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JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. B3, 2151, doi:10.1029/2002JB002067, 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 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 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 4 1018 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-Vp 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 H2O. 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
INDEX TERMS: 1236 Geodesy and
frequently observed after large earthquakes in this area.
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 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.
0148-0227/03/2002JB002067$09.00
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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].
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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
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.
[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 Mw = 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 139.20E, 42.78N, 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.
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UEDA ET AL.: POSTSEISMIC CRUSTAL DEFORMATION
al. [2000] explained the strain derived from 1995 – 1997
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: 940020 on Okushiri Island (Figures 3a, 3b,
and 3c) and 940017 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 960517 (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.
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Figure 3. Time series of movement of GPS stations (a, b,
and c) 940020 and (d, e, and f ) 940017. The horizontal and
vertical movements are from the Wakkanai (Figure 1) and
960517 (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 (sr):
"
as2f
12s2w
sr ¼
þ
gT 3
gb T 2
#1=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 sw and sf 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
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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 960517 station at Oshoro. Two GPS
stations in Okushiri Island (940020 and 960527) 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 960527, 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
1998. 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).
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UEDA ET AL.: POSTSEISMIC CRUSTAL DEFORMATION
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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
pffiffierror in first-order leveling is
regulated to within 2:5 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.
consider a viscoelastic structure consisting of an elastic first
layer with thickness H1, a Maxwell body viscoelastic
second layer with thickness H2 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
H1, H2 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 H1, H2, and h that
minimize the misfit:
S¼
N
X
C 2
wi sO
;
i si
ð2Þ
i¼1
where N is the total number of data items, wi is the weight
coefficient for the ith data item, and siO and siC 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-
4. Viscoelastic Relaxation Model
Table 1. Viscoelastic Structure 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
Layer
Vp, km/s
Vs, km/s
r, g/cm3
Thickness, km
Viscosity, Pa s
1
2
3
6.59
7.50
7.98
3.77
4.30
4.75
2.85
3.20
3.36
H1
H2
1
1
h
1
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UEDA ET AL.: POSTSEISMIC CRUSTAL DEFORMATION
tively. For the horizontal velocities, sO
i in equation (2) is
replaced by siO vS, where vS is an additional unknown
vector that represents average crustal deformation due to the
subduction of the Pacific plate. For GPS data, we assign wi
the reciprocal of the square of the measurement error of
corresponding data. The error in GPS velocity is 1.3– 2.4
mm/yr for the horizontal component, and 2.8– 4.1 mm/yr
for the vertical component. For the tide and leveling data,
we assign wi the reciprocal of the square of 2 mm/yr and 1
mm, 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 to
1019 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 fit
model: H1 = 40 km, H2 = 50 km, and h = 4 1018 Pa s, and
the corresponding average horizontal velocity vS 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
Sj ( j = 1, 2, 3) corresponding to the data subsets. We regard
models that simultaneously satisfy the condition of Sj/Sj0 < 2
for each data subset as acceptable, where Sj0 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
UEDA ET AL.: POSTSEISMIC CRUSTAL DEFORMATION
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6-7
of the acceptable model parameters are H1 = 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 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 vS 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 A0, B0, C0, D0, and E0 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 vS is 10 mm/yr to in
direction of N81W. 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.
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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.
6. Discussion
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
(A0, B0, C0, D0, and E0). 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.
6.1. 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 150– 200 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 40N 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-Vp zone exists at the same depth
UEDA ET AL.: POSTSEISMIC CRUSTAL DEFORMATION
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6-9
boundary is clearly shallower than the lower limit of the
high-temperature and low-Vp 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
H2O, temperature, and pressure.
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 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 model
parameters of the viscoelastic structure.
as the high-temperature portion. The depth of the hightemperature portion exceeding 800C is 50– 130 km and
the low-Vp zone is situated 60– 140 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 Vp
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 H2O 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
H2O is expressed from the descending slab at a depth of 140 –
150 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 H2O 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-Vp
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 H2O.
[30] Although the lower boundary of the viscoelastic
layer is not as constrained as the upper boundary, the lower
6.2. 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 Vp 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 Vp
structure derived by Nakajima et al. [2001] shows that lowVp 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-Vp 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-Vp portion
[Nakajima et al., 2001].
ETG
6 - 10
UEDA ET AL.: POSTSEISMIC CRUSTAL DEFORMATION
ing to the high-temperature and low-Vp 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
1019 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.
6.3. 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 (Mw =
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 4 1018 Pa s riding on an
elastic half-space. The depth of the low-viscosity zone
correlates closely with that of the low-Vp 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 H2O.
[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
UEDA ET AL.: POSTSEISMIC CRUSTAL DEFORMATION
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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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, Tennôdai, Tsukuba-shi, Ibaraki-ken, 305-0006, Japan.
([email protected])