89 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 90 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. 91 Figure 2. 2D tsunami simulation by the present technique. 92 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. 93 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) 94 Figure 5. 3D tsunami simulation of the 1998 Sanriku-oki, Japan earthquake tsunami. 95 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. 96 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 97 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 98 Figure 9. Three dimensional tsunami simulation about the 1983 Nihonkai-chubu earthquake tsunami. 99 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. 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