and low-v p zones suggests that the primary origins of the low-viscosity zone beneath southwestern Hokkaido are the high temperature of the mantle wedge, and the presence of partial melted mantle material mixed with H 2 O. [30] Although the lower boundary of the viscoelastic layer is not as constrained as the upper boundary, the lower boundary is clearly shallower than the lower limit of the high-temperature and low-v p zones. High pressure at depth may contribute to raising the viscosity. Further investigations are needed to reveal a quantitative relationship among viscosity of the mantle wedge, content of partial melt and H 2 O, temperature, and pressure Difference Beneath the Back Arc and Forearc Sides [31] In the forearc side of northeast Japan, postseismic crustal deformation has been reported for several large earthquakes associated with the subduction of the Pacific plate: the 1978 Miyagi-oki [Ueda et al., 2001], the 1989 Sanriku-oki [Miura et al., 1993], the 1992 Sanriku-oki [Kawasaki et al., 1995] and the 1994 Sanriku-Haruka-oki earthquakes [Heki et al., 1997; Heki and Tamura, 1997; Nishimura et al., 2000]. All of these cases are attributed to be due to afterslips. This contrasts with our finding that the postseismic deformation following the Hokkaido Nanseioki earthquake was mainly due to viscoelastic relaxation in the uppermost mantle. [32] The difference in the nature of postseismic effect is probably attributable to the difference in viscoelastic structure between the forearc and back arc sides of the volcanic front. There exist between them large differences in thermal and V p structures. The thermal structure derived by Peacock and Wang [1999] shows the temperature of the wedge mantle in the forearc side to be several hundred degrees centigrade lower than that in the back arc side. The V p structure derived by Nakajima et al. [2001] shows that low- V p zones are distributed in parallel with the subducting Pacific plate and spread from the crust beneath the volcanic front to the deeper portion of the wedge mantle beneath the back arc side. The low-v p zones in the forearc side are weaker than those in the back arc side. These observations strongly suggest that the viscosity of the wedge mantle in the forearc side is much higher than that in the back arc side. Figure 12 shows a schematic view of a cross section of the viscoelastic structure in northeastern Japan as suggested by these observations. We speculate that there exists an especially low-viscosity zone in the wedge mantle correspond- Figure 12. Schematic view of an east-west cross section of the viscoelastic structure beneath northeastern Japan. The shaded area represents the low-viscosity portion in the uppermost mantle, probably corresponding to high-temperature [Peacock and Wang, 1999] and low-v p portion [Nakajima et al., 2001].

10 ETG 6-10 UEDA ET AL.: POSTSEISMIC CRUSTAL DEFORMATION ing to the high-temperature and low-v p portion beneath the eastern margin of the Japan Sea. [33] If this is the case, significant viscoelastic relaxation is expected to occur not only after the Hokkaido Nanseioki earthquake but also after other large earthquakes in the back arc side of the northeastern Japan arc. The postseismic deformation following the 1896 Riku-u earthquake (Figure 1), which occurred 20 km west of the volcanic front in northern Honshu, was interpreted as viscoelastic relaxation in the uppermost mantle [Thatcher et al., 1980]. Their estimate for the viscosity of the uppermost mantle is Pa s, which is of the same order as our estimate for the Hokkaido Nansei-oki earthquake. Their finding supports our hypothesis that postseismic deformation induced by viscoelastic relaxation is commonly observed after large earthquakes in the back arc side of the northeastern Japan arc. However, their model can explain the deformation only in the back arc side: a conspicuous disagreement with the observations emerges in the forearc side. They attributed this discrepancy to the effects of the subduction of the Pacific plate. We propose an alternative hypothesis: that the difference in viscosity between the forearc and back arc sides affects postseismic deformation. Since the source region of the Hokkaido Nansei-oki earthquake is far from the volcanic front, the effect of the difference in viscosity is probably small for the postseismic deformation following the earthquake. Therefore it is reasonable to assume a horizontally uniform structure in this study. However, further studies are needed to clarify the effect of lateral heterogeneity of viscosity on postseismic deformation. [34] Another reason for the contrast in the dominant mechanism of postseismic deformation may be a difference in the frictional properties of fault planes. There is a large difference in seismic activity between the area east of the Pacific coast and the eastern margin of the Japan Sea. On the plate boundary east of the Pacific coastline, large interplate earthquakes frequently occur: e.g., the 1952 Tokachi-oki (M = 8.2), the 1968 Tokachi-oki (M = 7.9), the 1973 Nemuro-oki (M = 7.4), and the 1994 Sanriku-Haruka-oki earthquakes (M = 7.5). The eastern margin of the Japan Sea also sees many large thrust earthquakes, suggesting the existence of a plate boundary [Nakamura, 1983; Kobayashi, 1983]. However, the beginning of convergent deformation in the east margin of the Japan Sea is 3.5 Ma [Sato, 1994], which is much later than the beginning of subduction of the Pacific plate. In the focal area of the Hokkaido Nansei-oki earthquake, historical data shows that no large earthquakes have occurred, at least in the last 300 years [Hatori and Katayama, 1977]. These studies suggest that the fault gouge of the plate boundary in the east margin of the Japan Sea is not yet as well developed as that of the Pacific plate. The results of laboratory frictional experiments by Marone et al. [1990] show that a fault with a thick fault gauge tends to show stable sliding. The dominance of afterslips on the boundary of the Pacific plate may be attributable to weak coupling of the plate boundary, brought about through a long history of subduction Importance of Vertical Deformation Measurements and Future Scope [35] As was shown in sections 4 and 5, the vertical component of postseismic deformation is satisfactorily explained by the viscoelastic relaxation model (Figure 5), but cannot be explained by the afterslip model without the adoption of unrealistic assumptions (Figures 9b and 10b). In contrast, the horizontal component is explained by both of the models (see Figures 4, 9a and 10a). This is similar to the case of strike slip faulting, for which both of the models produce the same horizontal postseismic deformations parallel to the fault strike [Savage and Prescott, 1978; Savage, 1990]. This indicates the importance of observation of vertical crustal deformations for discriminating between physical mechanisms. In our analysis, we used the vertical component of GPS data, tide gauge records and leveling data. By use of vertical crustal deformation data, we are extending our study of postseismic deformations to other large earthquakes in the eastern margin of the Japan Sea to clarify whether or not viscoelastic relaxation is a common characteristic of the region. [36] The viscoelastic structure we modeled describes the gross features of the postseismic deformation following the Hokkaido Nansei-oki earthquake, but some discrepancies remain. It is plausible that the actual viscoelastic structure may be more nonhomogeneous both laterally and depth wise. The postseismic deformation near the volcanic front may be affected by the difference in the viscoelastic structure between the forearc and the back arc sides. Furthermore, the crustal deformation near the Pacific coast may be affected by the subducting Pacific plate. However, it is difficult to distinguish between such effects using our simple layered structure model. It will be necessary to consider three-dimensional variation of viscosity to allow the development of a more detailed viscoelastic model of postseismic deformation. 7. Conclusion [37] On the basis of geodetic measurement data, we revealed that a significant postseismic crustal deformation followed the 1993 Hokkaido Nansei-oki earthquake (M w = 7.8) in southwestern Hokkaido. The deformation is characterized by the westerly movement of southwestern Hokkaido, subsidence of Okushiri Island, and uplift of the Oshima Peninsula. By simultaneously analyzing GPS, tide gauge and leveling data, we found that the major cause of the postseismic deformation was viscoelastic relaxation of the coseismic stress change in the uppermost mantle. An afterslip model, on the other hand, cannot explain this deformation without the adoption of unrealistic assumptions. [38] The viscoelastic structure we estimated from the postseismic deformation consists of an elastic first layer with thickness of 40 km and a viscoelastic second layer with thickness 50 km and viscosity of Pa s riding on an elastic half-space. The depth of the low-viscosity zone correlates closely with that of the low-v p zones and the high-temperature portion of the mantle wedge beneath the coast of the Japan Sea in northern Honshu. This agreement suggests that the low viscosity results from the high temperature of the mantle material and the presence of partial melt and H 2 O. [39] This correlation also suggests that the low-viscosity zone in the uppermost mantle may be widely distributed in the back arc side and that postseismic deformation induced

11 UEDA ET AL.: POSTSEISMIC CRUSTAL DEFORMATION ETG 6-11 by the viscoelastic relaxation may be commonly observed after large earthquakes in this region. We intend to extend this study to other large earthquakes along the eastern margin of the Japan Sea by adopting a viscoelastic structure model with lateral nonhomogeneity. [40] Acknowledgments. We are grateful to the Geographical Survey Institute for providing us with GPS data, tide gauge records and leveling data. We thank Jim Savage, Paul Segall, and an anonymous associate editor for their thorough reviews and helpful comments. We also thank Shin ichi Miyazaki for helpful suggestions. The maps and figures were generated using Generic Mapping Tools (GMT) software [Wessel and Smith, 1995]. We used the BAYSEA computer program, developed by Akaike and Ishiguro at the Institute of Statistical Mathematics, for processing tide records. This research was done as part of the Ph.D. thesis of Hideki Ueda at Tohoku University. 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