Geophys. J . Int. (1992) 111, 617-629
Cyclic crustal movement, steady uplift of marine terraces, and
evolution of the island arc-trench system in southwest Japan
Toshinori Sato' and Mitsuhiro Matsu'ura2
'Earthquake Research Institute, Universify of Tokyo, Tokyo 113, Japan
'Department of Earth and Planetary Physics, Uniuersify of Tokyo, Tokyo 113, Japan
Accepted 1992 June 22. Received 1992 June 22; in original form 1992 March 2
SUMMARY
In southwest Japan, where the Philippine Sea Plate is descending beneath the
Eurasian Plate at the Nankai Trough, we can observe cyclic crustal movement
related to the periodic occurrence of interplate earthquakes with the time interval of
10' yr, steady uplift of the marine terraces formed by eustatic sea-level changes for
the last lo5yr, and gradual evolution of the island arc-trench system through the last
4 x 10' yr. We demonstrate that these phenomena with very different characteristic
time-scales can be consistently explained by a single-plate subduction model. In our
model, the lithosphere-asthenosphere system is represented by a stratified viscoelastic half-space under gravity, consisting of a high-viscosity surface layer and a
low-viscosity substratum, and interaction between oceanic and continental plates by
steady slip motion over the whole plate boundary and its perturbation associated
with the periodic occurrence of earthquakes. The effects of accretion of oceanic
sediments at plate boundaries, erosion on land, and sedimentation on inner trench
walls are also considered in the model. From comparison of theoretical results with
observed data we obtained the following conclusions valid for young subduction
zones: observed deformation cycles cannot be explained by a simple rebound model
in which the effect of steady-plate subduction is ignored. The steady-plate
subduction brings about steady uplift of marine terraces. The present patterns of
surface topography and gravity anomalies are held nearly stable by the balance of
erosion (sedimentation) rates and substantial growth rates.
Key words: earthquake cycle, gravity anomalies, marine terrace uplift, plate
subduction, southwest Japan.
1 INTRODUCTION
Interaction between oceanic and continental plates at
subduction zones produces various phenomena such as
cyclic crustal deformation associated with the periodic
occurrence of earthquakes, steady uplift of marine terraces,
and evolution of island arc-trench systems. In southwest
Japan, where the Philippine Sea Plate is descending beneath
the Eurasian Plate at the Nankai Trough, we can observe
the periodic occurrence of large interplate earthquakes with
a recurrence interval of 10'yr (Ando 1975). From the
comparison of repeated geodetic measurements, crustal
deformation during the last earthquake cycle (1890-1980)
has been revealed in detail by Thatcher (1984) and
Miyashita (1987). The crustal deformation cycle is
characterized by instantaneous changes associated with the
occurrence of the 1946 Nankaido earthquake, rapid
recovery motion in the postseismic period, and gradual
movements in the interseismic period. An important fact
indicated by these geodetic data is that a certain amount of
permanent vertical displacement remains after the completion of one earthquake cycle. Along coastlines in southwest
Japan we can observe a series of well-developed marine
terraces, formed by eustatic sea-level changes for the last
10'yr (Yoshikawa, Kaizuka & Ota 1964; Yonekura 1968;
Ota 1975). The uplift rate of these marine terraces is
2 mm yr-' at Muroto, Shikoku Island, and decreases
gradually with distance from the Nankai Trough. The rate
and pattern of uplift of marine terraces roughly agree with
those of the permanent surface deformation on a long-term
average. This suggests that the characteristic patterns of
topography and gravity anomalies observed in southwest
Japan have been formed as a result of the accumulation of
the permanent deformation. According to the detailed maps
617
618
T. Sat0 and M. Matsu’ura
of ocean-bottom topography and free-air gravity anomalies
in and around Japan (Tomoda & Fujimoto 1982), the
patterns of topography and gravity anomalies across the
Nankai Trough are characterized by island-arc high, trench
low, and outer-rise gentle high. Such characteristic patterns
of topography and gravity anomalies are commonly
observed at all subduction zones in the world.
A number of authors have quantitatively explained each
of these phenomena in each time-scale with conceptually
independent models. Thatcher & Rundle (1984) have
explained the cyclic crustal deformation in southwest Japan
by using a viscoelastic coupling model based on the general
formalism for earthquake cycles developed by Savage
(1983). They assumed that steady-state plate subduction did
not contribute to vertical surface deformation, and so the
deformation process was completely cyclic. This assumption
is clearly in contradiction with the secular uplift motion
observed at Muroto Promontory. Stuart (1988) has
simulated the cyclic earthquake process at the Nankai
Trough by using a rate- and state-dependent friction law. In
this simulation, however, viscoelastic properties of the
asthenosphere are not taken into account. The viscosity of
the asthenosphere is of the order of 1018-10’9Pas. Then,
the relaxation time of the asthenosphere is of the order of
1-10 yr, but the effective relaxation time of the lithosphereasthenosphere system, which depends on the characteristic
wavelength of deformation, is much longer than it
(Matsu’ura & Sat0 1989). In any case the effect of
viscoelastic relaxation in the asthenosphere cannot be
neglected.
Yoshikawa, Kaizuka & Ota (1964) have explained the
rate and pattern of uplift of the marine terraces at Muroto
Promontory by assuming that a fraction of coseismic vertical
displacement remains after the completion of each
earthquake cycle. However their explanation is inconsistent
with the fact that the marine terraces are developed even at
places where the coseismic change is subsidence.
A number of attempts to explain the whole patterns of
topography and/or gravity anomalies across island arctrench systems have been made, for example, by Davies
(1981) in terms of the bending of a thin elastic plate subject
to stresses transmitted through a descending slab and a
mantle wedge, by Melosh (1978), Melosh & Raefsky (1980)
and Zhang, Hager & Raefsky (1985) in terms of the stress
induced by viscous flow in the lower part of a bending plate,
and by Tharp (1985) in terms of the deflection of a surface
layer with a low-strength megathrust zone and a
high-density descending slab subject to horizontal shortening at a constant rate. None of these models, however,
could explain consistently the gross features of topography
and/or gravity anomalies across island arc-trench systems,
namely, island-arc high, trench low, and outer-rise gentle
high.
In these studies, phenomena with different time-scales are
treated independently, but the fundamental cause of them is
the same: the subduction of oceanic plates. We have
constructed a plate subduction model, which explains
consistently all of the phenomena with different time-scales,
in a series of papers (Matsu’ura & Sat0 1989; Sat0 &
Matsu’ura 1988, 1992). Matsu’ura & Sato (1989) have
developed a dislocation model for the earthquake cycle at
subduction zones. They considered the perfectly elastic
lithosphere overlying the viscoelastic asthenosphere under
gravity, and demonstrated that the steady-plate subduction
brought about the permanent vertical deformation of the
lithosphere. This permanent deformation continuously
develops the marine terraces near subduction zones. As a
natural extension of the earthquake cycle model, Sat0 &
Matsu’ura (1988) have treated long-term (-lo6 yr) deformation of the elastic lithosphere at subduction zones, and
successfully explained the characteristic patterns of topography and gravity anomalies across island arc-trench
systems. The assumption of the perfectly elastic lithosphere
leads to the conclusion that island arc-trench systems go on
growing at a constant rate unless the steady-plate subduction
is interrupted. The steady growth of island arc-trench
systems is consistent with the steady uplift of marine
terraces, but inconsistent with the fact that the patterns of
topography and gravity anomalies are nearly stable at old
subduction zones. To overcome this contradiction, Sato &
Matsu’ura (1992) have constructed a plate subduction model
which explains the whole evolution process of island
arc-trench systems, considering viscoelasticity of the
lithosphere, accretion of oceanic sediments and rocks at
plate boundaries, and effects of erosion and sedimentation.
In the present paper, using the plate subduction model,
we explain the cyclic crustal movement, the steady uplift of
marine terraces, and the characteristic patterns of
topography and gravity anomalies observed at the
subduction zone in southwest Japan.
2
PLATE SUBDUCTION M O D E L
We model the lithosphere-asthenosphere system by a
stratified viscoelastic half-space under gravity, which consists
of a high-viscosity surface layer and a low-viscosity
substratum. The analyses of post-glacial uplift data (Cathles
1975; Iwasaki & Matsu’ura 1982) show that the asthenosphere behaves like a Maxwell fluid, and the lithosphere
behaves like a perfectly elastic body on a time-scale shorter
than 105yr. On the other hand, the studies on the
deformation of the lithosphere subjected to passive loads
such as volcanic islands or sea mounts (Walcott 1970; Sleep
& Snell 1976; Beaumont 1978; Lambeck & Nakiboglu 1981)
show that relaxation of stresses takes place even in the
lithosphere on a time-scale longer than lo6 yr. Although the
physical mechanism of the stress relaxation in the
lithosphere may differ from that in the asthenosphere, we
simply assume that both layers behave like a Maxwell fluid
in shear and an elastic solid in bulk. Then the constitutive
equations for the kth layer (k = 1,2) are written in tensor
form as
where A ( k ) and p ( * ) are the Lam6 constants, q ( k ) is the
viscosity, and q,, E,) and b,, are the stress tensor, strain
tensor, and the unit diagonal tensor, respectively. The dot
indicates differentiation with respect to time.
We introduce an infinitely long dislocation surface Z,
which divides the stratified viscoelastic half-space into two
parts, oceanic and continental parts, as shown in Fig. 1.
Here, it should be noted that the infinitely long dislocation
Crustal movement in southwest Japan
Figure 1. Schematic diagram showing the coordinate system and
the structure model used in the present study. The two-layered,
viscoelastic half-space is divided into continental (left) and oceanic
(right) parts by a plate interface P.
surface is not the approximation of an isolated plate
boundary with a finite length, but the approximation of a
sequence of various types of plate boundaries, which makes
the circuit of the earth. We represent interaction between
oceanic and continental plates by the increase of
discontinuity in tangential displacement across the plate
boundary. The displacement discontinuity (dislocation) is
mathematically equivalent to the force system of a double
couple without moment (Maruyama 1963; Burridge &
Knopoff 1964). The force system of a double couple has no
net force and no net torque. In general, such a property
must be satisfied for any force system acting on the plate
boundary, since it is the internal force imposed by a
dynamic process within the earth. This is one of the reasons
why we represent the plate interaction by the displacement
discontinuity. Another reason is more practical; that is, the
configurations of plate boundaries and the average slip rates
across them can be precisely determined from present-day
observations.
In Fig. 2a we show schematically the slip motion
proceeding on the plate boundary. Below the lithosphereasthenosphere boundary, steady-slip motion proceeds
uniformly. In the shallower part of the lithosphere, slip
occurs instantaneously at the time of earthquake (r = T). In
this region, coupling between the oceanic and continental
plates is very strong, and so tectonic stress accumulates
gradually with time through the interseismic period. In the
deeper part of the lithosphere, post-seismic slip occurs
aseismically. In this region, the oceanic and continental
plates are coupled with each other except during the
post-seismic period. Therefore, after the post-seismic slip
motion terminates, the process of tectonic stress accumulation proceeds in the same way as in the strongly coupled
region where coseismic slip occurs. These slip motions
repeat on the plate boundary with a recurrence interval of
T.
Following the general formalism for earthquake cycles
developed by Savage (1983), we decompose the total slip
motion into a steady and uniform slip over the whole plate
boundary and its perturbation related to the periodic
occurrence of earthquakes. Then the surface deformation
associated with the earthquake cycle is represented by the
superposition of viscoelastic responses to the steady slip
over the whole plate boundary and the periodic slip
repeated at the coupling region. We suppose that both the
steady-slip motion and the periodic motion started at the
time t = 0. The space-time slip function for the steady slip
T-
Ta
Ta OtT+
+
+
T-T+
619
P
T - T+
Depth
f
1
0 Ta T
2T
Figure 2. Schematic diagram showing the decomposition of a cyclic slip motion on the plate boundary. The total slip motion (a) during one
earthquake cycle is decomposed into three elemental slip motions; (b) a steady-slip motion over the whole plate boundary, (c) a periodic-slip
motion at a coupling region, and (d) a periodic-slip motion at a post-seismic-slip region. The thick lines represent the tautochrones of slip
motion. T and Ta denote the recurrence time of earthquakes and the duration time of post-seismic slip, respectively. The dashed line
corresponds to the lithosphere-asthenosphere boundary.
620
T. Sat0 and M . Matsu'ura
(Fig. 2b) is given by
L(L t ) = U,ltH(t),
(2)
where upl denotes the plate convergence rate, H ( t ) the unit
step function, and E the coordinates of a point on the plate
boundary. The periodic slip motion is further divided into
two parts. One part represents the effect of interseismic
coupling between the oceanic and continental plates (Fig.
2c). This effect can be expressed by a steady back slip at the
coupling region, namely the region where coseismic or
post-seismic slip occurs. We denote the degree of coupling
at 5 by C ( 5 ) ; C(E)= 1 corresponds to complete coupling,
and C(E)=O to complete decoupling. Another part
represents the post-seismic slip (Fig. 2d). We denote the
rate of the post-seismic slip by u,, which is assumed to be
constant for simplicity, the duration time by Ta, and the
normalized distribution of slip by A ( 5 ) . The total amount of
post-seismic slip over a cycle at 5 is given by u,TdA(E).
Then the space-time slip function for the periodic slip
during the (n + 1)th earthquake cycle is written as
n
and
t , = min(t, n T
1,
= upl[ u s ( x . t - t)d t - upl ' u , ( x , t - t)dt
+
u , ( x , t - t)d t
Jn T
1,
nT
W(X,
nT
t
< ( n + 1)T,
(5)
(6)
+ t ) - W(X, n T + ) .
(11)
Here, the time t is also measured from just after the
occurrence of the nth earthquake. At t = T - , just before
the occurrence of the next earthquake, the surface
displacement becomes
We consider two representative cases: the first is the case of
young subduction zones, where the duration time ( n T ) of
steady-plate subduction is much longer than the effective
stress relaxation time in the asthenosphere ( t a- 10-102 yr,
assuming the viscosity of the asthenosphere to be
1018-10'yPas), but much shorter than that in the
lithosphere ( t l 106-107 yr, assuming the viscosity of the
lithosphere to be 1023-1024Pas).The second is the case of
old subduction zones, where the duration time of
steady-plate subduction is much longer than the effective
stress relaxation time in the lithosphere. In the first case
(t,<< nT << t l ) , as demonstrated by Matsu'ura & Sat0
(1989), viscoelastic response to a step slip in the
asthenosphere vanishes at t = nT, but to a step slip in the
lithosphere it becomes constant in time, because the
lithosphere still behaves like an elastic plate on this
time-scale. Therefore, all of the integrands in equation (12)
can be regarded as constants. Then, using the relation (4),
-
I
(10)
Here, q ( x , t ; 6, t) indicates the vertical component of
surface displacement at a point x and a time t due to a
unit-step slip at a point E and a time t. Concrete expressions
for q ( x , t ; E, t ) are given in Sat0 & Matsu'ura (1992).
Equation (5) gives a general expression for the crustal
deformation at subduction zones: the first term represents
the surface displacement due to the steady-plate subduction,
the second term the effect of interseismic coupling, the third
term the viscoelastic response to the sequence of periodic
coseismic slips, and the fourth term the viscoelastic response
to the sequence of periodic post-seismic slips. The
summations in the third and fourth terms of equation (5)
can be analytically evaluated (Matsu'ura & Sat0 1989).
To measure the surface deformation during an earthquake
cycle, we need a frame of reference. As the frame of
reference we take the configuration of the earth's surface
just after the occurrence of the nth earthquake ( t = n T + ) ,
and define the surface displacement for the ( n + 1)th
earthquake cycle by
Aw(x, I )
Here, u , , D ( ~ ) Tgives the amount of coseismic slip at 5. The
first term of equation (3) corresponds to the steady back slip
representing the effect of interseismic coupling, the second
term to the coseismic slip, and the third term to the
post-seismic slip.
The vertical surface displacement w ( x , t) due to the slip
motion on the plate boundary can be obtained from
viscoelastic response to a unit-step slip by using the
technique of hereditary integral;
+ T,).
Crustal movement in southwest Japan
621
with
we may rewrite equation (12) as
du,(x, t )
In the second case (t,<< t l<< n T ) , viscoelastic step response
at f = n T vanishes even for the slip in the lithosphere,
because not only the asthenosphere but also the lithosphere
behaves like a perfect fluid on this time-scale. Therefore, all
of the terms in equation (12) vanish, except for
uplTud(x,O+).Then we may rewrite equation (12) as
AW(X, T - ) = -uplTud(x, O+).
(14)
Here, u,,Tud(x, O+) is the elastic response to the coseismic
slip, and so the surface displacement just after the
occurrence of the next earthquake (t = T + )becomes
Aw(x, T + )= uplTu,(x,nT)
(15)
for the young subduction zones, and
g h , t ) = L__.
3x2
In the case of young subduction zones (t,<< t << t J , both
u,(x, t) and g,(x, t) become constant in time. Therefore,
denoting them by u:(x) and g:(x), we can evaluate the
growth rate as
+s(x,
t)
up!(
u:(x) - u a c /'K :[x
= uplu:(x - uaCfez),
- uac(t - t)e21dt
I
x 5 0.
(21)
This means that the pattern of the growth rate does not
change in time; it migrates seaward at the accretion rate ua,
as a whole. When subduction zones are sufficiently old
(r, << t l<< t ) , both u,(x, 1 ) and gs(x, t) vanish, and so the
growth rate can be evaluated as
Aw(x, T + )= 0
for the old subduction zones. Namely, at the young
subduction zones, a certain amount of surface displacement
due to the steady-plate subduction remains after the
completion of one earthquake cycle, but not at the old
subduction zones. The surface deformation at the old
subduction zones is completely cyclic. This means that the
island arc-trench systems grow at a constant rate in the early
stage of plate subduction, but its growth rate decreases with
time and finally becomes zero, because of the viscoelastic
relaxation of the lithosphere.
On a very long time-scale, as demonstrated by Sat0 &
Matsu'ura (1992), the accretion of oceanic sediments and
rocks at plate boundaries strongly affects the deformation
process of island arc-trench systems. In southwest Japan the
existence of a large amount of accreted material has been
reported by Taira et al. (1982), and so we must consider the
effect of accretion. Since the accreted oceanic sediments and
rocks ultimately coalesce into continental land masses
(Moore & Silver 1987), the accretion process can be
regarded as the process of successively creating a new plate
boundary in front of old plate boundaries. In the present
study, we simply assume that the plate boundary migrates
seaward at a constant accretion rate u,, without change in
its shape. The effect of accretion on the long-term
deformation of continental plates can be incorporated into
our model by replacing the first term of equation (5) by
(20)
~ s ( ~ 9=
t)
-uplu,,
r
g:[x
- u,Jt - t)ezl dt
= uPl[u:(x- u,,te2) - u:(x
- u,,te2 + uactleZ)l,
xso.
(22)
In this case the growth rate depends on the accretion rate
uac;if u,, is very small, +,(x, t) becomes zero.
Other important factors controlling the evolution process
of island arc-trench systems are erosion and sedimentation.
The rate of erosion depends generally on various factors
such as climate, vegetation, properties of rocks, height and
inclination of land surfaces (Bloom 1978). From the detailed
study on erosion at mountainous regions in Japan, Ohmori
(1978) has obtained an empirical relation that the rate of
erosion depends mainly on land height and is in proportion
to its square. We adopt this relation in our modelling. As to
the rate of sedimentation, unfortunately, we have little
information. In the present study, we simply assume the
sedimentation rate on inner trench walls to be in proportion
to the square of marine depth, on the basis of the fact that
inner trench walls are generally covered with thick
sediments (e.g. Iwasaki et al. 1990). We neglect the effect of
sedimentation on oceanic plates, because the sediments
covering ocean floors and outer trench walls are very thin.
Then the height change, Aw,(x,t), due to erosion and
sedimentation during a short time interval At can be
expressed as
Aw,(x, t) = - y sgn [w(x, t - At)][w(x, t - At)12 At
(23)
for the continental region, and
with
u,(x
Aw,(x,t)=O
- v,,se,, t - t)=
I,
q ( x , I;5 + uatzez,t)4,
(18)
where e2 denotes the unit vector pointing in the direction of
the x 2 axis. Then the growth rate ~ s ( xt ,) of island arcs due
to steady-plate subduction becomes
W,
t ) = upl[u,(x, t ) - u,, [gS+
- u,,(t - t ) e 2 ,Z) d r ] ,
x ~ 0 ,(19)
(24)
for the oceanic region. Here, y denotes the rate of erosion
(sedimentation), and w(x, t - At) is the height of the earth's
surface at the time t - At. The direct effect of erosion and
sedimentation is, of course, the levelling of surface
topography. This process is always accompanied by mass
transfer from island arcs to trenches and brings about
loading and unloading on the earth's surface. Therefore, as
pointed out by King, Stein & Rundle (1988), the crustal
deformation caused by the loading and unloading must be
taken into account as the secondary effect of erosion and
622
T. Sat0 and M . Matsu'ura
sedimentation. We denote the surface deformation produced by the height change Awc due to erosion and
sedimentation during a period from t = (k - 1) At to t = k At
by Aw,(x, t ; k At). A concrete expression for Aw, is given in
Sat0 & Matsu'ura (1992). Then the height of the earth's
surface at each time step can be successively evaluated by
the following algorithm:
w(x, n At) = w,(x, n At) +
c
n
Aw,(x, k At)
k=l
+ c Aw,(x, n At; k At).
n
k=l
Here, the first term corresponds to the vertical surface
displacement due to the steady-plate subduction, the second
term to the direct effect of erosion and sedimentation, and
the third term to the effect of the loading and unloading
associated with erosion and sedimentation.
3
APPLICATION TO SOUTHWEST J A PA N
We apply the plate subduction model to southwest Japan,
where the Philippine Sea Plate is descending beneath the
Eurasian Plate at the Nankai Trough (Fig. 3). The relative
motion of the Philippine Sea Plate to the Eurasian Plate is
about 4 cm yr-' in the direction of N50"W (DeMets et al.
1990). From geological data it has been estimated that the
plate subduction at the Nankai Trough started about
6~ 10"yr BP (Niitsuma 1985). On the basis of this
estimation and a simple calculation of the time required for
the plate subduction to reach a steady state, we assume the
duration time of steady-plate subduction to be 4 x 10" yr.
From the hypocentre distributions of micro-earthquakes in
this region, Mizoue et al. (1983) have estimated the shape of
the upper boundary of the descending Philippine Sea Plate.
The vertical sections of the upper plate boundary across the
Nankai Trough, which are used for the present computation, are shown in Figs 4(a) (Shikoku Island) and (b) (Kii
Peninsula). The average thickness of the lithosphere in this
region is about 35 km (Kanamori & Abe 1968; Yoshii et al.
1974; Seekins & Teng 1977). Through the analyses of
post-glacial uplift data, the global average of the viscosity of
the asthenosphere has been estimated as 4 x 10'' Pa s
(Cathles 1975). At subduction zones, however, the viscosity
of the asthenosphere will take a somewhat smaller value
than this average because of heat production at plate
boundaries. In fact, Matsu'ura & Iwasaki (1983) have
obtained the value of 5 x 10l8 P a s through the analysis of
transient crustal movement after the 1923 Kanto
earthquake. We use this value for the present computation.
As to the viscosity of the lithosphere we have only rough
estimates ( 1023-1024Pa s) based on the analyses of flexure
for the oceanic and/or continental lithosphere (Walcott
1970; Sleep & Snell 1976; Beaumont 1978; Ida 1984;
Turcotte 1987). Then we assume the viscosity of the
lithosphere to be 5 X loz3Pa s.
Southwest Japan has many structural belts of terranes,
which make an accretionary complex formed in association
with the subduction of the Philippine Sea Plate. For the
accretion rate at the Nankai Trough we adopt the value of
0.5 cm yr-l on the basis of a geological study by Taira et al.
(1982). For the erosion (sedimentation) rate we adopt the
value of 0.7 mm yr-' at a height of 1000 m on the basis of a
geographical study by Ohmori (1978).
Figure 3. Location map of southwest Japan. The thick lines with open squares and the solid triangles indicate levelling routes and tidal gauge
stations, respectively. The epicentre of the 1946 Nankaido earthquake is marked by the star. The thick arrow indicates the direction of the
motion of the Philippine Sea Plate relative to the Eurasian Plate.
Crustal movement in southwest Japan
(a) SHIKOKU
$
623
SHI KOKU
200-
n
(b) KII
E
h
u 200
n
-
A
1OOkm
a
2
Y
I
400 km
1%
(
I
d. 1964- 1979
0
w
>
J
r
A
L
-
e. 1897 1979
5,,,,
0
Figure 4. The structure models used for the present computation.
The plate interface, which is indicated by the thick line, dips
gradually from 0" at the surface to 20" at the depth of 25 km in the
case of Shikoku (a), and to 25" at the depth of 25 km in the case of
Kii (b). In either case, the P-wave velocity, S-wave velocity,
density, and viscosity of the lithosphere are taken as 7.0 km s-I,
4.0 km s-', 3.0 g cm-3, and 5 x loz3Pas, respectively; and those of
the asthenosphere as 8.0 km s-', 4.4 km s-'. 3.3gcm-', and
5 x 10" Pas, respectively. The triangles indicate the positions of
trench axes.
3.1 Cyclic crustal movement
According to historical records of great earthquakes in
southwest Japan, the average recurrence time of interplate
earthquakes at the Nankai Trough is about 115yr for the
last six events (Ando 1975). We adopt this value for the
computation of the deformation cycle. In southwest Japan,
geodetic surveys started in the 1890s and were repeated at
the interval of 20-30 yr since then. Therefore these data
almost completely cover the whole deformation cycle
associated with the 1946 Nankaido earthquake. Thatcher
(1984) has compiled the levelling data from 1895 to 1980 and
revealed details of the deformation cycle in southwest
Japan. From Thatcher's paper we have reproduced the
profiles of vertical displacements along two representative
levelling routes, one of which crosses Shikoku Island and
another extends along the western coast of Kii Peninsula, in
Figs 5 and 6. Here the profiles of vertical displacements in
the post-seismic period (1947-64 for Shikoku and 1947-67
for Kii) are shifted upward as a whole, on the basis of a
re-evaluation of absolute level changes of reference points
using tidal gauge data (Kato & Tsumura 1979; Thatcher
1984).
From Figs 5 and 6 we can see that the 1946 Nankaido
earthquake brought about coseismic uplift of 0.8 m at
Muroto and 0.4 m at Kushimoto and subsidence of 0.6 m at
I
TAKAMATSU
KOCHI MUROTO
I
I
L
300
200
I
loo
0
DISTANCE FROM TRENCH AXIS (km)
Figure 5. Changes in vertical displacement at Shikoku for the (a)
pre-seismic, (b) coseismic, (c) post-seismic, and (d) interseismic
periods of one earthquake cycle. The total change (e) during the
earthquake cycle is shown at the bottom. The open squares indicate
the observed data. The solid curves indicate the theoretical results.
The solid triangles show the elevation changes of tidal gauge
stations.
inland areas (b). Following the coseismic crustal deformation, rapid recovery motion proceeds in the post-seismic
period (c), but this rapid recovery motion dies out soon.
After that, gradual crustal movement continues through the
interseismic period (d). Pre-seismic crustal deformation (a)
is notable in Shikoku, but not in Kii. For reference we show
the total amount of crustal deformation (e) during these
80yr at the bottom of Figs 5 and 6. The observed
deformation cycle is not complete because of the lack of
data for the latter half of the interseismic period, but we can
roughly estimate the amount of permanent deformation
after the completion of the earthquake cycle by extrapolating to the expected recurrence time. From such estimation
we conclude that a significant amount of permanent
deformation remains after the completion of the earthquake
cycle.
These features of the deformation cycle observed in
southwest Japan are well explained by our plate subduction
model, assuming the cyclic space-time slip motion shown in
Fig. 7. The vertical displacement profiles computed from {he
plate subduction model are compared with the observed
data in Figs 5 and 6. In the computation, the effects of
accretion and erosion (sedimentation) were not taken into
624
T. Sat0 and M . Matsu’ura
KII
15Or
account, because these effects are negligible for short-term
phenomena such as the deformation cycle. In either case of
Shikoku and Kii the lower bound of the region where
coseismic slip occurred is well-constrained by the observed
coseismic displacement data. In the case of Kii the
coseismic-slip region extends through the entire thickness of
the lithosphere, and so there is no region where post-seismic
slip or interseismic steady slip occurs at the depths of the
plate boundary. In the case of Shikoku, on the other hand,
the coseismic-slip region does not extend down to the
lithosphere-asthenosphere boundary. The lower bound of
the coseismic-slip region is at 30 km in depth, and from this
depth the region where post-seismic slip or interseismic
steady slip occurs extends downward. The notable uplift
motion observed in the pre-seismic period is well explained
by the interseismic steady slip on this region. When the
plate boundary is strongly coupled down to the lithosphereasthenosphere boundary, the surface deformation produced
by the viscoelastic relaxation of coseismic stress changes in
the asthenosphere is remarkable in the post-seismic period,
but not in the pre-seismic period (Matsu’ura & Sat0 1989).
This is just the case of Kii. When the plate boundary is
decoupled at depths and the interseismic steady slip
proceeds there, which is the case of Shikoku, the surface
deformation produced by the post-seismic stress relaxation
in the asthenosphere is not so remarkable (Matsu’ura &
Sat0 1989). Therefore, to explain the post-seismic recovery
motion observed in Shikoku, the post-seismic slip at the
depths of the plate boundary is necessary.
a. 1899- 1929
0
-0
-
a-
0
I-
o
-0
I
4f
,
KAINAN
-_-
KUSHIMOTO
I
1
300
,
--
.
100
200
0
DISTANCE FROM TRENCH AXIS (km)
Figure 6. Changes in vertical displacement at Kii for the (a)
pre-seismic, (b) coseismic, (c) post-seismic, and (d) interseismic
periods of one earthquake cycle. The total change (e) during the
earthquake cycle is shown at the bottom. The open squares indicate
the observed data. The solid curves indicate the theoretical results.
The solid triangles show the elevation changes of tidal gauge
stations.
(a) SHIKOKU
20
We can observe a series of well-developed marine terraces,
which were formed by eustatic sea-level changes during the
last lo5 yr, along coastlines in southwest Japan (Yoshikawa,
Kaizuka & Ota 1964; Yonekura 1968; Ota 1975). Through a
simple analysis of the present heights of the marine terraces
formed at previous different times, it is concluded that the
(b) KII
OC T a T -
Tt
I
I
I
3.2 Steady uplift of marine terraces
Slip
Slip
OC TaT-
I
I
u
2m
1
30K
1 ...........
Depth
km
Figure 7. Cyclic patterns of slip motion on the plate boundary at (a) Shikoku, and (b) Kii. In either case the recurrence time T of earthquakes
and the duration time T, of post-seismic slip are taken to be 115 and 5 yr, respectively. The dashed line corresponds to the
lithosphere-asthenosphere boundary.
Crustal movement in southwest Japan
(a) SHIKOKU
MUROTO
*r
(b)KII
'i
KUSHIMOTO
1.
150
0
1
2
'
.
"
--.-
100
50
.,i
625
left the direct effect of erosion and sedimentation during the
last 10'yr out of our calculations, because the heights of
markers of past shorelines are not affected by erosion and
sedimentation. In Fig. 8 we compare the profiles of the
computed uplift rates with those of the observed uplift rates.
The difference in the pattern of steady uplift motion
between Shikoku and Kii is ascribed to the difference in the
shape of plate boundary between these two regions. The
good agreement of the computed results with the observed
data leads us to the conclusion that the steady uplift of
marine terraces can be explained by the steady-plate
subduction.
The accretion rate at the Nankai Trough is fairly large
(0.5 mm yr-'), but its effect is not yet remarkable, because
the Nankai Trough is still young (the duration time of steady
subduction at the Nankai Trough is 4 X 106yr, while the
effective relaxation time of the lithosphere is about
5 X 10'yr). At very old subduction zones, the substantial
growth rates, uplu,(x, t ) , of island arc-trench systems tend to
zero. Even in such a case, as discussed in Section 2, we can
expect the steady uplift of marine terraces, if the accretion
process proceeds at a sufficiently large rate.
DISTANCE FROM TRENCH AXIS (km)
Figure 8. Profiles of the uplift rates of marine terraces at (a)
Shikoku, and (b) Kii. The open squares indicate the observed data.
The solid curves indicate the theoretical results.
uplift of marine terraces (land) has proceeded at a constant
rate throughout the last 10'yr. In Fig. 8 we show the
profiles of the uplift rates of land along the western coast of
Muroto Promontory and the western coast of Kii Peninsula,
estimated respectively from the present heights of M1
Terrace and L1 Terrace, both of which were formed at
1.2 x 1O'yr BP. In the estimation of uplift rates, following
Chappell (1974, 1983), we assumed that the sea-level at
1.2 x 10syr BP was 4 m above the present sea-level. In the
case of Shikoku the observed uplift rate takes a maximum
value of 1.6 mm yr-' at Muroto and decreases rather steeply
with distance from the Nankai Trough. The abrupt change
in the uplift rate near Muroto is due to a local faulting. In
the case of Kii, the general tendency is the same as in the
case of Shikoku (the uplift rate takes a maximum value at
the southernmost point and decreases with distance from the
Nankai Trough), but the maximum uplift rate is only
OSmmyr-' and the decrease away from the maximum
point is rather gradual.
These features of the uplift motion of marine terraces
(land) observed in southwest Japan can be naturally
explained by our plate subduction model. We compute the
average uplift rates over the last lo5 yr (3.9-4.0 x lo6 yr
after the initiation of plate subduction) with the algorithm in
equation (25), where the time increment At is taken to be
105yr. The plate subduction model used for the
Computation is essentially the same as that used for the
computation of the deformation cycle in Section 3.1. In the
computation of the long-term average of uplift rates, we can
neglect the effects of the periodic slip motion, because the
amount of permanent surface deformation remaining after
the completion of one earthquake cycle does not depend on
details of the slip process during the earthquake cycle. We
3.3 Patterns of topography and gravity anomalies
At young subduction zones, as demonstrated in Section 3.2,
steady-plate subduction brings about the steady uplift of
land. Therefore, it is quite natural to consider the island-arc
high to be formed as a result of the uplift due to the
steady-plate subduction. We show the profiles of surface
topography and free-air gravity anomalies across the Nankai
Trough in Figs 9 (Shikoku) and 10 (Kii). These profiles are
characterized by island-arc high, trench low, and outer-rise
gentle high. Such characteristic patterns of topography and
gravity anomalies, which are commonly observed at all
subduction zones in the world, are also well explained by
our plate subduction model.
We computed topographic changes during 4 x 10" yr after
the initiation of plate subduction. The plate subduction
model used for the computation is essentially the same as
that used in Sections 3.1 and 3.2. In the computation of the
topographic changes, we can neglect the effects of the
periodic slip motion for the same reason as stated in Section
3.2, but not the effects of the other factors such as accretion
and erosion (sedimentation). We also computed the gravity
anomalies produced by the topographic changes with the
method developed by Talwani, Worzel & Landisman
(1959). The profiles of topographic changes and gravity
anomalies computed from the plate subduction model are
compared with the observed data in Figs 9 (Shikoku) and 10
(Kii). The computed topographic changes, which are
indicated by thick lines, represent the changes from an
initial isostatic state. Therefore, to compare directly the
computed result with the observed topography, we must add
an initial isostatic level to it. We took the initial isostatic
level so that it fits with the sea-level on the continental side
and the mean marine depth on the oceanic side. The
synthesized surface topographies are indicated by thin lines
in Figs 9 and 10. As to gravity anomalies, on the other hand,
we may directly compare the computed results with the
observed data, if the effects of a dense downgoing slab and a
lateral change in crustal structure are correctly taken into
626
T. Sat0 and M . Matsu'ura
CALCULATED
OBSERVED
E
$
O
t:
-2001 mgal
:
:
E
9
6 k m
l ; :2
I
I
-200 mgal
1OOkm
l00km
E
SHIKOKU
0
w
400 km
Figure 9. Profiles of topography and gravity anomalies along a line crossing the Nankai Trough at Shikoku. Left column: observed data; right
column: theoretical results. The thick lines indicate the topographic change and gravity anomalies directly computed from the plate subduction
model. The thin lines indicate the synthesized topography and gravity anomalies, which can be directly compared with the observed data. The
structure model used for the computation is shown at the bottom of the right column.
account. The existence of a dense downgoing slab produces
large-scale positive gravity anomalies on the continental
side. The gravity anomalies produced by a lateral change in
crustal structure at the continental margin have a relatively
short-scale sinusoidal pattern. Adding these effects to the
computed results, we obtain the patterns of synthesized
gravity anomalies as shown in Figs 9 and 10, where the
computed and synthesized gravity anomalies are indicated
by thick and thin lines, respectively. As can be seen from
Figs 9 and 10, the agreement of the theoretical results with
the observed data is fairly good in either case of Shikoku
and Kii.
The Nankai Trough is a young subduction zone, and so
the substantial growth rate of the island arc-trench system is
CALCULATED
OBSERVED
9 l km
2oo
1 ; : 2
-2001 mgd
I
u
-200 mgal
1OOkm
KII
I
1OOkm
E
w
n
400
km
Figure 10. Profiles of topography and gravity anomalies along a line crossing the Nankai Trough at Kii. Left column: observed data; right
column: theoretical results. The thick lines indicate the topographic change and gravity anomalies directly computed from the plate subduction
model. The thin lines indicate the synthesized topography and gravity anomalies, which can be directly compared with the observed data. The
structure model used for the computation is shown at the bottom of the right column.
Crustal movement in southwest Japan
still large. The simple extrapolation of the present uplift rate
of land over 4 X lo6 yr yields an island-arc of 8000 m high.
On the other hand, the actual height of the island-arc in
southwest Japan is only 2000m. This difference is mainly
ascribed to the effects of erosion. The rate of erosion
(sedimentation) is in proportion to the square of land height
(marine depth). Therefore the levelling of surface
topography due to erosion and sedimentation is accelerated
as the growth of the island arc-trench system. From these
considerations we can conclude that the present patterns of
surface topography and gravity anomalies are held nearly
stable by the balance of the levelling due to erosion and
sedimentation and the substantial growth due to steadyplate subduction.
4
DISCUSSION A N D CONCLUSIONS
We demonstrated that the cyclic crustal movement, the
steady uplift of marine terraces, and the patterns of
topography and gravity anomalies observed in southwest
Japan could be consistently explained by a single-plate
subduction model based on elastic dislocation theory. The
agreement of the theoretical results with the observed data
is fairly good, but there still exists a significant discrepancy
between them.
The significant discrepancy is found in the post-seismic
recovery motion in Kii (Fig. 6c). In this region we assumed
the interplate coupling to be complete through the entire
thickness of the lithosphere; otherwise the observed
pre-seismic and coseismic crustal deformation could not be
explained. Hence the cause of the rapid recovery motion
627
following the coseismic crustal deformation should be
ascribed to the post-seismic stress relaxation in the
asthenosphere. In fact, when the interplate coupling is
complete through the entire thickness of the lithosphere, the
post-seismic stress relaxation produces sufficiently large
crustal deformation to explain the observed data. The
problem is the discrepancy in its spatial pattern between the
theoretical results and the observed data. This discrepancy
can be resolved if we consider the effect of a post-seismic
slip beneath Kii Strait. Yabuki & Matsu'ura (1992) have
recently investigated the distribution of fault slip at the time
of the 1946 Nankaido earthquake through an inversion
analysis of coseismic surface displacement data. According
to their result, the coseismic fault slip distribution has two
main peaks, located off Kii Peninsula and Muroto
Promontory (Fig. 11). The two high-slip areas are clearly
separated by a low-slip zone beneath Kii Strait. If the
release of tectonic stress at the depths of the low-slip zone
proceeded gradually in the post-seismic period, it would
produce notable post-seismic level changes of bench marks
in the western part of Kii Peninsula. Our assumption that a
post-seismic slip occurred at the depths of the low-slip zone
does not contradict the good agreement in the rate and
pattern of marine terrace uplift between the theoretical
results and the observed data, because they do not depend
on the details of the pattern of cyclic slip motion on the
plate boundary. The essential factors controlling the rate
and pattern of marine terrace uplift are the rate of plate
convergence and the configuration of the plate boundary.
The conclusions which we obtained through the present
study are as follows. The pattern of cyclic slip motion on the
Figure 11. The fault slip distribution at the time of the 1946 Nankaido earthquake estimated by Yabuki & Matsu'ura (1992) through the
inversion analysis of coseismic surface displacement data. The configuration of the upper boundary of the Philippine Sea Plate, determined
from the distributions of micro-earthquakes, is shown by the isodepth contours (thick lines). The area enclosed by the thin line indicates the
surface projection of a model fault region taken on the curved plate boundary.
628
T. Sato and M. Matsu’ura
plate boundary is essentially different between Kii and
Shikoku, as far as the latest cycle is concerned. In the case
of Kii the coseismic-slip region extends down to the
lithosphere-asthenosphere boundary. In the case of
Shikoku, on the other hand, the plate boundary is
decoupled at depths, where the steady slip proceeds at a
constant rate. In either case the observed deformation cycle
cannot be explained by a simple rebound model, in which
the effect of steady-plate subduction is ignored. The
steady-plate subduction brings about the steady uplift of
marine terraces at young subduction zones regardless of the
rate of accretion at plate boundaries. The present patterns
of surface topography and gravity anomalies across the
Nankai Trough are held nearly stable by the balance of the
levelling due to erosion and sedimentation and the
substantial growth due to steady-plate subduction.
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~
ACKNOWLEDGMENTS
We gratefully acknowledge Tetsuichiro Yabuki of the
Hydrographic Department, Maritime Safety Agency, for
providing us with the original figure of coseismic fault slip
distribution. The computations were made on HITAC S-820
at the Computer Centre, University of Tokyo.
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