Postseismic crustal deformation following the 1993 Hokkaido Nansei-

oki earthquake, northern Japan: Evidence for a low-viscosity zone

in the uppermost mantle

Hideki UedaNational Research Institute for Earth Science and Disaster Prevention, Tsukuba, Japan

Masakazu Ohtake and Haruo SatoDepartment 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 2003.

[1] Postseismic crustal deformation following the 1993 Hokkaido Nansei-oki earthquake(M = 7.8), northern Japan, was observed by GPS, tide gauge, and leveling measurementsin southwestern Hokkaido. As a result of comprehensively analyzing these three kinds ofgeodetic data, we found the chief cause of the postseismic deformation to beviscoelastic relaxation of the coseismic stress change in the uppermost mantle. Afterslipon the main shock fault and its extension, by contrast, cannot explain the deformationwithout unrealistic assumptions. The viscoelastic structure, which we estimated from thepostseismic deformation, consists of three layers: an elastic first layer with thickness of 40km, a viscoelastic second layer with thickness of 50 km and viscosity of 4 � 1018 Pa s,and an elastic half-space. This model suggests the presence of an anomalously low-viscosity zone in the uppermost mantle. The depth of the viscoelastic layer roughly agreeswith that of the high-temperature portion and the low-Vp zones of the mantle wedgebeneath the coast of the Japan Sea in northern Honshu. These correlations suggest that thelow-viscosity primarily results from high temperature of the mantle material combinedwith partial melt and the presence of H2O. These correlations also suggest that the low-viscosity zone in the uppermost mantle is widely distributed in the back arc side of thevolcanic front and that postseismic deformation induced by viscoelastic relaxation may befrequently 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:10.1029/2002JB002067, 2003.

1. Introduction

[2] Following a large earthquake, postseismic crustaldeformation has been observed by various kinds of geodeticmeasurements [e.g., Brown et al., 1977; Thatcher et al.,1980; Heki et al., 1997; Ueda et al., 2001]. Most of thedeformations have been assumed to be due to one of twopossible mechanisms: afterslip on the fault plane and itsextension [e.g., Thatcher, 1975; Brown et al., 1977; Bar-rientos et al., 1992; Heki et al., 1997; Donnellan andLyznga, 1998; Reilinger et al., 2000; Ueda et al., 2001],or viscoelastic relaxation of the coseismic stress change inthe ductile lower crust and upper mantle [e.g., Thatcher andRundle, 1979; Thatcher et al., 1980; Wahr and Wyss, 1980;

Tabei, 1989; Pollitz and Sacks, 1992]. After the 1994Sanriku-Haruka-oki earthquake (M = 7.5), GPS measure-ments revealed significant postseismic deformation, whichwas interpreted as being a large afterslip on the main shockfault [Heki et al., 1997; Heki and Tamura, 1997]. Nishimuraet al. [2000] revealed that the afterslip further extendedtoward the south and toward the downdip direction of theplate interface. On the other hand, the postseismic elevationchanges seen after the 1946 Nankaido earthquake (M = 8.2)were explained by viscoelastic relaxation in the uppermantle [Miyashita, 1987]. It is important to clarify thephysical mechanism of postseismic deformation, sincemodeling of this type of deformation can provide importantinformation on the constraints on the frictional properties ofthe fault [Marone et al., 1991] and on the viscoelasticstructure of the medium [e.g., Thatcher et al., 1980; Pollitzet al., 2000, 2001].

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. B3, 2151, doi:10.1029/2002JB002067, 2003

Copyright 2003 by the American Geophysical Union.0148-0227/03/2002JB002067$09.00

ETG 6 - 1

[3] However, limitations on observations with respect tospace, time and accuracy make it difficult to discriminatebetween the two possible causes. The postseismic crustaldeformation following the 1992Landers earthquake (M=7.5)observed by GPS was initially interpreted as an afterslip onthe downdip extension of the main shock fault [Shen et al.,1994; Savage and Svarc, 1997]. However, by reexaminationusing interferometric synthetic aperture radar (InSAR) datacontaining the vertical component of the postseismic defor-mation, it was confirmed that the postseismic deformationhad been caused by viscoelastic relaxation of the medium[Deng et al., 1998; Pollitz et al., 2000]. In this paper, wecarefully investigate the postseismic deformation followingthe 1993 Hokkaido Nansei-oki earthquake, and clarify itscause.

2. Hokkaido Nansei-Oki Earthquake

[4] The Mw = 7.8 Hokkaido Nansei-oki earthquake of 12July 1993 occurred 50 km west of the coast of Hokkaido,northern Japan (Figure 1). The hypocenter was located bythe Japan Meteorological Agency at 139.20�E, 42.78�N, 34km deep. Large tsunamis generated by the earthquake

caused serious damage to the Japan Sea coastline. Theeastern margin of the Japan Sea is characterized by theoccurrence of large thrust earthquakes [e.g., Ohtake, 1995],and the Hokkaido Nansei-oki earthquake occurred betweenthe focal regions of the 1940 Shakotan earthquake (M = 7.5)to the north and the 1983 Japan Sea earthquake (M = 7.7) tothe south. Kobayashi [1983] and Nakamura [1983] pro-posed that a nascent trench (the dashed line in Figure 1) ispresent along the margin. This nascent trench is believed tobe a plate boundary between the Amurian and the NorthAmerican plates [Heki et al., 1999] or between the Eurasianand Okhotsk plates [Seno et al., 1996]. The HokkaidoNansei-oki earthquake was a reverse-fault type, but thefault model obtained by Tanioka et al. [1995] (Figure 2)has a complex fault geometry. The fault, which is consistentwith the aftershock distribution, consists of a northernmostsubfault A with a shallow dip to the east, subfaults B and Cwith shallow dips to the west, and subfaults D and C withsteep dips to the west. The slip, oriented approximately east-west, 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 andKurile Trenches, is one of the most archetypal subductionzones in the world. Horizontal strain in the arc derived fromgeodetic observations is characterized by compressionalstrain in a roughly east-west direction [Shen-Tu and Holt,1996; Mazzotti et al., 2000; Sagiya et al., 2000]. Mazzotti et

Figure 1. Map showing the aftershock area of the 1993Hokkaido Nansei-oki earthquake (shaded area) and thetectonic environment of northeastern Japan. The rectangleindicates the study area shown in Figures 2, 4, 5, 9, and 10.Dashed and dotted curves indicate the plate boundaryproposed by Nakamura [1983] and the volcanic front,respectively. A solid star and a circle show the epicenter ofthe 1896 Riku-u earthquake and the Wakkanai GPS station,respectively. AM, Amurian plate; EU, Eurasian plate; OK,Okhotsk plate; NA, North American plate.

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 theepicenter of the Hokkaido Nansei-oki earthquake. Shadedrectangles and thick arrows indicate the main shock faultconsisting of subfaults A, B, C, D, and E, and their slipvectors of overriding blocks, respectively [after Tanioka etal., 1995]. Thick lines denote the upper boundary of thesubfaults.

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al. [2000] explained the strain derived from 1995–1997GPS observation data by loading of the relative motion ofthe Pacific plate to the continental plate. After theHokkaido Nansei-oki earthquake, a marked horizontalcrustal deformation was observed by GPS in the OshimaPeninsula and Okushiri Island, southwestern Hokkaido(Figure 2). Mazzotti et al. [2000] pointed out that therelatively large velocities in the southwestern part ofHokkaido cannot be explained by elastic loading from theJapan and west Kurile Trenches. Ito et al. [2000] alsointerpreted the compressional strain in the northeasternJapan arc by loading of the relative motion of the Pacificplate to the continental plate. They pointed out thatanomalous extensional deformation, which cannot beexplained by their model, exists in the southwesternHokkaido. These studies strongly suggest the occurrenceof a postseismic crustal deformation following theHokkaido Nansei-oki earthquake. However, details of thedeformation and its mechanism have not yet been clarified.[6] Postseismic crustal deformations have been investi-

gated for several large interplate earthquakes along theJapan Trench. All of them have been interpreted by largeafterslips 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]. Althoughpostseismic crustal deformations are also reported for the1964 Niigata [Taguchi and Fujii, 1989] and the 1983 JapanSea [Miura et al., 1990] earthquakes that occurred along theeast margin of the Japan Sea, the characteristics of post-seismic deformation in the region are as yet unknown.Using geodetic data obtained after the Hokkaido Nansei-oki earthquake, we study its postseismic deformation andclarify the physical mechanism of the deformation on thebasis of the assumption that it was generated by afterslip orviscoelastic relaxation.

3. Data

[7] This study utilizes GPS data, tide gauge records andleveling data obtained by the Geographical Survey Instituteof Japan (GSI) in the western part of Hokkaido. Figure 2illustrates the locations of the observation stations and theleveling route. The GPS stations are part of the nationwideGlobal Positioning Network (GEONET) permanent array,established by the GSI in 1994 [Miyazaki et al., 1997]. TheGPS data we use are site velocities estimated from the dailyestimates of coordinates of the stations in the period fromApril 1996 to December 1999 (3.8 years) at 23 stations(triangles in Figure 2), and from June 1997 to December1999 (2.6 years) at 9 stations (diamonds in Figure 2). We donot use data from before April 1996, since the number ofstations was limited to only 7 in the area covered by Figure2. Figure 3 shows the time series of movements at typicalGPS stations: 940020 on Okushiri Island (Figures 3a, 3b,and 3c) and 940017 on the northwest coast of the OshimaPeninsula (Figures 3d, 3e, and 3f ). The horizontal andvertical components are movements relative to the Wakka-nai station (solid circle in Figure 1) and 960517 (Oshoro),respectively. Linear curves indicate the average rate ofdeformation fitted to the data using the least squaresmethod. Fitting is very good for the horizontal components,although less reliable for the vertical component.

[8] Zhang et al. [1997] and Mao et al. [1999] havesuggested that errors in the GPS time series consist of whiteand colored noise caused by unmodeled effects includingmonument instabilities, uncertainty in satellite orbit param-eters, atmospheric and local environmental effects. SinceMao et al. [1999] analyzed a 3-year time series andconcluded that the noise characteristics of the coordinatetime series can be modeled by a combination of white plusflicker noise, we take account of white noise and flickernoise in evaluating GPS velocity errors. They provide anapproximate expression for the total velocity error (sr):

sr ¼12s2wgT3

þas2fgbT2

" #1=2

; ð1Þ

where g is number of measurements per year, T is the totaltime span in years, a and b are empirical constants (a = 1.78and b = 0.22), and sw and sf are the magnitudes inmillimeters of white and flicker noise, respectively (therandom walk component is neglected here). We obtain arough estimate of velocity errors by using the formula andmean values of the magnitude of white and flicker noiseobtained by Mao et al. [1999] for stations located in regionsother than North America, western Europe and the tropicalregions [Mao et al., 1999, Table 8]. The velocity errorsobtained 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

Figure 3. Time series of movement of GPS stations (a, b,and c) 940020 and (d, e, and f ) 940017. The horizontal andvertical movements are from the Wakkanai (Figure 1) and960517 (Figure 2) GPS stations, respectively. The solidlines indicate the regression lines fitted to the data.

UEDA ET AL.: POSTSEISMIC CRUSTAL DEFORMATION ETG 6 - 3

2.6 years are 2.4 mm/yr (east), 1.9 mm/yr (north), and 4.1mm/yr (vertical). Dixon et al. [2000] pointed out that errorsgiven by Mao et al. [1999] may be values too large formodern analyses or different site locations. Since thevelocities relative to Wakkanai and Oshoro stations mustcontain errors in velocities of the reference station, weconservatively use the estimation based on work by Mao etal. [1999] in this study.[9] Figure 4 shows the horizontal velocities (solid arrows)

at the GPS stations relative to the Wakkanai station. West-ward movement is seen at all stations with maximumvelocity along the west coast of the Oshima Peninsula.Figure 5 shows the vertical velocities (solid arrows) of GPSstations relative to the 960517 station at Oshoro. Two GPSstations in Okushiri Island (940020 and 960527) indicateclear subsidence, in contrast to a small uplift in the northernpart 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, weshow daily mean tide records at the Oshoro and Okushiristations, respectively. The tide records fluctuate stronglywith amplitudes of up to 400 mm peak to peak due tooceanographic and atmospheric influences. By taking thedifference of these two tide gauge records, we can minimizethe fluctuations, and obtain the relative vertical deformationbetween the two tide gauge stations (Figure 6c). We furtherprocess the difference in tide records by using a medianfilter [e.g., Ueda et al., 2001] to remove high-frequency

noise, and by using BAYSEA [Ishiguro, 1986] to removeseasonal fluctuations. Thus we obtained the final resultshown in Figure 6d, which is expected to represent therelative vertical displacement between the two stations. Thefiltering procedure followed the method of Ueda et al.[2001]. The Oshoro tide gauge station, located relativelydistant from the focal zone of the Hokkaido Nansei-okiearthquake, is reasonably stable, with a very small long-term rate of tide level change of �0.3 mm/yr for the periodfrom 1958 to 2000 [Geographical Survey Institute, 2000].Thus the difference in tide levels in Figure 6d is almostcompletely attributable to the subsidence of the Okushiristation. The velocity of subsidence is �13.3 ± 0.2 mm/yr inthe period from January 1995 to September 2000, shown bya solid arrow in Figure 5. This velocity is anomalously highcompared with other tide gauge stations in Japan registeredat the Coastal Movements Data Center [GeographicalSurvey Institute, 2000]. The vertical velocity at the Okushiritide gauge station is very close to that at the nearest GPSstation 960527, �12.2 mm/y r. This agreement shows thatthe vertical component of GPS data is useful in detectingcrustal deformations in spite of a larger observational errorthan 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. Itcontains 71 benchmarks with a spacing of �2 km. The GSIperformed first-order leveling surveys along this route inAugust 1993, 1 month after the earthquake, and in August1998. Figure 7 shows the height change between the twosurveys. The results indicate uplift of BM 24 by �30 mm

Figure 4. Observed horizontal velocities with confidenceellipses of 1s at GPS stations (solid arrows) averaged overthe period from April 1996 to December 1999 for 23stations (triangles in Figure 2), and the period from June1997 to December 1999 for 9 stations (diamonds in Figure2) relative to the Wakkanai station (Figure 1). Superimposedare theoretical velocities (open arrows) calculated from thebest fit viscoelastic model.

Figure 5. Observed vertical velocities at GPS andOkushiri tide gauge stations (solid arrows) relative to theOshoro tide gauge station with confidence ellipses of 1s.Superimposed are theoretical vertical velocities calculatedfrom the best fit viscoelastic relaxation model (openarrows).

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relative to Oshoro. The error in first-order leveling isregulated to within 2:5

ffiffis

pmm, where s is the length of

leveling route in km, which predicts a maximum error of 28mm over the leveling route. Since actual surveys areperformed with higher accuracy than the regulation, theleveling data shows clear evidence of uplift along the level-ing route. The leveling data are consistent with the GPS datashowing the uplift of the northern part of the OshimaPeninsula.[12] Three independent sets of geodetic data show the

presence of marked crustal deformation following theHokkaido Nansei-oki earthquake. The postseismic deforma-tion is characterized by the westerly movement of south-western Hokkaido, the subsidence of Okushiri Island, andthe uplift of the Oshima Peninsula.

4. Viscoelastic Relaxation Model

4.1. Method

[13] In this section, we model the postseismic crustaldeformation assuming viscoelastic relaxation of the coseis-mic stress change. For modeling the deformation, we

consider a viscoelastic structure consisting of an elastic firstlayer with thickness H1, a Maxwell body viscoelasticsecond layer with thickness H2 and viscosity h, and anelastic half-space. Each layer respectively represents thecrust, the upper mantle and the subducting Pacific plate.Seismic wave velocity and the density of each layer are setas shown in Table 1. The properties of the first and secondlayers are based on a reflection profile obtained by Okada etal. [1973] for the area west of the coast of the ShakotanPeninsula (see Figure 2 for location). For the third layer, thevelocity is that in the Pacific plate beneath northeast Japan[Obara et al., 1986], and the density is that of the Prelimi-nary Reference Earth Model [Dziewonski and Anderson,1981] at a depth of 150 km. Unknown model parameters areH1, H2 and h. The viscoelastic deformation is synthesizedusing the method of Matsu’ura et al. [1981] with the three-layered viscoelastic structure. The fault model of Tanioka etal. [1995] is used for the calculation.[14] We conducted a grid search to find the best fit values

of the unknown model parameters H1, H2, and h thatminimize the misfit:

S ¼XNi¼1

wi sOi � sCi

�� ��2; ð2Þ

where N is the total number of data items, wi is the weightcoefficient for the ith data item, and si

O and siC are the ith

observed and calculated crustal deformations, respectively.The data we used are the horizontal and vertical velocitiesof the GPS stations, the vertical velocity of the Okushiri tidegauge station and the vertical displacement along the level-ing route. The horizontal and vertical data are referred to theWakkanai station and the Oshoro tide gauge station, respec-

Figure 6. Daily mean tide gauge records at the (a) Oshoroand (b) Okushiri stations. (c) The difference in the dailymean tide records between Figures 6a and 6b. (d) Thedifference of tide records processed by BAYSEA [Ishiguro,1986] and a median filter [e.g., Ueda et al., 2001] to removeseasonal and short period fluctuations, respectively. Thedashed curve in Figure 6d shows the theoretical verticaldisplacement calculated from the best fit viscoelasticrelaxation model. The vertical line shows the occurrencetime of the Hokkaido Nansei-oki earthquake.

Figure 7. Elevation changes (solid squares) over �5 yearsafter the Hokkaido Nansei-oki earthquake along the levelingroute shown in Figure 2 relative to the Oshoro tide gaugestation. The solid curve shows the theoretical verticaldisplacement calculated from the best fit viscoelasticrelaxation model.

Table 1. Viscoelastic Structure Model

Layer Vp, km/s Vs, km/s r, g/cm3 Thickness, km Viscosity, Pa s

1 6.59 3.77 2.85 H1 12 7.50 4.30 3.20 H2 h3 7.98 4.75 3.36 1 1

UEDA ET AL.: POSTSEISMIC CRUSTAL DEFORMATION ETG 6 - 5

tively. For the horizontal velocities, siO in equation (2) is

replaced by siO � vS, where vS is an additional unknown

vector that represents average crustal deformation due to thesubduction of the Pacific plate. For GPS data, we assign wi

the reciprocal of the square of the measurement error ofcorresponding data. The error in GPS velocity is 1.3–2.4mm/yr for the horizontal component, and 2.8–4.1 mm/yrfor the vertical component. For the tide and leveling data,we assign wi the reciprocal of the square of 2 mm/yr and 1mm, respectively.[15] The search range is 30–80 km for H1, and 5–150 km

for H2, both in steps of 5 km. For h, the range is 1017 Pa s to1019 Pa s, where the step is 1017 Pa s for 1018–1019 Pa s,and 1018 Pa s for 1018–1019 Pa s.

4.2. Results

[16] As a result of the analysis, we obtained the best fitmodel: H1 = 40 km, H2 = 50 km, and h = 4 � 1018 Pa s, andthe corresponding average horizontal velocity vS is 8 mm/yrin 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 andcalculated horizontal velocities derived from the best fitmodel. The best fit model reproduces the basic feature of thewesterly movements of GPS stations over the entire studyarea, although the residuals are somewhat large in thesouthern part of the Oshima Peninsula. The comparison ofthe vertical velocities at the GPS and tide gauge stations isshown in Figure 5. The best fit model also agrees with thebasic feature of the long-wavelength postseismic deforma-tion characterized by the subsidence of Okushiri Island anduplift of the Oshima Peninsula. For leveling data, the solidcurve in Figure 7 shows the calculated vertical displace-ment. The vertical displacement derived from the best fitmodel closely reproduces the tilt to the northeast along theleveling route, although the best fit model is unable toreproduce some of the short-wavelength deformations. Thetime series of the synthetic deformation of the Okushiri tidegauge station is shown in Figure 6d by a dashed curve. Thissynthetic curve shows close agreement with the differencein tide gauge records. Thus the viscoelastic model matchesthe gross observational features in both space and time.Some discrepancies seen in Figure 4 and 5 may be attrib-utable to other effects, including lateral variation in viscos-ity and the subduction of the Pacific plate.[17] The computation of postseismic deformation does

not include the effect of gravity. Rundle [1982] showed thatin relation to the Maxwell relaxation time, the effect ofgravity is small over the short period following an earth-quake. The viscosity we obtained corresponds to a Maxwelltime of roughly 2 years. The time span of our data is about 3relaxation times. The result obtained by Rundle [1982]shows that the effects of gravity are still not significantover such a short postseismic period. It is therefore reason-able 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 thepostseismic crustal deformation. Since the model must showa good fit to all the data types simultaneously, we selectedthe model as acceptable using the following criteria. Wedivided all the data into three data subsets: the horizontalcomponent of the GPS data ( j = 1), the vertical component

of the GPS data and the tide gauge record ( j = 2), and theleveling data ( j = 3). We also divided S in equation (2) intoSj ( j = 1, 2, 3) corresponding to the data subsets. We regardmodels that simultaneously satisfy the condition of Sj/Sj

0 < 2for each data subset as acceptable, where Sj

0 is the misfit ofeach 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

Figure 8. The investigated model parameter space of thethree-layered viscoelastic structure. The stars and crossesindicate the best fit model and acceptable models,respectively.

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of the acceptable model parameters areH1 = 30–55 km,H2 =30–90 km, and h = 2 � 1018 to 7 � 1018 Pa s, respectively.

5. Afterslip Model

[20] Afterslip of the fault plane is also one of the potentialcauses of postseismic crustal deformation, since afterslipsfollowing large earthquakes have been frequently reportedfor 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]. Weexamined whether the postseismic deformation followingthe 1993 Hokkaido Nansei-oki earthquake can be inter-preted 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 inFigure 2. We assume slips of constant rates, since thepostseismic deformation shown in the horizontal componentof the GPS data is almost linear from April 1996 toDecember 1999 (see Figure 3). Postseismic deformation issynthesized by the method of Okada [1992] with an elastichalf-space. We evaluated the slip rates of the subfaults so asto minimize equation (2). In the estimation, we did not usethe leveling data, since information on the time history ofthe deformation during the 5 years is not included in thedata and we do not know the time history of the postseismicdeformation before 1995 when tide level observationsstarted at the Okushiri station.[22] The slip rates of each subfault of the best fit afterslip

model are shown in Figure 9b, and the correspondingaverage horizontal velocity vS is 9.6 mm/yr to in directionof N78� W. Figure 9 shows the comparison between theobserved (solid arrows) and calculated (open arrows) veloc-ities derived from the best fit model for the horizontal(Figure 9a) and vertical (Figure 9b) components. Thecalculated vectors show fairly good agreement with thoseof GPS observation for the horizontal component, butdisagree for the vertical component. In the northern partof the Oshima Peninsula, calculated vertical changes, show-ing small subsidence, contradict the large uplift observed byGPS and precise leveling.[23] We investigate another afterslip model for confirma-

tion of the result. In the model, we assume that afterslips ofdifferent amounts occurred on the subfaults A, B, C, D, andE, with their downdip extensions having the same size asthe main shock fault: subfaults A0, B0, C0, D0, and E0 inFigure 10a. The slip rates of each subfault of the best fitafterslip model are shown in Figure 10b, and the corre-sponding average horizontal velocity vS is 10 mm/yr to indirection of N81�W. Figure 10 shows the comparisonbetween the observed (solid arrows) and calculated (blankarrows) velocities derived from the best fit model for thehorizontal (Figure 10a) and vertical (Figure 10b) compo-nents. The calculated vectors show fairly good agreementwith those of GPS observation for the horizontal andvertical components. However, the slip rates are extremelyhigh, exceeding 10 m/yr for some subfaults and amountingto �4 m/yr on average. Moreover, the best fit modelrequires a range of different slip directions and unlikelybackslips for some subfaults. The afterslip model is toounrealistic judging from the slip directions and slip ratesobtained; in usual cases, slip direction is nearly the same as

Figure 9. Comparison of the observed velocities (solidarrows) with confidence ellipses of 1s at the GPS andOkushiri 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 fitmodel was obtained by assuming that afterslip is limited tothe main shock fault. Shaded rectangles and thick arrowsshow the subfaults of the Hokkaido Nansei-oki earthquake(A, B, C, D, and E), and slip rates of the overriding blockfor the afterslip model, respectively. The Wakkanai stationand the Oshoro tide gauge station are fixed for thehorizontal and vertical velocities, respectively.

UEDA ET AL.: POSTSEISMIC CRUSTAL DEFORMATION ETG 6 - 7

the coseismic slip direction and the slip rate is in the orderof several hundred millimeters per year [e.g., Heki et al.,1997] except immediately after the earthquake [e.g., Hekiand Tamura, 1997].[24] An extremely high rate can be seen, especially for the

downdip extensions of the main shock fault. A high slip rateis needed to explain the vertical component of the post-seismic deformation, because the vertical component cannotbe explained at all by the best fit model that is obtained byassuming that afterslip is limited to the main shock fault(Figure 9). This discrepancy is probably due to the fact thatslippage of faults at shallow depths is unlikely to causevertical crustal deformations in distant areas. Even if wewere to use a more complicated afterslip model, we wouldprobably need to adopt unrealistic assumptions, includingan extremely high slip rate on the downdip extension of themain shock fault. For these reasons, we conclude thatafterslip is not acceptable as the dominant mechanism ofthe postseismic crustal deformation of the 1993 HokkaidoNansei-oki earthquake.

6. Discussion

6.1. Comparison With Other Observations

[25] We find that the postseismic crustal deformationfollowing the Hokkaido Nansei-oki earthquake can beexplained by the viscoelastic relaxation of the coseismicstress change in a simple three-layered structure. The after-slip model, by contrast, cannot explain the deformationwithout adopting unrealistic assumptions. This result indi-cates that viscoelastic relaxation was clearly the dominantmechanism of the postseismic deformation.[26] The modeling of the postseismic deformation pro-

vides a rough picture of the viscoelastic structure beneathsouthwestern Hokkaido. The depth range of the viscoelasticlayer 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 thecoastline of the Japan Sea in the northern part of Honshu[Zhao et al., 1990], and the depth of the upper doubleseismic plane is 150–200 km in southwestern Hokkaido[Kosuga et al., 1996]. The most plausible reason for thedisagreement is that the viscoelastic layer we revealed maypresent a zone of extremely low viscosity, which allows ashort-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) [afterPeacock and Wang, 1999] and P wave velocity perturbation(dashed curve) [after Nakajima et al., 2001] beneath thecoastline of the Japan Sea in northern Honshu. The profilesare for latitude 40�N for the temperature and the average innorthern Honshu for velocity, respectively. The temperatureof the uppermost mantle is one of the most important causesof low viscosity, since high temperature generally leads tolower viscosity. The back arc side of the volcanic front innortheastern Japan arc is characterized by high heat flow[e.g., Uyeda and Horai, 1964]. The high-temperature por-tion corresponds to the high heat flow present beneath theback arc side. The velocity structure can also provide uswith information on the origin of low viscosity. Thestructure shows that a low-Vp zone exists at the same depth

Figure 10. Comparison of the observed velocities (solidarrows) with confidence ellipses of 1s at GPS and Okushiritide gauge stations with theoretical velocities (open arrows)calculated from the best fit afterslip model for (a) thehorizontal and (b) vertical velocities. The shaded rectanglesshow the subfaults of the Hokkaido Nansei-oki earthquake(A, B, C, D and E) and corresponding downdip extensions(A0, B0, C0, D0, and E0). Thick arrows on the subfaultsindicate slip rates of the overriding block for the afterslipmodel. The Wakkanai station and the Oshoro tide gaugestation are fixed for the horizontal and vertical velocities,respectively.

ETG 6 - 8 UEDA ET AL.: POSTSEISMIC CRUSTAL DEFORMATION

as the high-temperature portion. The depth of the high-temperature portion exceeding 800�C is �50–130 km andthe low-Vp zone is situated �60–140 km in depth. Theyroughly agree with the depth of the viscoelastic layerallowing 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 ofhot mantle material from depth, including partial melt. TheVp

structure beneath northern Honshu was also modeled byIwamori and Zhao [2000] on a mineralogical basis. In theirmodel, melting is initiated beneath the back arc side with thetransportation of H2O from the descending slab. Their idea issupported byWyss et al. [2001] by combing the tomographicimage of Nakajima et al. [2001] with the frequency-magni-tude distribution of earthquakes. Wyss et al. [2001] state thatH2O is expressed from the descending slab at a depth of 140–150 km beneath the back arc side and induces the partialmelting of the mantle material in the mantle wedge.[29] The presence of partial melt and H2O lowers the

viscosity of the mantle material [Cooper and Kohlstedt,1984; Karato et al., 1986]. Therefore the correlation of theviscoelastic layer with the high-temperature and low-Vp

zones suggests that the primary origins of the low-viscosityzone beneath southwestern Hokkaido are the high temper-ature of the mantle wedge, and the presence of partialmelted mantle material mixed with H2O.[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 thehigh-temperature and low-Vp zones. High pressure at depthmay contribute to raising the viscosity. Further investiga-tions are needed to reveal a quantitative relationship amongviscosity of the mantle wedge, content of partial melt andH2O, temperature, and pressure.

6.2. Difference Beneath the Back Arc andForearc Sides

[31] In the forearc side of northeast Japan, postseismiccrustal deformation has been reported for several largeearthquakes associated with the subduction of the Pacificplate: the 1978 Miyagi-oki [Ueda et al., 2001], the 1989Sanriku-oki [Miura et al., 1993], the 1992 Sanriku-oki[Kawasaki et al., 1995] and the 1994 Sanriku-Haruka-okiearthquakes [Heki et al., 1997; Heki and Tamura, 1997;Nishimura et al., 2000]. All of these cases are attributed tobe due to afterslips. This contrasts with our finding that thepostseismic deformation following the Hokkaido Nansei-oki earthquake was mainly due to viscoelastic relaxation inthe uppermost mantle.[32] The difference in the nature of postseismic effect is

probably attributable to the difference in viscoelastic struc-ture between the forearc and back arc sides of the volcanicfront. There exist between them large differences in thermaland Vp structures. The thermal structure derived by Peacockand Wang [1999] shows the temperature of the wedgemantle in the forearc side to be several hundred degreescentigrade lower than that in the back arc side. The Vp

structure derived by Nakajima et al. [2001] shows that low-Vp zones are distributed in parallel with the subductingPacific plate and spread from the crust beneath the volcanicfront to the deeper portion of the wedge mantle beneath theback arc side. The low-Vp zones in the forearc side areweaker than those in the back arc side. These observationsstrongly suggest that the viscosity of the wedge mantle inthe forearc side is much higher than that in the back arc side.Figure 12 shows a schematic view of a cross section of theviscoelastic structure in northeastern Japan as suggested bythese observations. We speculate that there exists an espe-cially low-viscosity zone in the wedge mantle correspond-

Figure 11. Comparison of the viscoelastic structure (solidline) and the thermal structure (dotted curve) [after Peacockand Wang, 1999], and the distribution of the averaged Vp

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 modelparameters of the viscoelastic structure.

Figure 12. Schematic view of an east-west cross sectionof the viscoelastic structure beneath northeastern Japan. Theshaded area represents the low-viscosity portion in theuppermost mantle, probably corresponding to high-tem-perature [Peacock and Wang, 1999] and low-Vp portion[Nakajima et al., 2001].

UEDA ET AL.: POSTSEISMIC CRUSTAL DEFORMATION ETG 6 - 9

ing to the high-temperature and low-Vp portion beneath theeastern margin of the Japan Sea.[33] If this is the case, significant viscoelastic relaxation

is expected to occur not only after the Hokkaido Nansei-oki earthquake but also after other large earthquakes in theback arc side of the northeastern Japan arc. The postseis-mic deformation following the 1896 Riku-u earthquake(Figure 1), which occurred �20 km west of the volcanicfront in northern Honshu, was interpreted as viscoelasticrelaxation in the uppermost mantle [Thatcher et al., 1980].Their estimate for the viscosity of the uppermost mantle is1019 Pa s, which is of the same order as our estimate for theHokkaido Nansei-oki earthquake. Their finding supports ourhypothesis that postseismic deformation induced by viscoe-lastic relaxation is commonly observed after large earth-quakes in the back arc side of the northeastern Japan arc.However, their model can explain the deformation only inthe back arc side: a conspicuous disagreement with theobservations emerges in the forearc side. They attributedthis discrepancy to the effects of the subduction of thePacific plate. We propose an alternative hypothesis: thatthe difference in viscosity between the forearc and back arcsides affects postseismic deformation. Since the sourceregion of the Hokkaido Nansei-oki earthquake is far fromthe volcanic front, the effect of the difference in viscosity isprobably small for the postseismic deformation followingthe earthquake. Therefore it is reasonable to assume ahorizontally uniform structure in this study. However, fur-ther studies are needed to clarify the effect of lateral hetero-geneity of viscosity on postseismic deformation.[34] Another reason for the contrast in the dominant

mechanism of postseismic deformation may be a differencein the frictional properties of fault planes. There is a largedifference in seismic activity between the area east of thePacific coast and the eastern margin of the Japan Sea. On theplate boundary east of the Pacific coastline, large interplateearthquakes frequently occur: e.g., the 1952Tokachi-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 seesmanylarge thrust earthquakes, suggesting the existence of a plateboundary [Nakamura, 1983; Kobayashi, 1983]. However,the beginning of convergent deformation in the east marginof the Japan Sea is�3.5Ma [Sato, 1994], which is much laterthan the beginning of subduction of the Pacific plate. In thefocal area of the Hokkaido Nansei-oki earthquake, historicaldata shows that no large earthquakes have occurred, at least inthe last 300 years [Hatori and Katayama, 1977]. Thesestudies suggest that the fault gouge of the plate boundary inthe east margin of the Japan Sea is not yet as well developedas that of the Pacific plate. The results of laboratory frictionalexperiments byMarone et al. [1990] show that a fault with athick fault gauge tends to show stable sliding. The dominanceof afterslips on the boundary of the Pacific plate may beattributable to weak coupling of the plate boundary, broughtabout through a long history of subduction.

6.3. Importance of Vertical DeformationMeasurements and Future Scope

[35] As was shown in sections 4 and 5, the verticalcomponent of postseismic deformation is satisfactorilyexplained by the viscoelastic relaxation model (Figure 5),

but cannot be explained by the afterslip model without theadoption of unrealistic assumptions (Figures 9b and 10b).In contrast, the horizontal component is explained by bothof the models (see Figures 4, 9a and 10a). This is similarto the case of strike slip faulting, for which both of themodels produce the same horizontal postseismic deforma-tions parallel to the fault strike [Savage and Prescott,1978; Savage, 1990]. This indicates the importance ofobservation of vertical crustal deformations for discrim-inating between physical mechanisms. In our analysis, weused the vertical component of GPS data, tide gaugerecords and leveling data. By use of vertical crustaldeformation data, we are extending our study of postseis-mic deformations to other large earthquakes in the easternmargin of the Japan Sea to clarify whether or notviscoelastic relaxation is a common characteristic of theregion.[36] The viscoelastic structure we modeled describes the

gross features of the postseismic deformation following theHokkaido Nansei-oki earthquake, but some discrepanciesremain. It is plausible that the actual viscoelastic structuremay be more nonhomogeneous both laterally and depthwise. The postseismic deformation near the volcanic frontmay be affected by the difference in the viscoelasticstructure between the forearc and the back arc sides.Furthermore, the crustal deformation near the Pacific coastmay be affected by the subducting Pacific plate. However, itis difficult to distinguish between such effects using oursimple layered structure model. It will be necessary toconsider three-dimensional variation of viscosity to allowthe development of a more detailed viscoelastic model ofpostseismic deformation.

7. Conclusion

[37] On the basis of geodetic measurement data, werevealed that a significant postseismic crustal deformationfollowed the 1993 Hokkaido Nansei-oki earthquake (Mw =7.8) in southwestern Hokkaido. The deformation is char-acterized by the westerly movement of southwesternHokkaido, subsidence of Okushiri Island, and uplift ofthe Oshima Peninsula. By simultaneously analyzing GPS,tide gauge and leveling data, we found that the majorcause of the postseismic deformation was viscoelasticrelaxation of the coseismic stress change in the uppermostmantle. An afterslip model, on the other hand, cannotexplain this deformation without the adoption of unreal-istic assumptions.[38] The viscoelastic structure we estimated from the

postseismic deformation consists of an elastic first layerwith thickness of 40 km and a viscoelastic second layer withthickness 50 km and viscosity of 4 � 1018 Pa s riding on anelastic half-space. The depth of the low-viscosity zonecorrelates closely with that of the low-Vp zones and thehigh-temperature portion of the mantle wedge beneath thecoast of the Japan Sea in northern Honshu. This agreementsuggests that the low viscosity results from the high temper-ature of the mantle material and the presence of partial meltand H2O.[39] This correlation also suggests that the low-viscosity

zone in the uppermost mantle may be widely distributed inthe back arc side and that postseismic deformation induced

ETG 6 - 10 UEDA ET AL.: POSTSEISMIC CRUSTAL DEFORMATION

by the viscoelastic relaxation may be commonly observedafter large earthquakes in this region. We intend to extendthis study to other large earthquakes along the easternmargin of the Japan Sea by adopting a viscoelastic structuremodel with lateral nonhomogeneity.

[40] Acknowledgments. We are grateful to the Geographical SurveyInstitute for providing us with GPS data, tide gauge records and levelingdata. We thank Jim Savage, Paul Segall, and an anonymous associate editorfor their thorough reviews and helpful comments. We also thank Shin’ichiMiyazaki for helpful suggestions. The maps and figures were generatedusing Generic Mapping Tools (GMT) software [Wessel and Smith, 1995].We used the BAYSEA computer program, developed by Akaike andIshiguro at the Institute of Statistical Mathematics, for processing tiderecords. This research was done as part of the Ph.D. thesis of Hideki Uedaat Tohoku University.

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�����������������������M. Ohtake and H. Sato, Department of Geophysics, Graduate School of

Science, Tohoku University, Aoba-ku, Sendai 980-8578, Japan.H. Ueda, National Research Institute for Earth Science and Disaster

Prevention 3-1, Tennodai, Tsukuba-shi, Ibaraki-ken, 305-0006, Japan.(ueda@bosai.go.jp)

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