Download Interplate coupling in southwest Japan deduced from inversion

Physics of the Earth and Planetary Interiors 115 Ž1999. 17–34
www.elsevier.comrlocaterpepi
Interplate coupling in southwest Japan deduced from inversion
analysis of GPS data
Takeo Ito
a
b
a,)
, Shoichi Yoshioka a , Shin’ichi Miyazaki
b
Department of Earth and Planetary Sciences, Graduate School of Science, Kyushu UniÕersity, Hakozaki 6-10-1, Higashi ward, Fukuoka
812-8581, Japan
Satellite Geodetic DiÕision, Geodetic ObserÕation Center, Geographical SurÕey Institute, Kitasato 1, Tsukuba, Ibaraki 305-0811, Japan
Received 5 August 1998; received in revised form 16 April 1999; accepted 16 April 1999
Abstract
Recently, the Geographical Survey Institute of Japan completed the installation of a GPS continuous observation network
in Japan, which has enabled us to investigate real-time crustal movements. In this study, we attempt to obtain spatial
distribution of interplate coupling and relative plate motion between subducting and overriding plates in southwest Japan,
using horizontal and vertical deformation rates, which were observed at 247 GPS observation stations during the period from
April 6, 1996 to March 20, 1998. For this purpose, we carried out an inversion analysis of geodetic data, incorporating
Akaike’s Bayesian Information Criterion ŽABIC.. As a result, strong interplate coupling was found off Shikoku and
Kumanonada regions, which corresponds well with the fault regions of the 1946 Nankai ŽM 8.1. and the 1944 Tonankai ŽM
8.0. earthquakes, respectively. We also found that interplate coupling becomes weak at depths deeper than about 30 to 40
km beneath the Shikoku and Kii peninsula. The recurrence time of great trench-type earthquakes was roughly estimated as
107 years, which is consistent with previous research. The direction of relative plate motion is oriented N538W, which is
close to the direction predicted from the plate motion model. On the other hand, a large forward slip was found in the
Hyuganada region off southeast of Kyushu. Since the coseismic displacements associated with the two 1996 Hyuganada
earthquakes ŽM 6.6, M 6.6. are removed from the GPS data, this suggests that after-slip occurred near the source region
andror that Kyushu moves southeastward stationarily due to other tectonic forces. q 1999 Elsevier Science B.V. All rights
reserved.
Keywords: GPS; Back slip; Interplate coupling; Relative plate motion; Forward slip
1. Introduction
Southwest Japan is the region where the Amurian
ŽAM. plate Žor the Eurasia ŽEU. plate., the Philippine Sea ŽPH. plate, and the Okhotsk ŽOK. plate Žor
)
Corresponding author. Tel.: q81-92-642-2647; fax: q81-92642-2684; E-mail: [email protected]
the North American ŽNA. plate. interact with each
other ŽFig. 1.. The plate motion in southwest Japan,
especially the eastward motion of the AM plate has
been debated by many researchers Že.g., Zonenshain
and Savostin, 1981; Kimura et al., 1986; Tsukuda,
1992; Ishibashi, 1995.. There are two theories concerning the location of the southern boundary of the
AM plate: one places it along the Median Tectonic
0031-9201r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved.
PII: S 0 0 3 1 - 9 2 0 1 Ž 9 9 . 0 0 0 6 3 - 1
18
T. Ito et al.r Physics of the Earth and Planetary Interiors 115 (1999) 17–34
Fig. 1. Map showing horizontal displacement rates relative to the stationary part of the Eurasian plate with confidence ellipses of 1 s at 247
GPS stations in southwest Japan during the period from April 6, 1996 to March 20, 1998. Coseismic crustal deformations associated with
the 1996 Hyuganada earthquakes ŽOctober ŽM 6.6., December ŽM 6.6.. and the 1997 Kagoshima–Hokuseibu earthquakes ŽMarch ŽM 6.3.,
May ŽM 6.2.., which occurred during the observation period, were removed. The epicenters of the four events are shown with star symbols.
The inset shows four plates in and around the Japanese islands. AM s Amurian Plate Žor EU s Eurasia plate.; OK s Okhotsk plate Žor
NA s North American plate.; PA s Pacific plate; PH s Philippine Sea Plate.
Line ŽMTL., and the other places it along the Nankai
trough. Geophysical exploration of underground
structure beneath the MTL ŽYoshikawa et al., 1992;
Yuki et al., 1992; Ito et al., 1996. and fault simulation using strain data obtained by Geographical Survey Institute ŽGSI. of Japan ŽHashimoto and Jackson, 1993. have been conducted. However, we have
not arrived at a conclusion to determine a preferred
theory. Moreover, the spatial pattern of tectonic
crustal movement in southwest Japan is complicated
due to elastic strain accumulation and release associ-
ated with the subduction of the PH plate along the
Nankai trough Že.g., Thatcher, 1984; Savage and
Thatcher, 1992; Tabei et al., 1996..
Great interplate earthquakes have occurred repeatedly along the Nankai trough, with recurrence interval of about 90 to 150 years Že.g., Shimazaki and
Nakata, 1980; Thatcher, 1984.. The most recent
events were the 1944 Tonankai ŽM 7.9. and the 1946
Nankai ŽM 8.0. earthquakes. It is believed that these
events released accumulated stress in association with
the subduction of the PH plate. Many studies have
T. Ito et al.r Physics of the Earth and Planetary Interiors 115 (1999) 17–34
been done to determine the coseismic slip distribution of the two earthquakes, using geodetic data,
seismic waves and tsunami data Že.g., Fitch and
Scholz, 1971; Kanamori, 1972; Ando, 1975, 1982;
Yoshioka et al., 1989; Yabuki and Matsu’ura, 1992;
Satake, 1993; Sagiya and Thatcher, 1999..
Some studies have also attempted to obtain interseismic interplate coupling using geodetic data. In
southwest Japan, Yoshioka Ž1991. investigated spatial distribution of the strength of interplate coupling
along the Nankai trough, based on leveling, tide
gauge, and trilateration data, using a three-dimension
finite element method. However, the results were
obtained using forward modeling, and the model was
not satisfactory to evaluate the spatial distribution of
interplate coupling objectively. Later, the strength of
19
interplate coupling and the direction of relative plate
motion were estimated more objectively through inversion analysis of leveling and trilateration data in
the Kanto–Tokai districts and southwest Japan
ŽYoshioka et al., 1993, 1994; Sagiya, 1995.. During
the last several years, the Geographical Survey Institute of Japan ŽGSI. has installed and maintained GPS
continuous observation networks throughout the
country. Recently, Nishimura et al. Ž1998. estimated
interplate coupling in southwest Japan, using horizontal displacement rates of GPS data, on the basis
of the least squares method. However, since their
analysis is based on forward modeling, the obtained
results cannot be evaluated objectively as well.
In this study, we attempt to obtain interplate
coupling, using an inversion analysis for continuous
Fig. 2. An example of the time series obtained at the CHIYODA station Žlatitude 34.6778N, longitude 140.0888E.. Vertical and horizontal
axes represent displacement Žmm. and time Žyear., respectively. Ža. Uncorrected time series of north–south component. Žb. Annual change
of north–south component. Žc. Difference between uncorrected time series and annual change of north–south component. Žd. Uncorrected
time series of vertical component. Že. Annual change of vertical component. Žf. Difference between uncorrected time series and annual
change of vertical component.
20
T. Ito et al.r Physics of the Earth and Planetary Interiors 115 (1999) 17–34
GPS data obtained in southwest Japan. The real-time
observations have enabled us to reveal detailed crustal
movement in southwestern Japan, elucidating eastward motion of the AM plate. We used data of 247
horizontal and 237 vertical displacement rates from
April 6, 1996 to March 20, 1998. The purpose of this
study is to obtain the direction of relative plate
motion and the spatial distribution of the strength of
interplate coupling on the plate boundary between
the subducting PH plate and the overriding continental plate through inversion analysis, using Akaike’s
Bayesian Information Criterion ŽABIC. ŽYabuki and
Matsu’ura, 1992..
2. GPS data and their correction
We employed Bernese version 4 software for
analysis of GPS data. We used International GPS
Service for Geodynamics ŽIGS. final orbits for satellite information and International Earth Rotation Service ŽIERS. bulletin B for Earth rotation parameters.
Only the TSKB station, which is one of the IGS
global sites in the GSI campus in Tsukuba, is used
for the tie with IGS global site because we adopted a
distributed strategy. We resolved ambiguities by the
sigma dependent strategy Že.g., Rothacher and Mervart, 1996.. The reference frame we used is ITRF94
Fig. 3. Horizontal displacement rates which were obtained correcting the eastward motion of the Amurian plate. The area in the north of the
boundary along the Median Tectonic Line, Arima–Takatsuki Tectonic Line, and the western part of Lake Biwa is regarded as the AM plate.
We corrected the movement in this area as the motion of rigid body based on Euler vector Ž218S, 1088E, v s y0.0928rMyr. by Heki et al.
Ž1998..
T. Ito et al.r Physics of the Earth and Planetary Interiors 115 (1999) 17–34
ŽITRF International Terrestrial Reference Frame..
Following Heki et al. Ž1998., we obtained the crustal
velocity field relative to the EU plate by subtracting
its absolute motion from ITRF velocities for each
site because the kinematic part of ITRF94 is nnrNUVEL1a plate motion model ŽArgus and Gordon,
1991..
The horizontal displacement rates were calculated
by a least-square approach ŽMiyazaki et al., 1998..
We did not use the full covariance information because the computation time is unrealistic. The scale
of the formal error written in the digit file is 1 s . The
root-mean-square is 3 mm on average, but some sites
which had episodic displacement or transient deformation have larger values, reaching 7 mm.
We excluded annual change of the data according
to the method proposed by Miyazaki et al. Ž1998..
They modeled time series as a linear combination of
constant, linear term, trigonometric function whose
period is 1 year, and jumps for episodic events. One
problem is that we did not estimate postseismic
deformation because it strongly couples with annual
variations. Fig. 2 shows an example of the time
series obtained at the CHIYODA site Žlatitude
34.6778N, longitude 140.0888E.. Fig. 2Ža. and Žd.
represent the uncorrected time series of north–south
and vertical components, respectively. We clearly
find that the scatter of the vertical component is
larger than that of horizontal component. Fig. 2Žb.
and Že. show north–south and vertical components
of annual change, respectively. The annual change D
can be expressed as the following form:
D s A sin v Ž t y t 0 . q B sin2 v Ž t y t 1 .
Ž 1.
where A, B are amplitudes for annual and semi-annual changes, respectively, and v is angular frequency for annual changes. t 0 , t 1 are phases of
annual and semi-annual changes, respectively. Fig.
2Žc. and Žf. are north-south and vertical components
of corrected time series, respectively, excluding the
calculated annual changes.
The horizontal components of displacement rates
of the GPS obtained by GSI show movements relative to the TSKB station Žlatitude 36.1038N, longitude 140.0888E.. Since it is difficult to estimate
accurate interplate coupling from these data, we
converted the GPS data into plate motion relative to
21
the stationary part of the EU plate. According to
Heki Ž1996., the horizontal movement of the TSKB
station relative to the stationary part of the EU plate
is 2.7 mmryr to the north and 20.5 mmryr to the
west. The result was obtained so as to minimize the
difference in the horizontal displacement rates between the Very Long Baseline Interferometry ŽVLBI.
observations and the model predictions by applying a
small translation and rotation for the entire network.
Therefore, as a first approximation, the addition of
this correction to the horizontal displacement rates at
all observation stations enables us to obtain plate
motion of southwest Japan relative to the stationary
part of the EU plate.
Fig. 1 shows horizontal displacement rates relative to the stationary part of the EU plate with
confidence ellipses of 1 s at all GPS stations in
southwest Japan. Coseismic crustal deformations as-
Table 1
Displacement rates of vertical component at 22 tidal stations.
Ti: absolute uplift rates at tidal stations deduced from tidal records
during the period from 1951 to 1987 ŽKato, 1989.. Gi: uplift rates
at GPS stations nearest to the tidal stations. Vi s TiyGi. Negative values indicate subsidence. The locations of the tidal stations
are shown in Fig. 4
No. Location
Ti Žmmryr. Gi Žmmryr. Vi Žmmryr.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
y0.80
1.60
2.30
1.90
y3.70
y5.70
y1.60
y4.10
3.50
5.90
0.00
y1.40
y1.30
0.80
0.50
3.10
0.40
0.80
1.30
0.00
0.50
y1.30
0.12
Onisaki
Owase
Shirahama
Kainan
Sumoto
Uno
Komatsujima
Muroto-misaki
KochiŽgsi.
Tosakure
Tosashimizu
Kure
Tokuyama
Matsuyama
Oita
Akune
Misumi
Hakata
Shimonoseki
Hagi
Sakai
Maizuru
Average
4.03
0.54
y7.79
y8.01
y5.80
7.17
16.09
7.14
11.17
13.57
9.17
7.30
7.48
7.30
10.79
y3.02
7.39
7.32
7.03
7.48
7.59
y6.47
4.89
y4.83
1.06
10.09
9.91
2.10
y12.87
y17.69
y11.24
y7.67
y7.67
y9.17
y8.70
y8.78
y6.50
y10.29
6.12
y6.99
y6.52
y5.73
y7.48
y7.09
5.17
y4.76
22
T. Ito et al.r Physics of the Earth and Planetary Interiors 115 (1999) 17–34
sociated with the 1996 Hyuganada earthquakes ŽOctober 19 ŽM 6.6, depth 39 km., December 3 ŽM 6.6,
depth 35 km.. and the 1997 Kagoshimaken–Hokuseibu earthquakes ŽMarch 26 ŽM 6.3, depth 8 km.,
May 13 ŽM 6.2, depth 8 km.., which occurred during
the observation period, were removed. From the
figure, large movements can be seen at the stations
on the Pacific coast side, and the amount of the
movement decreases farther inland. The direction is
oriented nearly northwestward except for the stations
in Kyushu. In the Chugoku district, however, the
eastward component is dominant, suggesting eastward motion of the AM plate relative to the EU
plate. Therefore, we removed the plate motion, using
the Euler pole Ž218S, 1088E. and rotation rate
Žy0.0928rMyr. of the AM plate relative to the EU
plate ŽHeki et al., 1998., which were determined
based on GPS observation. Here, we investigated the
case for which the southern boundary of the AM
plate is located along the MTL in Kyushu and
Shikoku districts. In the Kinki district, we assumed
that the boundary is along the Arima–Takatsuki
tectonic line, referring to Hashimoto and Jackson
Ž1993.. The area to the north of this boundary is
regarded as the AM plate. Fig. 3 represents horizontal displacement rates that were obtained correcting
the eastward motion of the AM plate. Comparing
Fig. 1 with Fig. 3, we find that the EW component
of the displacement rates is nearly zero in the
Chugoku district.
Fig. 4. Absolute vertical displacement rates with confidence ellipses of 1 s at 237 GPS stations during the period from April 6, 1996 to
March 20, 1998. The locations of 22 tidal stations are also shown with symbols of open squares Žsee Table 1.. The upward and downward
vectors represent uplift and subsidence, respectively.
T. Ito et al.r Physics of the Earth and Planetary Interiors 115 (1999) 17–34
The vertical component of the GPS data also
shows movement relative to the TSKB station. Here,
we attempt to estimate absolute vertical displacement
rate at each GPS station, which is necessary to
estimate accurate back-slip distribution, using tidal
records. Here, we regarded the sea level as an absolute standard, assuming that eustatic movement is
negligible. We assumed that the absolute vertical rate
at each tidal station in southwest Japan during the
period from 1951 to 1987 estimated by Kato Ž1989.
had been continuing for the observation period of the
GPS data. Since Kato Ž1989. calculated absolute
vertical rates based on the data of 30 years, we
excluded tidal stations where coseismic and postseismic crustal deformations were evident during the
period. We determined the amount of the correction
so as to minimize the following quantity E:
E s Ý Ž Ti y Ž Gi y D h . .
2
Ž 2.
23
the tidal station i, D h is the correction which should
be added to all the GPS stations. We used the data at
22 tidal stations and obtained D h s y4.76 mmryr
ŽTable 1..
Fig. 4 shows the obtained absolute vertical rates
at all the GPS stations, together with the locations of
the used tidal stations. Although we find that most of
the GPS stations tend to subside, vertical movements
reflecting subduction of the PH plate Že.g., Yoshioka
et al., 1993, 1994. cannot be clearly seen in the
figure. As can be seen in Figs. 1 and 4, the accuracy
of the GPS data of the horizontal movements is
much better than that of vertical movements.
3. Back-slip model and method of analysis
i
where Ti is absolute vertical rate at tidal station i, Gi
is observed vertical rate at the GPS station nearest to
In this section, we briefly describe the model used
in this analysis, following Yoshioka et al. Ž1993,
Fig. 5. Ža. Schematic illustration showing the back-slip model. The effects of locking at an intermediate depth Žleft. can be represented by
the superposition of the effects of a uniform steady slip over the whole plate boundary Žright top. and a back slip at the intermediate depth
Žright bottom. Žmodified from Yoshioka et al., 1993.. Žb. The forward-slip model.
24
T. Ito et al.r Physics of the Earth and Planetary Interiors 115 (1999) 17–34
1994.. Strain accumulation is considered to be caused
by interaction between the subducting PH plate and
the overlying continental plate. The situation is
schematically illustrated in Fig. 5. Interplate coupling proceeds at the locked region along the plate
boundary. On the other hand, decoupling is dominant
along shallower and deeper portions of the plate
boundary because of high pore pressure due to the
existence of water and low viscosity due to high
temperature, respectively. As a result, steady slip
takes place at the shallower and the deeper portions,
and tectonic stress accumulates in the locked region.
Such a situation can be divided into two situations
geometrically. One is the state that uniform steady
slip proceeds over the whole plate boundary. The
other is the state to give back slip in the locked
region ŽSavage, 1983.. Assuming that we can disregard the former situation because surface deformation produced by the former has long wavelength
and its amplitude is small, the present state of stress
accumulation can be approximately expressed by
giving the back slip in the locked region. On the
other hand, stress release is represented by forward
slip, whose slip direction is opposite that of the back
slip. The application of the two-dimensional back-slip
model by Savage Ž1983. to a three-dimensional case
has already been done by Yoshioka et al. Ž1993,
1994. and Sagiya Ž1995..
In this study, we attempted to obtain spatial distribution of the magnitude of back slip and the direc-
Fig. 6. Iso-depth contours Žin km. of the upper boundary of the Philippine Sea plate subducting beneath southwest Japan. The contour
interval is 5 km.
T. Ito et al.r Physics of the Earth and Planetary Interiors 115 (1999) 17–34
25
Fig. 7. The spatial distribution of slip rates on the plate boundary, inverted from the displacement rates of the GPS data. The slip motion on
the overlying continental plate relative to the subducting Philippine Sea plate is shown. The contour lines denote the amount of back slip.
The contour interval is 1.0 cmryr. The areas with low reliability Žthe ratio of the obtained back slip to estimation error is less than four. are
shaded.
tion of relative plate motion through inversion analysis ŽYabuki and Matsu’ura, 1992., using displacement rates of GPS data in southwest Japan.
On the model source region where back slip or
forward slip is given, we express spatial distribution
of moment tensor corresponding to slip by superposing basis functions Žbi-cubic B-spline functions..
Here, we can express observation equations with N
observation data as:
d i s Ý A i j a j q ei
j
Ž i s 1, . . . , N .
Ž 3.
where d i are observed surface displacements, a j are
coefficients of superposing basis functions Žmodel
parameters., e i are random errors, and A i j are elastic response at a point i to a unit slip at a point j on
the model source region. The response function A i j
can be calculated by dislocation theory in a semi-infinite homogeneous perfect elastic body ŽMaruyama,
1964.. The more detailed form is given in ŽYabuki
and Matsu’ura, 1992.. Our purpose is to find the
model parameters as the best solution, and to estimate the back-slip distribution on the model source
region. Here, we consider the likelihood function of
T. Ito et al.r Physics of the Earth and Planetary Interiors 115 (1999) 17–34
26
a j . Assuming that the error e i to be NŽ0, s 2 E ., the
likelihood function pŽ d < a; s 2 . of the model parameter a j can be expressed as:
p Ž d < a; s 2 . s Ž 2ps 2 .
yN r2
=exp y
5 E 5y1r2
1
2s 2
Ž d y Aa .
=Ey1 Ž d y Aa .
some degree. Here, we can denote the probability
density function q Ž a; r . with a hyper-parameter r 2
that controls the roughness of the slip distribution as:
q Ž a; r . s Ž 2pr 2 .
t
yK r2
5 L K 5 1r2 exp y
1
2r2
a t Wa
Ž 5.
Ž 4.
where 5 E 5 denotes the absolute value of the determinant of E, and s 2 is unknown covariance for e i .
On the other hand, the back-slip distribution has a
prior information that the distribution is smooth to
where W is a symmetric matrix, whose concrete
expression is given in ŽYabuki and Matsu’ura, 1992..
K is the rank of the matrix W, and 5 L K 5 is the
absolute value of the product of non-zero eigenvalues. We can estimate the back-slip distribution on
the model source region, combining the prior infor-
Fig. 8. Displacement rates at each GPS station calculated from the inverted back-slip distribution Žthick arrows. and the observed
displacement rates Žthin arrows.. Ža. Horizontal displacement rates. Žb. Vertical displacement rates.
T. Ito et al.r Physics of the Earth and Planetary Interiors 115 (1999) 17–34
27
Fig. 8 Žcontinued..
mation with the observation Eq. Ž3.. Here, we united
the likelihood function from the data distribution of
Eq. Ž4. with the probability density function from the
prior information of Eq. Ž5. by using Bayes’ theorem. The Bayesian model is highly flexible with the
two hyper-parameters, s 2 and r 2 . We can represent
the model as:
with:
l Ž a; s 2 , r 2 d .
To find the best estimates of the two hyperparameters, we used ABIC proposed by Akaike
Ž1980. on the basis of the entropy maximization
principle. It is a criterion to minimize the influence
of the error included in the data and to derive hidden
information to its maximum, in order to determine
s Ž 2p .
y Ž NqK .r2
syNryK 5 E 5y1r2 5 L K 5 1r2
=exp yS Ž a; s 2 , r 2 .
Ž 6.
S Ž a; s 2 , r 2 .
1
s
t
Ž d y Aa . Ey1 Ž d y Aa .
2s 2
1
q 2 a t Wa.
2r
Ž 7.
T. Ito et al.r Physics of the Earth and Planetary Interiors 115 (1999) 17–34
28
the hyper-parameters uniquely, which represent the
degree of smoothness of the slip distribution. Once
we have determined the two hyper-parameters, s 2
and r 2 , we can calculate the model parameter a. We
can represent the solution for the model parameter a,
ˆ
using a 2 which is defined by s 2rr 2 as:
aˆ s Ž At Ey1A q a 2 .
y1
At Ey1 d.
Ž 8.
As a result, we can determine the back-slip distribution objectively and uniquely on the plate boundary,
that is, the amount of interplate coupling and the
direction of relative plate motion. The covariance for
the model parameter aˆ is given by:
C s sˆ 2 Ž At Ey1A q aˆ 2 W .
y1
Ž 9.
where sˆ 2 is the best estimate of s 2 . We can obtain
the estimation error of each slip on the model source
region from Eq. Ž9.. The optimal value of a which
minimizes ABIC in this study was estimated to be
0.15, which is relatively small. From the definition
of a 2 Žsee also Eqs. Ž6. and Ž7.., large value of a 2
indicates smooth distribution of back slip and forward slip.
In this study, we constructed the model source
region on the three-dimensional upper surface of the
subducting PH plate obtained from spatial distribution of microearthquakes ŽSatake, 1993., whose strike
direction is taken almost parallel to the axis of the
Nankai ŽFig. 6.. Since the trough axis changes its
direction abruptly in the region between Kyushu and
Shikoku, we separated the model source regions into
two parts. Since outside of the model source region
is assumed to be completely decoupled in this analysis, we constructed relatively large model source
regions. The sizes of the model source regions off
southeast of Kyushu and Shikoku to Kii peninsula
were taken to be 180 km = 200 km and 140 km = 400
km, respectively. We divided the respective model
source regions into 9 = 10 and 7 = 20 subsections,
and distributed 12 = 13 and 10 = 23 basis functions
so as to cover the respective whole regions homogeneously. The distribution of slip rate on the model
source region is represented by the superposition of
the bi-cubic B-spline functions with various amplitudes. The boundary condition for the model source
region is assumed to be semi-fixed, reducing numbers of bi-cubic B-spline functions which express
distribution of slip rate on the model source regions.
Therefore, stress concentration, which appears near
the edge of the model source regions for conventional uniform slip model, is suppressed considerably
in this study.
In this study, we deduced 772 model parameters
from the 247 horizontal and 237 vertical displacement rates of the GPS data, and determined the
spatial distribution of slip rate. We excluded 10
vertical data from the data set because the observation errors of the 10 data are anomalously large, and
because considering that data with large observation
errors are not so important in our inversion analysis
in which weight of the errors are considered. In this
study, we carried out inversion analysis for both
horizontal and vertical displacement rates, considering weight of confidence ellipse of 1 s for the
respective components at each GPS station. As we
described before, the accuracy of the GPS data of the
horizontal movements is much better than that of
vertical movements.
For the model source region off Shikoku to Kii
peninsula, we carried out inversion analysis, giving
the constraint that the direction of back slip is within
"458 of the direction of plate motion of the PH
plate relative to the EU plate ŽSeno et al., 1993.,
using non-negative least-squares ŽNNLS. by Lawson
and Hanson Ž1974..
4. Results
4.1. Slip distributions on the model source regions
Fig. 7 represents distributions of slip rate on the
model source regions between the PH plate and the
continental plate obtained from inversion analysis
based on the GPS data of the crustal movements
ŽFigs. 3 and 4..
In the model source region off Shikoku to Kii
peninsula the average back-slip rate is 4.0 cmryr for
the area with back slips greater than 3.0 cmryr,
where interplate coupling appears to be strong. This
corresponds well to the coseismic slip regions at the
T. Ito et al.r Physics of the Earth and Planetary Interiors 115 (1999) 17–34
time of the 1944 Tonankai ŽM 7.9. and the 1946
Nankai ŽM 8.0. earthquakes ŽSagiya and Thatcher,
1999.. A weakly coupled region that separates these
large back-slip regions is located beneath the Kii
channel and its southern extensional region.
The average direction of the back slip was obtained as N538W" 118 for the model source region
off Shikoku to Kii peninsula. The direction differs by
48 from the direction of plate motion of the PH plate
relative to the EU plate ŽN498W. ŽSeno et al., 1993.
On the other hand, we find large forward slip,
reaching 11 cmryr, on the model source region
southeast off Kyushu.
In Fig. 7, reliability, which is defined by the ratio
of the obtained back slip to estimation error on the
29
model source region calculated from Eq. Ž9., is also
shown. Reliability is low from the eastern part of
Shikoku to the west of Kii peninsula, including the
region beneath the Kii channel. The low reliability is
probably due to the large distance between the model
source region and the GPS stations: the model source
region deepens abruptly beneath the Kii channel, and
no GPS stations exist there.
We also calculated distribution of slip rate on
different model source regions so as to fill the gap
between the two source regions in the present analysis. However, we hardly found a difference in distribution of slip rate on the original model source
regions. From these considerations, we may say that
the influence of the edge effects can be disregarded.
Fig. 9. Map showing the rates of the converted 666 baseline length changes from the horizontal displacement rates of the GPS. The dashed
and solid lines denote contraction and extension, respectively. The thickness of each line represents the displacement rate of baseline length
change.
30
T. Ito et al.r Physics of the Earth and Planetary Interiors 115 (1999) 17–34
4.2. Surface displacement rates calculated from the
inÕerted back-slip distribution
Fig. 8Ža. and Žb., respectively, represent horizontal and vertical displacement rates at each GPS station calculated from the inverted back-slip distribution, together with the observed displacement rates.
Concerning the horizontal movement, we find that
most of the observed displacement rates are well
explained by our model, except in the southern part
of Kyushu, the western part of Shikoku, and the
Chubu district. In the southern part of Kyushu, the
observed horizontal displacement rates have south-
ward components as compared to those in the northern region. The observation errors are large there,
and we accordingly weighted the errors when we
carried out inversion analysis. For these reasons, the
fitting of horizontal movements between observation
and calculation is considered to be poor. In the
western part of Shikoku, the cause of the difference
is probably due to large spatial variation of the
directions of the observed horizontal movement. In
the Chubu district, since there exists westward displacement rates with comparable magnitude in the
inland region away from the eastern model source
region, the calculation dose not fit the observation
Fig. 10. The spatial distribution of slip rates on the plate boundary, inverted from the baseline length changes. The slip motion on the
overlying continental plate relative to the subducting Philippine Sea plate is shown. The contour lines denote the amount of back slip. The
contour interval is 1 cmryr. The areas with low reliability Žthe ratio of the obtained back slip to estimation error is less than four. are
shaded.
T. Ito et al.r Physics of the Earth and Planetary Interiors 115 (1999) 17–34
well. Therefore, the crustal movement in this region
is considered to be caused by tectonic stresses other
than subduction of the PH plate.
Vertical movement is poorly fit in all regions. The
reason is that the errors of the observation data of
vertical movement are several times as large as those
of the horizontal movement ŽFigs. 1 and 4., and we
weighted the observation errors accordingly in the
inversion analysis.
4.3. Slip distributions obtained from baseline length
changes
Until Section 4.2, we have discussed slip distributions obtained from the inversion of horizontal and
vertical displacement rates of GPS data. However,
we have to consider effect of fixed point for the
horizontal data. To solve this problem, we converted
the horizontal displacement rates of the GPS data to
666 baseline length changes ŽFig. 9.. For the data
set, we carried out the similar inversion analysis. In
this case, we also found that interplate coupling
becomes weak at depths deeper than about 40 km
beneath the Shikoku and Kii peninsula ŽFig. 10.. The
direction of average back slips is oriented N538W"
38, which is close to the direction predicted from the
plate motion model by Seno et al. Ž1993.. On the
other hand, no slip occurs in the southeast off Kyushu
where reliability is fairly low.
5. Discussion
Our inversion analysis indicates the strong coupling between the PH and the continental plates in
the model region off Shikoku to Kii peninsula ŽFigs.
7 and 10.. The strongly coupled region has been
suggested by Hyndman et al. Ž1995. in which a
transient thermal model using the finite element
method was constructed ŽHyndman and Wang, 1993..
Their model allows comparison of the thermally
estimated downdip extent of the seismogenic zone
with that from seismicity, tsunami data and the
crustal deformation data in the Nankai subduction
zone. The locked zone by Hyndman et al. Ž1995.
corresponds well with the large back-slip region
obtained in this study. This result indicates that the
geodetically obtained result is consistent with the
31
thermal model. In the south of the model source
region, the Kinan seamount chain is ranging in the
NS direction on the Shikoku basin. The subduction
of such seamounts might be related to weak interplate coupling in this region ŽYoshioka, 1991.. The
relation between seamounts and interplate coupling
is discussed by Zhao et al. Ž1997., in which the
morphology of the upper surface of the subducting
Pacific plate beneath the Japanese islands was estimated using SP and sP converted waves at the upper
boundary of the slab. The subducting seamounts
have kept roughly their original shapes probably
because the seamounts are stronger and less deformable than the inner slope materials, and are not
scraped off at the trench so that the slab subducts at
a steeper dip angle. Hence, the PH plate may subduct
with steeper dip angle beneath the Kii channel than
in other regions, corresponding to weak interplate
coupling.
Moreover, we find that the amount of the back
slip becomes very small at depths deeper than about
30 to 40 km on the model source region, indicating
weak interplate coupling there. This is probably due
to ductile characteristics and flow of rocks due to the
high temperature there. This depth is shallower than
the depth of 60 km estimated from experimental
studies of rock rheology in northeast Japan
ŽShimamoto, 1990.. Combining a rheological model,
which is represented by single crystal of olivine and
plagioclase, with the thermal structure of the subduction zone, Shimamoto Ž1989. suggested the depth of
transition from brittle or plastic deformation to ductile deformation to be about 60 km in northeast
Japan. The difference in the depths in northeast and
southwest Japan could be caused by the fact that the
PH plate in southwest Japan is younger and warmer
than the Pacific plate, which is subducting beneath
northeast Japan, as suggested by previous studies
Že.g., Yoshioka, 1991..
On the other hand, on the basis of the idea that
the Nankai trough is the southern limit of the AM
plate, we carried out a similar inversion analysis,
after making necessary corrections for the horizontal
GPS data. As a result, we obtained N778W" 148 as
the direction of the average back slip, which is
different from the direction of Seno et al. Ž1993. by
288. Comparing this with the result obtained assuming that the southern boundary of the AM plate is
32
T. Ito et al.r Physics of the Earth and Planetary Interiors 115 (1999) 17–34
along the MTL, the latter is closer to the results of
the plate motion model by Seno et al. Ž1993. in
terms of the direction of the average back slip.
Therefore, we conclude that the idea that the MTL is
the southern boundary of the AM plate is preferable,
based on our inversion of the GPS data.
We also estimated recurrence times of the Tonankai and the Nankai earthquakes from the results
of the model source region off Shikoku to Kii peninsula. The amount of the average coseismic slip on
the model source region was estimated to be 342 cm
from the result of inversion analysis of coseismic
geodetic data associated with the 1944 Tonankai and
the 1946 Nankai earthquakes ŽSagiya and Thatcher,
1999.. On the other hand, the amount of the average
back slip on the corresponding region obtained in
this study is 3.2 cmryr. Dividing the amount of the
average coseismic slip by that of the back slip, the
recurrence time of the trench-type great earthquakes
that have occurred at the Nankai trough is roughly
estimated as 107 years, consistent with the recurrence interval of 90 to 150 years in this region Že.g.,
Ando, 1975; Shimazaki and Nakata, 1980; Thatcher,
1984..
Large forward slip was found on the model source
region southeast off Kyushu for the inversion of the
horizontal displacement rates. Since the forward slip
appears in spite of the removal of the coseismic
crustal deformations associated with the two 1996
Hyuganada earthquakes ŽOctober ŽM 6.6., December
ŽM 6.6.. from the GPS data, a possible explanation
of the forward slip might be after-slip of the Hyuganada earthquakes. However, horizontal displacement rates of GPS observation before the 1996 Hyuganada earthquakes had already shown southeastward movements in Kyushu ŽGeographical Survey
Institute, 1996.. Also, no slip can be found on the
model source region southeast off Kyushu for the
inversion of rates of the baseline length changes.
These indicate that deformation of Kyushu dose not
behave like an elastic body but a rigid body. Therefore, the NS oriented extension in Kyushu associated
with the expansion of the Okinawa trough ŽShiono et
al., 1980; Tada, 1980. andror southeastward drag of
Kyushu due to the upwelling of mantle material
beneath the East China Sea Že.g., Seno, 1998. may
be the cause of the southeastward displacement rates
in Kyushu.
6. Conclusions
In this study, we calculated the distribution of
interseismic slip rate on the plate boundary between
the subducting Philippine Sea plate and the continental plate in southwest Japan, based on the displacement rates obtained from the continuous GPS observations by the Geographical Survey Institute of Japan.
The obtained results are as follows.
Ž1. We found back slip of more than 3 cmryr on
the model source regions off Shikoku and Kumanonada, indicating strong interplate coupling. These correspond well to the large coseismic slip areas of the
1946 Nankai ŽM 8.0. and the 1944 Tonankai ŽM 7.9.
earthquakes, respectively. Weak interplate coupling
can be found in the region beneath off Kii channel
and in the region deeper than about 30 to 40 km.
Ž2. We estimated the recurrence time of the
trench-type great earthquakes along the Nankai
trough to be about 107 years from coseismic slip and
back slip obtained from inversion analyses of the
coseismic crustal deformations associated with the
Nankai and the Tonankai earthquakes, and the GPS
data in this study, respectively. The recurrence time
is consistent with the results obtained in the previous
studies.
Ž3. The average direction of the back slip is
N538W on the model source region off Shikoku to
Kii peninsula, which is concordant with the direction
of N498W from the plate motion model by Seno et
al. Ž1993..
Ž4. In the Hyuganada region off southeast of
Kyushu, although we excluded coseismic crustal deformations associated with the 1996 Hyuganada
earthquakes ŽOctober ŽM 6.6., December ŽM 6.6..
and the 1997 Satsuma earthquakes ŽMarch ŽM 6.3.,
May ŽM 6.2.., we obtained large forward slip from
inversion analysis of the horizontal and vertical displacement rates. The forward slip corresponds to the
process of stress release, indicating after-slip in the
vicinity of the coseismic slip region of these events.
However, from the inversion using baseline length
changes, we found that no slips can be seen in the
southeast off Kyushu. These indicates that deformation of Kyushu does not behave like an elastic body
but a rigid body. The N–S oriented extension in
Kyushu associated with expansion of the Okinawa
trough andror southeastward drag of Kyushu due to
T. Ito et al.r Physics of the Earth and Planetary Interiors 115 (1999) 17–34
the upwelling of mantle material beneath the East
China Sea may be a preferable cause of the southeastward horizontal displacement rates in Kyushu.
Ž5. We inverted the GPS data for two cases,
assuming that the southern boundary of the Amurian
plate is located along the Median Tectonic Line and
the Nankai trough. Comparing the two cases, the
former is closer to the results of the plate motion
model than the latter in terms of the direction of the
average back slip. Therefore, the idea that the Median Tectonic Line is the southern boundary of the
Amurian plate is preferable from our inversion analysis of the GPS data.
Acknowledgements
We are thankful to T. Yabuki for allowing us to
use his source code for geodetic data inversion. We
are indebted to B.A. Romanowicz, K. Hudnut and R.
Burgmann
for their critical reviews. W. Spakman is
¨
gratefully acknowledged for providing graphic software. We also thank S. Takenaka and H. Sanshadokoro for their valuable comments and kind help
through calculation.
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