w h y s . J. Int. (1993) 113,607-621
Interplate coupling and relative plate motion in the Tokai district,
central Japan, deduced from geodetic data inversion using ABIC
Shoichi Yoshioka,l* Tetsuichiro Yabuki? Takeshi Sagiya? Takashi Tada3 and
Mitsuhiro Matsu'ura'
'Department of Earth and Planetary Physics, University of Tokyo, Tokyo 113, Japan
'Hydrographic Department, Maritime Safety Agency, Tokyo 104, Japan
Geographical Sutvey Institute, Ibaraki 305, Japan
Accepted 1992 October 12. Received 1992 September 28; in original form 1992 May 8
The spatial distribution of the strength of interplate coupling between the
subducting Philippine Sea and overlying continental plates in the Tokai district,
central Japan, was investigated in detail through the inversion analysis of geodetic
data using Akaike's Bayesian Information Criterion (ABTC). The geodetic data used
for the analysis are annual rates of level changes (1972-1984) and horizontal length
changes (1977-1988), which presumably represent average crustal movements
during the interseismic period. The result of the inversion analysis shows the
existence of a strongly coupled region extending from 10 to 30 km in depth. The
total seismic moment accumulated in this area since the last event (the 1854 Ansei
earthquake) is roughly estimated to be 5.5 X Id7 dyne cm, which corresponds to
M,= 7.8. The interplate coupling becomes weaker toward the shallower and deeper
portions. This is consistent in general tendency with a rheological model inferred
from petrological viewpoints. The strength of coupling also tends to decrease toward
northeast over the west coast of Suruga Bay. The direction of plate convergence
inferred from the inversion analysis is oriented N30"W. This is significantly different
from the direction of relative plate motion between the Philippine Sea and Eurasian
plates but concordant with that between the Philippine Sea and North American
plates.
Key words ABIC, Bayesian modelling, geodetic data inversion, interplate coupling,
relative plate motion.
1 INTRODUCTION
The Tokai district, central Japan, is located in a region
attracting our interest in plate tectonics. The region is
considered to be subject to interaction of three different
plates: the Philippine Sea plate, the Eurasian plate, and the
North American plate (Kobayashi 1983; Nakamura 1983).
According to Sen0 (1977) and Minster & Jordan (1979), the
oceanic Philippine Sea plate is subducting beneath the
continental Eurasian and North American plates in the N W
direction with a low dip angle at the Suruga and Sagami
troughs (Fig. 1). At the northern tip of the Jzu peninsula,
the Philippine Sea plate has been colliding with the
'Present address: Department of Theoretical Geophysics, University of Utrecht, Po Box 80.021,Budapestlaan 4, 3508 TA Utrecht,
The Netherlands.
continental plates since the Tertiary (Matsuda & Uyeda
1971; Sugimura 1972), leading to an active and complicated
tectonic regime. In addition, volcanic activity is relatively
high around the Izu peninsula, because the volcanic front
related to the subduction of the oceanic Pacific plate
beneath these three plates is passing through there with a
strike of the N-S direction (Sugimura 1959).
Historical documents show that large interplate
earthquakes have repeatedly occurred along the Nankai
trough with an average interval of about 120yr (e.g. Utsu
1974). The recent events which occurred in the Tokai and
1854 Ansei (M8.4),
Kinki districts are the 1707 Hoei (M8.4),
and 1944 Tonankai (M8.0)earthquakes. On the basis of the
distributions of seismic intensity, co-seismic crustal movements, and the running height of excited tsunami waves,
Ishibashi (1977, 1981) concluded that the faulting areas of
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SUMMARY
608
S. Yoshioka et al.
2 D A T A A N D THEIR TECTONIC
IMPLICATIONS
0
0
Figure 1. Tectonic setting in and around Japan. (a) Map showing
relative plate motions [modified from Kakimi (1991)l. EUR:
Eurasian plate; NA: North American plate; PAC: Pacific plate;
PHS: Philippine Sea plate. Relative plate motions are taken from
Sen0 et al. (1987, 1989). The dashed lines indicate the hypothetical
plate boundaries between EUR and NA (Kobayashi 1983;
Nakaumura 1983). The tsunami genetic areas of the 1854 Ansei and
1944 Tonankai earthquakes are taken from Hatori (1974) and
Omote (1948), respectively. (b) Detailed map of the Tokai, South
Kanto district [the boxed region in (a)]. The shaded area indicates
regions with height above loo0 m.
the former two events covered the Nankai to Suruga
troughs, while the faulting area of the last event did not
reach the Suruga trough. Therefore, the area extending from
off Omaezaki to the northern end of Suruga Bay can be
In order to grasp the spatial pattern of vertical crustal
movements in the Tokai district, we compiled the first- and
second-order levelling data during the period from 1972 to
1984, reported by Geographical Survey Institute of Japan
(GSI). For the levelling data in each survey, we carried out
readjustment so as to minimize the sum of observation
errors for all closed loops, fixing a bench mark at Uchiura
[Fig. 2(a)]. Comparing the compiled data at the same point
for two different surveys, we obtain the level changes
relative to Uchiura during the period. Since the time
intervals of levelling are different route by route, we take
the annual rates of level changes, assuming that the rates
have been constant in time during the period. The calculated
annual rates (Oi)
at Uchiura, Yaizu, Omaezaki and Maisaka
are given in the second column of Table 1.
In order to obtain the absolute uplift rates at all bench
marks, we link these data with tidal records. Kato &
Tsumura (1979, 1983) have developed a method to evaluate
absolute crustal movements from tidal records, and revealed
long-term (1951-1982) vertical crustal movements at about
100 tide-gauge stations along the coastlines of the Japanese
islands. In their analysis, although the effects of atmospheric
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regarded as a seismic gap, where tectonic stress to generate
a large interplate earthquake has been accumulated since
the 1854 Ansei earthquake. Since this urgent warning
against the impending ‘Tokai earthquake’, spatially and
temporally dense observations in various kinds, such as
seismic activity, crustal movement, electrical resistivity, and
hydrological and geochemical changes, have been conducted
to detect premonitory phenomena of the Tokai earthquake,
and further to predict its occurrence (e.g. Hamada 1992).
Among the various kinds of observations geodetic data
obtained through levelling, trilateration, and tidal observation would be useful to elucidate the process of stress
accumulation for the occurrence of the Tokai earthquake in
the complicated tectonic regime. Since the Suruga trough is
located very close to the land area, there is a high
possibility to detect the crustal movements related to the
interplate coupling between the subducting Philippine Sea
and overlying continental plates from these geodetic data.
So far the strength of coupling at plate boundaries running
along the Japanese islands has been estimated from geodetic
data with a finite element method by many investigators
(e.g. Bischke 1974; Shimazaki 1974; Smith 1974; Scholz &
Kato 1978; Kato 1979; Sen0 1979; Miyashita 1987; Sat0
1988; Miura, Ishii & Takagi 1989; Yoshioka 1991). However,
these previous studies are insufficient because of the 2-D
and/or forward modelling. In the present study, we use a
newly developed analytic inversion method (Yabuki &
Matsu’ura 1992) to tackle this problem, taking account of
slip distribution on a 3-D realistic plate boundary. This
enables us for the first time to elucidate the spatial
distribution of the strength of interplate coupling and the
direction of relative plate motion. Our present purpose is to
estimate the strength of interplate coupling and the direction
of relative plate motion in the Tokai district from geodetic
data and to clarify their tectonic implications in central
Japan.
Interplate coupling from geodetic data inversion
(a)
o b s.
609
Table 1. Annual rates of level changes at Uchiura, Yaizu, Omaezaki, and Maisaka.
c m/y r
0 -1.0
f
x +1.0
Location
Oi(cm/yr)
T(cm/yr)
D,(cm/yr)
V;.(cm/yr)
Uchiura
Yaizu
Omaezaki
Maisaka
0.000
-0.524
-0.744
0.076
0.027
-1.102
-1.226
0.114
-0.113
0.001
0.080
0.105
-0.086
-1.101
-1.146
0.219
Oj:relative uplift rates at bench marks deduced from levelling data
(Uchiura is fixed). T : absolute uplift rates at tide-gauge stations
deduced from tidal records. 4: uplift rates at bench marks relative
to the corresponding tide-gauge stations, deduced from supplementary levelling data. 6 (=T + Di): absolute uplift rates at bench
marks deduced from tidal records. Negative values indicate
subsidence.
(v.)
4
Q
70 20 3 0 k m
S(C) =
i=l
[ y - (Oi - C)]?
',
1972.73
- 1976.77
-5
Figure 2. Vertical crustal movements in the Tokai district. (a)
Annual rates of absolute vertical movements at all bench marks
during the period from 1972 to 1984. The octagons and crosses
represent subsidence and uplift, respectively. The size of each mark
is in proportion to the annual rate. The solid stars indicate the
locations of the four tide-gauge stations; Uchiura, Yaizu, Omaezaki
and Maisaka. (b) Contour map of cumulative vertical movements
for the period from 1900 to 1973 [modified from GSI (1978)l. The
reference point Numazu is fixed. (c) Contour map of cumulative
vertical movements for the period from 1972-1973 to 1976-1977
[modified from GSI (1978)l. The reference point Numazu is fixed.
pressure, seasonality, and regional sea-level changes were
corrected, the estimated crustal movements may still include
some effect of eustatic sea-level changes. The average uplift
rates (7;) over the period from 1976-77 to 1982 at Uchiura,
Yaizu, Omaezaki and Maisaka tide-gauge stations are given
The calculated correction C is 0.231 cm yr- which should
be subtracted from the relative uplift rates at all bench
marks.
In Fig. 2(a) we show the annual rates of absolute vertical
crustal movements at all bench marks obtained on the basis
of the above method. The octagons and crosses represent
subsidence and uplift, respectively. Since earthquakes large
enough to affect crustal movements did not occur during this
period, the observed crustal movements are regarded as
ones related to the stress accumulation during the
interseismic period of the Tokai earthquake. From Fig. 2(a)
we can find that the region along the western coast of
Suruga Bay has been continuously subsiding through the
interseismic period. At the northern end of Suruga Bay and
near Omaezaki, the subsidence rate reaches almost
1cm yr-'. In particular, the subsidence rate increases along
the three levelling routes toward Omaezaki. The overall
pattern of the subsidence rate has a tendency to decrease
gradually toward the west in proportion to the distance from
the Suruga trough, and an upheaval region appears in the
northeastern extension of Lake Hamana. This may be
related to the uplift of the Akaishi mountain range, whose
upheaval rate has been fastest in the Japanese islands €or the
recent several decades (Dambara 1971). Comparing the
pattern of vertical crustal movements for the period from
1972 to 1984 with those for the previous two periods (GSI
1978) shown in Figs 2(b) and (c), where a bench mark at
Numazu is fixed, we can see that the overall features
mentioned above are similar among them. In other words,
we could say that the same tectonic force has been exerting
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in the third column of Table 1. In the present study we
assume that these values represent nearly absolute crustal
movements at the four stations. The uplift rates (Di) at the
four bench marks relative to the corresponding tide gauge
stations can be also estimated by using data of a
supplementary levelling route (the fourth column of Table
1). Thus we can obtain the annual rates
of absolute
crustal movements at the four bench marks by adding Dito
as shown in the fifth column of Table 1. Finally, in order
to obtain the absolute crustal movements at all bench marks,
we determine the correction C so as to minimize the
following quantity in the least-squares sense.
Omaezaki
610
S. Yoshioka et al.
In order to understand dominant strain fields more
clearly, we show the principal axes of strain changes during
the period from 1974-1977 to 1986-1988 (GSI 1990) in Fig.
3(b). The dashed and solid lines denote contraction and
extension, respectively, of each triangular area. Contraction
in the N-S to NW-SE direction appears to be predominant
for the western half of this district, while the directions of
contraction distribute randomly for the eastern half. The
domination of extension is also detectable near Shizuoka.
This might be related to the existence of the IrozakiShizuoka tectonic line (Mogi 1977) or the Sunzu fault
(Tsueneishi & Sugiyama 1978), and relatively high seismic
activity in this region (Yamazaki & Ooida 1979; Yoshida
1983; Aoki 1985).
We employ the levelling and trilateration data shown in
Figs 2(a) and 3(a) for the present inversion analysis. Total
numbers of the levelling and trilateration data used here are
198 and 137, respectively.
obs.
(a) cm/
(yr*lOkmm)
-1. 2
- - I
-
---
-0. 6
---
-0. 3
-
0. 0
-
-0.9
-0. 3
0. 0
0. 3
Figure 3. Horizontal surface deformation in the Tokai district. (a) Annual rates of side-length changes during the period from 1977 to 1988.
The dashed and solid lines denote contraction and extension, respectively. Thickness of the line represents the annual rate of contraction or
extension normalized by the sidelength of 10km. (b) The cumulative principal strains during the period from 1974-1977 to 1986-1988
[modified from GSI (1990)) The dashed and solid lines denote respectively contraction and extension of each triangular area. The numerals
indicate the maximum shear strains (X1OV6), and the bracketed numerals indicate the annual rates of the area of each triangular region
(xlO-6).
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over this area since the beginning of this century. However,
the subsidence rate appears to increase for the recent
period.
In addition to the data of vertical crustal movements, we
can use trilateration data during the period from 1977 to
1988 as an indicator of horizontal surface deformation. In
contrast to the horizontal displacement data obtained
through triangulation measurements, trilateration data have
the advantage that they d o not include systematic errors
caused by the movements of reference points. Taking an
temporal average over the period, we obtain the annual
rates of sidelength changes as shown in Fig. 3(a). The
dashed and solid lines denote contraction and extension,
respectively, and their thickness represents the rate of
contraction or extension normalized by the sidelength of
10 km. Most of the data indicate contraction, but some of
large extension are also found. This suggests complicated
horizontal surface deformation in the Tokai district.
Interplate coupling from geodetic data inversion
611
3 THE MODEL A N D M E T H O D FOR
INVERSION
Now we describe our model and method to analyse the
geodetic data. We consider the stress accumulation caused
by interaction between the subducting Philippine Sea and
overlying continental plates. The situation is schematically
illustrated in Fig. 4. During an interseismic period, a region
at an intermediate depth remains locked, while the
shallower and deeper portions are decoupled, and a steady
slip proceeds there. Then, as a result of the steady slip at the
shallower and deeper portions, the tectonic stress accumulates in the locked region. Such a situation can be expressed
as the superposition of a uniform steady slip over the whole
plate boundary and a back slip in the locked region. The
crustal deformation produced by the uniform steady slip has
a relatively long wavelength, and its rate is small compared
with the deformation rate due to the back slip (Matsu’ura &
Sat0 1989). Hence, neglecting the deformation due to the
uniform steady slip, we may regard the crustal deformation
in the interseismic period as the effect of the back slip in the
locked region.
In this study, in order to estimate the spatial distribution
of back slip from geodetic data, we employ the inversion
method newly developed by Yabuki & Matsu’ura (1992).
This method enables us to extract unbiased information
from insufficient and inaccurate data. Here, we briefly
describe the outline of the method. First, we determine the
geometry of a curved plate boundary (model surface) from
the information of microearthquake distributions. Once the
geometry of the model surface is given, representing the
distribution of back slip by the superposition of basis
functions (bi-cubic B-splines) defmed on the model surface,
we can obtain a set of linear observation equations;
di =
i
Hijaj + e,
(2)
where di are observed deformation rates, aj are coefficients
of the superposition of basis functions, ej are random errors,
and Hjj are elastic response to a unit back slip at observation
points. The response function Hjj can be calculated on the
basis of the representation theorem of elastodynamics
(Yabuki & Matsu’ura 1992). Our goal is to find the best
estimates of model parameters aj and reconstruct the
back-slip distribution on the model surface.
By the way, we have another sort of information about
the back-slip distribution; that is, the spatial variation of
back slip must be smooth in some degree because of the
finiteness of stress accumulation in the locked region. To
incorporate this sort of prior information into the
observation equations, we introduce a measure of the
roughness of back-slip distribution. In our notation, with the
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F i p e 3. (Continued)
612
S. Yoshioka et al.
Continental
plate
%
decoupled
Philippine Sea
plate
+
Continental
plate
locked
Philippine
plateSea
plate
Figure 4. Schematic diagram showing the back-slip model. The effects of locking at an intermediate depth (left) can be represented by the
superposition of the effects of a uniform steady slip over the whole plate boundary (right top) and a back slip at the intermediate depth (right
bottom). This diagram shows a special case; the rate of back slip is equal to the rate of relative plate motion, and so the locked portion is
completely coupled.
model parameters a,, it may be written as
with
(3)
where Rp, are the elements of a coefficient matrix, whose
concrete expressions are given in Yabuki & Matsu’ura
(1992). Using this quantity, we define a prior probability
density function (PDF) of the model parameters. We
assume a Gaussian distribution, N(0, aZE),for the data
errors ei and define a likelihood function of the model
parameters for given data di. Combining the prior PDF and
the likelihood function by using Bayes’ theorem, we can
constuct a posterior PDF of the model parameters, which is
called a Bayesian model. It should be noted that the
Bayesian model has a flexibility in the selection of the
relative weight of the two sorts of information. Then, our
problem is to find the best estimates of the relative weight
and the model parameters from observed data so as to
minimize the quantity
1
+ -5
CL
z
aPRP9a9
P.9
(4)
C,,= (E-l),,.
(5)
Here, the parameters uz and p2, which are called
hyperparameters, control the structure of the Bayesian
model. For the selection of the most appropriate values of
the hyperparameters, we use Akaike’s Bayesian Information
Criterion (ABIC) proposed by Akaike (1980) on the basis of
entropy maximization principle. Once the values of
hyperparameters are given, we can determine the best
estimates of model parameters so as to minimize the
quantity in e-q. (4) and evaluate the covariance of estimation
errors by using Jackson-Matsu’ura’s formula (Jackson &
Matsu’ura 1985).
The model source region and the iso-depth contours of
the upper boundary of the Philippine Sea plate, which has
been obtained from the distribution of microearthquakes by
Ishida (1992a), are shown in Fig. 5. Unlike the case of
co-seismic faulting, where the source region can be
determined from aftershock distributions, there is no a
priori information to specify the coupled (back slip) region
on the plate boundary. Hence, we take a sufficiently large
model source region to avoid the artificial effect produced
by limiting it. In the present analysis the outside of the
model source region is assumed to be completely decoupled.
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&coupled
/
Interplate coupling from geodetic data inversion
613
oceanic plate, inverted from the annual rates of crustal
movements. The areas with estimation errors larger than the
estimated back-slip rates are shaded. The strongly coupled
region with the back slip rate of about 4 cm yr-' is identified
beneath Kakegawa to Omaezaki. Considering the convergence rate, 3.2 cm yr-' (Seno 1977) 5.2 cm yr-' (Minster
& Jordan 1979), between the Philippine Sea and Eurasian
plates at the Suruga trough, we can say that the interplate
coupling is very strong, indicating an effective strian build
up for the forthcoming Tokai earthquake there. Incidentally,
assuming that the back-slip rate has been constant in time
since the 1854 Ansei earthquake, we can roughly estimate
the total seismic moment accumulated in this region by the
present. The seismic moment M, is generally defined by
-
36" N
35" N
36" N
137" E
138" E
Figure 5. Iso-depth contours (in km) of the upper boundary of the
Philippine Sea plate [modified from Ishida (1992a)l. The rectangle
indicates the model source region. The shaded area indicates the
area where the upper boundary of the Philippine Sea plate was
determined from hypocentral distributions or high-velocity zones.
The dashed lines and light shaded area denote uncertain results
because of the sparse distribution of earthquakes. The thick broken
lines and solid circles indicate respectively the volcanic front and
main Quaternary volcanoes associated with the subduction of the
Pacific plate. The large solid circles indicate volcanoes for which
historical documents of eruptions exist.
The eastern rim of the model source region is taken along
the strike of the Suruga trough.
We divide the model source region into 11X 8 subsections
and distribute 14 X 11 bi-cubic B-splines so that they cover
homogeneously the whole region; the distribution of each
component of back slip on the model surface is represented
by the superposition of 14 X 11 bi-cubic B-splines with
various amplitudes. Then our problem is to determine the
two hyperparameters and the 308 model parameters from
the 335 observed levelling and trilateration data. This is
equivalent to determine the spatial distribution of back-slip
vectors on the model surface.
4
RESULTS A N D DISCUSSION
4.1 The inverted back-slip distribution and its tectonic
implications
Figure 6 shows the distribution of the back-slip motion of
the overlying continental plate relative to the subducting
log,, M, = lSM, + 16.0
(M,> 7).
(7)
Another feature is that the estimated back-slip rates tend
to decrease towards the northeast over the west coast of
Suruga Bay. This may be related to deceleration of the NW
oriented convergence of the Philippine Sea plate due to the
collision of the Izu peninsula with continental plates.
Now we check the effect of uncertainty in the sea-level
trends at the tide gauge stations on the result of inversion
analysis. As is seem from Table 1, the differences, Oi between the relative and absolute uplift rates at the four
bench marks are not consistent with each other. Among
them the absolute uplift rate at Uchiura is relatively small,
probably due to its geographical condition. Hence, we may
suppose that the tidal record at Uchiura is less contaminated by various oceanographic or meterological noises.
Assuming the absolute uplift rate at Uchiura we recalculated
the annual rates of vertical crustal movements and estimated
the back-slip distribution by using them. The result shows a
very similar pattern to that in Fig. 6, except that the
back-slip rate is reduced by about 10 per cent as a whole. In
addition, we checked the effect of difference in the
configuration of the plate boundary. For the configuration of
the upper boundary of the Philippine sea plate in the Tokai
district, Yamazaki, Ooida & Aoki (1989) have proposed a
somewhat different model. We estimated the back-slip
distribution for this plate boundary model and obtained a
similar pattern to that in Fig. 6, but the back-slip rate is
reduced by about 30 per cent as a whole. These results
indicate that the overall pattern of back-slip motion is not so
affected by the uncertainty in the sea-level trends and the
difference in the configuration of the plate boundary.
Figure 7(a) shows change in the back-slip rates with
distance along the plate boundary at the cross section A-B
(Fig. 6). The error bars indicate the standard deviations of
estimation errors. Although the estimation errors tend to
increase in the shallower and deeper portions, we can find a
v,
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M, = pDS
(6)
where p is the rigidity of the medium, and D is the fault slip
averaged over a source area S. As the source area of the
forthcoming Tokai earthquake we take the area with back
slip rates greater than 3.0cmyr-I. Then the total seismic
moment M, accumulated in this area is estimated as
5.5 X loz7dyne cm-' with p = 3.0 X 10" dyne cm2, = 3.4
(cm yr-') X 139 (yr) = 473 cm, and S = 3.9 X
cm'. The
expected surface wave magnitude M, of the earthquake
becomes 7.8, following the empirical relation (Aki 1972)
614
S. Yoshioka et al.
significant depth dependence of the strength of interplate
coupling. The strongly coupled region extends from 10 to
30km in depth, and the strength of coupling tends to
decrease toward the shallower and deeper portions. This
would be the first case to succeed in revealing the depth
dependence of interplate coupling from geodetic data.
According to Shimamoto (1990), the plate boundary in
the Tohoku district, northeast Japan, is divided into three
different zones from petrological viewpoints: (1) a shallow
decoupled zone down to the depth of about 30 km, (2) an
intermediate seismogenic zone extending from about 30 to
60km in depth, and (3) a deeper aseismic slip zone [Fig.
7(b)]. The shallow zone (1) is weak and aseismic because of
the constant supply on an enormous amount of H,O due to
progressive metamorphism. On the other hand, the aseismic
slip in the deeper zone (3) is related to the ductile property
of rocks due to the high temperature there. Our result
obtained from the geodetic data inversion is consistent in
general tendency with this rheological model, but completely different in the depth extent of each zone. This
discrepancy might be due to a difference in the age of
subducting plate and thermal structure between the Tohoku
and Tokai districts. In the Tokai district the young and hot
Philippine Sea plate is subducting. In addition, the volcanic
front with a strike of the N-S direction is passing through
the eastern rim of the model region. Because of the heat
supply from the subducting plate itself and the possible
upwelling of diapir, the lower bound of the seismogenic
zone in the Tokai district might be much shallower than that
in the Tohoku district, where the low temperature
associated with the subduction of the cold Pacific plate is
expected.
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Figure 6. The spatial distribution of back-slip vectors on the plate boundary, inverted from the annual rates of crustal movements. The
back-slip motion of the overlying continental plate relative to the subducting oceanic plate is shown. The areas with estimation errors larger
than the estimated back-slip rates are shaded.
Interplate coupling from geodetic data inversion
615
plsuc 7. The depth dependence of the strength of interplate coupling. (a) Change in back-slip rates with distance along the plate boundary at
the cross section A-B in Fig. 6. The thick solid curve drawn from the point B toward the left bottom corner indicates the vertical cross-section
of the upper boundary of the subducting Philippine Sea plate. (b) Schematic diagram showing the strength of interplate coupling in the Tohoku
district, northeast Japan, inferred from petrological viewpoints [modified from Shimamoto (1990)l. T Japan trench; VF: volcanic front; A F
wismic front; M: mechanical boundary zone. An interplate seismogenic zone extends from A to B (SSF:seismic-slip front).
4.2 Surface deformation rates calculated from the
inverted back-slip model
We show the annual rates of vertical movements calculated
from the inverted back-slip model (Fig. 6) in Fig. 8(a) and
the residuals obtained by subtracting them from the
observed data [Fig. 2(a)] in Fig. 8(b). The observed data are
fairly well explained by the inverted back-slip model except
for some data in the westernmost and easternmost regions.
Figures 9(a) and (b) show the annual rates of sidelength
changes calculated from the inverted back-slip model and
the residuals obtained by subtracting them from the
observed data [Fig. 3(a)], respectively. Note that the
thickness of lines in Fig. 9(a) does not correspond to that in
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TOHOKU, J A P A N
616
S. Yoshioka et al.
(4
(4
cal.
cal.
cm/
c m/y r
---
0 -1.0
-0. 2
-
3. 0
_ -
__
r
0 -1.0
x +l. 0
-0. 4
-0. 1
0.0-
-0. 3
-0.
1
0.1
(b)
obs. -cal.
c m / (yr*lOkm)
---
-1. 2
-
-0. g
---
-0. 9
-
-0. 6
---
-0. 6
-
-0. 3
- - _
-0. 3
-
0. 0
0.0-
0.3
__
Figure 8. Annual rates of vertical crustal movements. (a)
Calculations from the inverted back-slip model in Fig. 6. (b) The
residuals obtained by subtracting the calculations from the
observations in Fig. 2(a).
Figs 3(a) and 9(b). This is for better understanding of the
overall feature of the calculated deformation field. The
inverted model appears to trace the relatively strong
NE-SW oriented contraction and NW-SE oriented
extension at the easternmost region. The discrepancy in the
rates of vertical movements at the easternmost region might
be caused by this apparent fitness to the trilateration data'
Another feature to be noticed is the relatively strong N-S to
NW-SE oriented contraction in the northern half of the
region. This is probably due to the effect of strong coupling
at the depth of around 20 km [Fig. 7(a)]. In contrast, in the
southern half, the magnitude of contraction is relatively
Figure 9- Annual rates of sidelength changes. (a) Calculations from
the inverted back-slip model in Fig. 6 (b) The residuals obtained by
subtracting the calculations from the observations in ~ i3(a).
~ ,
small, reflecting the weaker coupling in shallower portion.
On the whole the calculated horizontal deformation field is
characterized by weak contraction. The complicated pattern
Downloaded from http://gji.oxfordjournals.org/ at Pennsylvania State University on February 18, 2016
c m/y
- - - -0. 3 - _ _ -0. 2 .
x +l. 0
(yr*10km)
Interplate coupling from geodetic data inversion
of the observed horizontal deformation field is not well
explained by the inverted back-slip model. This may be due
to the complicated tectonic setting in the Tokai district.
4.3 The direction of back slip and its relation to platemotion models
geodetic data inversion (Matsu'ura et al. 1980) indicates that
the preferable direction of plate motion at the Sagami
trough is N29"W. Kobayashi (1983) and Nakamura (1983)
proposed a new hypothesis that northeast Japan, which has
been considered to be a part of the Eurasian plate, belongs
to the North American plate. The southwestern boundary
between the Eurasian and North American plates is
conjectured to be the Itoigawa-Shizuoka tectonic line
(ISTL), which is a Quaternary active fault system located
along the Fossa magna, the N-S oriented main graben
structure. As shown in Fig. ll(a), if we take account of a
relative motion between the Eurasian and North American
plates at the ISTL, the contradiction for the relative plate
motions at the Nankai, Suruga and Sagami troughs appears
to be worked out. However, it is still controversial whether
or not northeast Japan belongs to the North American plate
(e.g. Ishibashi 1984, 1986; Sen0 1985; Ishida 1992b), because
of no reliable information about relative plate motion at the
ISTL.
If the relative plate motions illustrated in Fig. l l ( a ) are
correct, the direction of N30"W at the Suruga trough
deduced from the present inversion analysis appears to be
contradictory. Recently, Yoshioka et al. (1993) have
investigated the interplate coupling at the Sagami trough by
using the same inversion method and obtained nearly the
same direction (N33"W f 8") of relative plate motion there.
A natural interpretation of this coincidence is that the
Philippine Sea plate is subducting beneath the same
continental plate at both the Suruga and Sagami troughs.
Judging from the direction of plate convergence, the North
American plate would be preferable as the overlying
continental plate. The assumption that the overlying
continental plate is the North American plate leads to the
conclusion that there is no relative plate motion at the
ISTL. In fact, the directions of P-axes of fault-plane
solutions do not necessarily support the existence of the
relative plate motion at the ISTL (e.g. Tsukahara &
Kobayashi 1991; Ishida 1992b). If this is the case, it is
naturally conjectured that the plate boundary between the
Eurasian and North American plates must be located
somewhere on the western side of the ISTL. On the other
hand, considering the fact that the fault-slip directions at the
time of the 1944 Tonankai (M8.0) and 1946 Nankaido
(M8.1) earthquakes (e.g. Kanamori 1972; Ando 1975;
Yabuki & Matsu'ura 1992), and the direction of interplate
coupling inferred from 3-D finite element analysis using
geodetic data during an interseismic period (Yoshioka 1991)
coincide with the direction of relative plate motion
estimated by Sen0 (1977), the boundary between the
Eurasian and North American plates must be located
somewhere on the eastern side of the eastern rim of the
fault region of the Tonankai earthquake. From these
considerations we may conclude that our results obtained
from the inversion analysis of geodetic data are consistent
with the idea that the boundary between the Eurasian and
North American plates is located along the FukuiNeodani-Ise Bay Line (Iio 1989) or that the relative plate
motion is consumed by slip motion along many faults
located within the broad region between the TsurugawanIsewan Tectonic Line (TITL) and the ISTL (Seno 1985;
Okada 1986) [Fig. ll(b)].
Downloaded from http://gji.oxfordjournals.org/ at Pennsylvania State University on February 18, 2016
In addition to the magnitude of back slip, the present
method of geodetic data inversion enables us to extract
another important information, namely, the direction of
back slip. In our model (Fig. 4) the opposite direction of
back-slip motion represents the direction of relative plate
motion in a steady state. Unlike the conventional methods
to estimate relative plate motions, the present method is
straightforward because of the use of geodetic data just
above the plate boundary during an interseismic period. It
should also be noted that the present analysis uses the data
completely independent of those used in the former
investigations. The result obtained through the present
analysis is shown in Fig. 6. The direction of the back-slip
vectors, which represents the direction of the motion of the
subducting Philippine Sea plate relative to the overlying
continental plate, is oriented N30"W f 9" on average over
the region with back-slip rates greater than 3.0 cm yr-l.
Comparing this result with the directions expected from the
former plate motion models, namely, N54"W by Sen0
(1977) and N44"W by Minster & Jordan (1979), we can find
a significant discrepancy among them. The direction of the
back-slip vectors obtained for another plate boundary model
(Yamazaki el al. 1989) mentioned in Section 4.1 is oriented
N36"W f 3" on average over the region with back-slip rates
greater than 2.5 cm yr-', indicating that the discrepancy is
still significant.
In Fig. lO(a) and (b) we show the fault-plane solutions of
subcrustal earthquakes that occurred in the Tokai district
during the period from 1978 to 1981 and the superposition
of their P - and T-axes, respectively (Ukawa 1982). As can
be seen from Fig. lO(a), strike-slip type events are dominant
in this region. The distribution of T-axes in Fig. 10(b)
indicates that the ENE-WSW oriented tension is dominant.
Although the P-axes are scattered in dip, we can also
recognize the NWN-SES oriented horizontal compression.
The direction or horizontal compression deduced from the
fault-plane solutions is significantly different from the
direction of relative motion between the Pacific and
Eurasian plates or the Philippine Sea and Eurasian plates,
expected from the global plate motion model [Fig. 10(b)].
The direction (N30"W) of relative plate motion obtained
from the present inversion analysis seems to be more
suitable to explain the alignment of P-axes in the
NWN-SES direction. The direction is also in good
agreement with the average direction (N27"W) of the
horizontal movements of most triangulation points in the
Kanto-Tokai district (Fujii & Nakane 1982).
Now we briefly describe the tectonic setting in central
Japan in terms of relative plate motion. So far the oceanic
Philippine Sea plate has been considered to be subducting
beneath the continental Eurasian plate at the Nankai,
Suruga and Sagami troughs in the NW direction (Seno 1977;
Minster & Jordan 1979). O n the contrary, the fault-slip
motion of the 1923 Kanto earthquake (M7.Y) deduced from
617
S. Yoshioka et al.
618
(a)
35
O
(b):-:.:f+..* Range of the strike of
subcrustal seismic zone
p-axis
T-axis
N
Subcrustal Earthquakes
Figure 10. Tectonic stress field in the Tokai district, central Japan, inferred from the focal mechanisms of subcrustal events. (a) Focal
mechanisms of subcrustal events plotted on the lower hemisphere by equal area projection [after Ukawa (1982)) (b) P - and T-axes of the
subcrustal events plotted on the lower hemisphere by equal area projection [modified from Ukawa (1982)) The open and solid circles indicate
the P- and T-axes, respectively. The two stippled arrows show the directions of motion of the Philippine Sea plate (PH) and the Pacific plate
(PC) relative to the Eurasian plate (EU). The solid arrow indicates the direction of plate convergence deduced from the geodetic data
inversion. The azimuthal range of the strike of the subcrustal seismic events is also indicated.
5
CONCLUSIONS
We have investigated the spatial distribution of the strength
of interplate coupling and the direction of relative plate
motion in the Tokai district through the inversion analysis of
geodetic data using ABIC. Significant results obtained here
are as follows: (1) a strongly coupled region extending from
10 to 30 km in depth is identified. The maximum back slip
rate reaches 4.0 cm yr-' beneath Kakegawa to Omaezaki,
indicating an effective strain build up for the forthcoming
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I
139'E
Interplate coupling from geodetic data inversion
619
Tokai earthquake there. The total seismic moment
accumulated in this region since the 1854 event is roughly
estimated to be 5.5 X loz7dyne cm, which corresponds to
M, = 7.8. The strength of coupling tends to decrease toward
the shallower and deeper portions. This is consistent in
general tendency with the interplate coupling model
proposed from petrological viewpoints. The strength of
coupling also appears to decrease toward northeast over the
west coast of Suruga Bay. (2) The results of the inversion
analysis show that the direction of plate convergence at the
Suruga trough is N30"W. This may indicate that the
continental plate overlying the Philippine Sea plate at the
Suruga trough is not the Eurasian plate but the North
American plate.
km
(bl
131'
I
E
138' E
I
Legend
Halo T' ect;;:
A c t l v e fault
3'7' N
lofrrred
Block Bouodar
F
/
We are grateful to Drs Katsuhiko Ishibashi, Takao Eguchi,
Takashi Miyatake and Yoshihisa Iio for their valuable
comments. We also thank two anonymous reviewers and
Prof. Brian Kennett for their helpful suggestions. We used
HITAC S-820/80 and HITAC M-680H computer systems at
the Computer Center of Tokyo University and the
Earthquake Prediction Data Center of the Earthquake
Research Institute, University of Tokyo. This research was
supported by grants for the Japanese Ministry of Education,
Science and Culture (No. 02952101).
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[I
36' N
35' N
5
Figure 11. Tectonic setting in central Japan. (a) Relative plate
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