A Study of the Effects of Seafloor Topography on Tsunami Propagation

For tsunami disaster mitigation, we consider the phenomena related to tsunami in terms of the generation, propagation, and run-up to the coast. With consideration for these three phenomena, we have to consider tsunami propagation to predict the arrival time and the run-up height of tsunami. Numerical simulations of tsunami that propagates from the source location to the coast have been widely used to estimate these important parameters. When a tsunami propagates, however, reflected and scattered waves arrive as later phases of tsunami. These waves are generated by the changes of water depth, and could influence the height estimation, especially in later phases. The maximum height of tsunami could be observed not as the first arrivals but as the later phases, therefore it is necessary to consider the effects of the seafloor topography on tsunami propagation. Since many simulations, however, mainly focus on the prediction of the first arrival times and the initial height of tsunami, it is difficult to simulate the later phases that are important for the tsunami disaster mitigation in the conventional methods. In this study, we investigate the effects of the seafloor topography on tsunami propagation after accommodating a tsunami simulation to the superposition of reflected and refracted waves caused by the smooth changes of water depths. Developing the new numerical code, we consider how the effects of the sea floor topography affect on the tsunami propagation, comparing with the tsunami simulated by the conventional method based on the liner long wave theory. Our simulation employs the three dimensional in-equally spaced grids in finite difference method (FDM) to introduce the real seafloor topography. In the simulation, we import the seafloor topography from the real bathymetry data near the Sendai-Bay, off the northeast Tohoku region, Japan, and simulate the tsunami propagation over the varying seafloor topography there. Comparing with the tsunami simulated by the conventional method based on the liner long wave theory, we found that the amplitudes of tsunamis are different from each other for the two simulations. The degree of the amplification of the height of tsunami in our method is larger than that in the conventional one. The height of the later phases of the tsunamis shows the discrepancy between the two results. We would like to conclude that the real changes of water depth affect the prediction of tsunami propagation and the maximum height. Because of the effects of the seafloor topography, the amplitude of the later phases is sometimes larger than the former ones. Due to the inclusion of such effects by the real topography, we believe our method lead to a higher accuracy of prediction of tsunami later phases, which would be effective for tsunami disaster mitigation.