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TSUNAMI SIMULATION TAKING INTO ACCOUNT SEISMICALLY INDUCED
DYNAMIC SEABED DISPLACEMENT AND ACOUSTIC EFFECTS OF WATER
TATSUO OHMACHI
Tokyo Institute of Technology, Tokyo, Japan
1. Introduction
Recently, we have presented a new technique to simulate generation and propagation of
tsunamis [1]. In contrast with convention [2] where the initial sea surface is assumed to be
the same as the seismically induced static displacement of the seabed and propagation
(tsunamis) is simulated using the long-wave approximation, the new technique takes into
account effects of dynamic seabed displacement resulting from seismic faulting, as well as
of acoustic water waves.
Due to an assumption of the new technique that the seawater-seabed system can be
regarded as a weakly coupled system, our numerical simulation is made up of two steps.
The first is earthquake ground motion simulation for which the boundary element method
(BEM) is used, and the second is tsunami simulation for which the finite difference method
(FDM) is used. Considering a rupture mechanism of seismic faulting, the dynamic seabed
displacement is first simulated, including the static displacement in near-fault area. The
velocity associated with the seabed displacement is input accordingly at the bottom of the
seawater, and the resulting seawater disturbance is simulated by solving the Navier-Stokes
equations without using the long wave approximation, introducing a height function. To
secure reliable solutions, the CFL stability criterion [3] is used.
2. Simulation in two Dimensions
An analytical model used in a 2-D simulation is shown in Fig. 1. The fault model is a
thrust-faulting with dipping at 30 degrees, 30km wide and 5km deep under the seabed.
Dislocation is 10m, rupture velocity is 3km/s, and rise time is 2sec. The fault rupturing
starts at the bottom and propagates upwards. The water depth is 3km, and simulated area
extends to 100km on both sides of the epicenter
Snapshots from the simulation are shown in Fig. 2, in which the lower and upper
surfaces represent the seabed and the sea surface, respectively. The time indicated in the
snapshots is elapsed time from the initial fault rupturing. At about 10 seconds after the fault
rupturing, the seabed shows the maximum uplift, which is 1.6 times as large as the static
displacement and a few seconds later, the sea surface shows the maximum water wave
height. At 15 seconds, the Rayleigh wave appears mainly on the right side of the peak, and
travels to the right along the seabed. A single peak on the sea surface is divided into two
peaks. One of them is propagated to the right at a same velocity as the Rayleigh wave,
A. C. Yalçıner, E. Pelinovsky, E. Okal, C. E. Synolakis (eds.),
Submarine Landslides and Tsunamis 89-99.
@2003 Kluwer Academic Publishers. Printed in Netherlands
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Water Depth
Fault Depth
-100km
0
+100km
Epicentra l Distance
Figure1 . A 2D tsunami simulation model.
.
producing several later phases. The water wave is called the oceanic Rayleigh wave. After
40 seconds, the seabed in this area stops its motion, and shows the static displacement.
After 50 seconds, a single peak on the sea surface is flattened a little, divided into two and
continue propagation as tsunami waves. The height of the water wave and velocity of the
tsunami are just the same as those of the long waves
Thus, the height of the water wave in near-field is found to be remarkably larger than
that of the static seabed displacement. In this case, it is almost twice. This is mainly due to
superposition of two types of waves. One is the oceanic Rayleigh wave and the other is
tsunami.
3. Simulation in Three Dimension the 1998 Sanriku-oki Earthquake Tsunami.
At the bottom of the Pacific Ocean, off Sanriku coast, Japan are deployed monitoring
systems for earthquakes and tsunamis by researchers of Tohoku University and University
of Tokyo [4]. On May 30, 1998, the systems recorded time histories of an earthquake (M w
6.1) followed by a tsunami at stations shown in Fig. 3, in which OBS1, OBS2 and OBS3
are ground motion stations, and TM1 and TM2 are tsunami stations. Fault parameters of the
earthquake are shown in Table 1.
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Figure 2. 2D tsunami simulation by the present technique.
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TABLE 1. Fault parameters.
･
Seismic moment (dyne/cm)
1.9×10
Length (km)
15
Width (km)
15
Depth (km)
10
Strike (degree)
25
204
Dip (degree)
13
Rake (degree)
95
Dislocation (m)
0.3
Rupture velocity (km/sec)
3.0
Rise time (sec)
1.0
41°
N
240km
40°
TM2
TM1
Kamaishi
OBS3
39°
OBS2
360km
OBS1
fault project ion
38°
50km
37°
141
142
143
144
145
° 3. Fault° plane projection,
°
°
° and
Figure
monitoring
stations
calculation area.
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Pressure (Pa)
4500
TM1
Max 3.3kPa
0
-4500
0
Pressure (Pa)
4500
500
1000
1500
(a) Water pressure observed at TM1
2000
Time (sec)
TM2
Max 2.1kPa
0
-4500
0
Pressure (Pa)
450
500
1000
1500
(b) Water pressure observed at TM2
2000
Time (sec)
Observed (TM1)
Computed (TM1)
0
-450
0
500
1000
1500
(c) High-cut water pressure at TM1
Pressure (Pa)
450
2000
Time (sec)
Observed (TM2)
Computed (TM2)
0
-450
0
500
1000
1500
(d) High-cut water pressure at TM2
Figure 4. Comparison of the observations and the results of the simulation.
2000
Time (sec)
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Figure 5. 3D tsunami simulation of the 1998 Sanriku-oki, Japan earthquake
tsunami.
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The simulation area is 360km long and 240km wide as shown in Fig. 3. In Fig. 4, time
histories of the water pressure at TM1 and TM2 are shown. Since high frequency
components are apparently predominant in the original records shown in (a) and (b), they
are reduced by a low-pass filter, with the results shown in (c) and (d) in which the
simulated time histories are also shown. Although the water level change equivalent to the
pressure change, which can be stated as a small tsunami, is as small as 1cm, the simulated
pressure agrees well with the observation, demonstrating validity of our technique.
According to snapshots shown in Fig. 5, sea surface disturbance generated by the oceanic
Rayleigh waves passes the stations TM1 and TM2 before 50seconds, from which the high
frequency components in the original pressure records in Fig. 4(a) and (b) are found to be
associated with seismic waves such as the oceanic Rayleigh waves.
4. The 1983 Nihonkai-chubu Earthquake Tsunami
The Nihonkai-chubu earthquake (M7.7) occurred on May 26, 1983. Among many fault
models, Sato’s model [5] estimated from seismic data is used in the present simulation, in
an attempt to reduce the difference between fault models from tsunami data and those from
seismic data. As shown in Fig. 6 and Table 3, the fault model consists of three sub-faults.
The first fault rupture supposedly started at the south tip of the southern sub-fault,
propagating in NE direction at 3km/s. After 10seconds interval, the second fault rupture
developed on the central sub-fault at 2km/s in NE direction, and finally the third rupture
propagated on the northern sub-fault in NNW direction at 1.5km/s, with the total rupture
time of 63sec, as shown in Figs. 7 and 8. From snapshots shown in Fig. 9, apparently the
patterns of the sea surface disturbance including tsunamis are somewhat different from that
simulated by the conventional (static) technique, especially in the near-fault area during
some time immediately after the fault rupturing. Because of the difference, to the author’s
belief, the present technique will help us to characterize near-field tsunamis with accuracy,
and to reduce the difference between fault models from tsunami data and those from
seismic data.
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43°
N
42°
N
41°
×
C
×
S
360km
×
40°
39°
240km
J apan Sea
38°
50km
37°
136°
137°
138°
139°
140°
141°
142°
Figure 6. Projection of the fault planes projections and calculation area of the 1983
Nihonkai-chubu earthquake tsunami.
Elapsed Time (sec)
80
N
60
C
40
20
0
0
S
20
40
60
80
Distance (km)
Figure 7. Relation between elapsed time and rupture distance.
100
120
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TABLE 2. Fault parameters of the 1983 Nihonkai-chubu earthquake.
South
･
Seismic moment (dyne/cm)
3×10
Central
27
2×10
27
North
3×10
Length (km)
35
35
35
Width (km)
35
35
35
Depth(km)
0
0
0
Strike (degree)
15
15
345
Dip (degree)
20
20
20
Rake (degree)
90
90
90
Dislocation(m)
6.8
4.6
6.8
Rupture velocity(km/sec)
2.0
2.0
3.0
Rise time(sec)
3.5
3.5
3.0
Rupture Velocity (km/s)
3
2
S
C
N
1
0
0
20
40
60
80
Distance (km)
Figure 8. Relation between rupture velocity and rupture distance.
100
120
27
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Figure 9. Three dimensional tsunami simulation about the 1983 Nihonkai-chubu earthquake
tsunami.
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5. Conclusions
A series of dynamic simulation of tsunami were conducted, taking into account the
effects of dynamic seabed displacement caused by seismic faulting and acoustic waves of
the seawater. Although there are several points to be improved in the present dynamic
simulation technique, findings drawn from the present study are the followings;
1. In comparison with the seismically induced static seabed displacement, the dynamic
seabed displacement makes a remarkable contribution to increase water wave height,
especially in the near-fault area.
2. The increase is mainly due to superposition of two types of water waves. One is the
tsunami that travels as a long wave, and the other is the oceanic Rayleigh wave that travels
much faster than the tsunami.
3. In the far-field, there is little difference between the wave height from dynamic
simulation and that from static simulations.
4. From case studies on the 1983 Nihonkai-chubu Earthquake tsunami and the 1989
Sanriku-oki Earthquake tsunami, the present technique has proved the validity of the
simulation results and advantage over the conventional techniques.
Acknowledgements
The author is grateful to Dr. H. Tsukiyama, Tsukiyama Research Inc., and Dr. H.
Matsumoto, Japan Marine Science and Technology Center, for their collaboration in the
present study.
References
1. Ohmachi, T., Tsukiyama, H, and Matsumoto, H. (2001): Simulation of Tsunami Induced by Dynamic
Displacement of Seabed due to Seismic Faulting, Bulletin of the Seismological Society of America, 91, 6, pp.
1898-1909.
2. Aida, I. (1984): A Source Model of the Tsunami Accompanying the 1983 Nihonkai-Chubu Earthquake, Bull. Res.
Inst., Vol. 59, pp. 93-104. (in Japanese)
3. Courant, R., K. O. Friendrichs, and H. Lewy (1967): On the partial difference equations of mathematical
physics, IBMJ Res. Dev., Vol. 11, pp. 215-234.
4. Hino, R., Tanioka, Y., Kanazawa, T., Sakai, S. and Nishino M. (2001): Micro-tsunami from a local interplate
earthquake detected by cabled offshore tsunami observation in northeastern Japan, Geophysical Research
Letters, Vol. 28, No. 18, pp.3533-3536, September 15..
5. Sato, T. (1985): Rupture Characterisitics of the 1983 Nihonkai-chubu (Japan sea) Earthquake as Inferred from
Strong Motion Accelerograms, Journal of Physics of the Earth, Vol. 33, pp.525-557.
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