Wataru Hirasawa

Generation and propagation of tsunami initial waveforms dependent on seabed topography changes

Tokuzo Hosoyamada

Japan has been subject to numerous earthquake and tsunami disasters, and the 2011 Tohoku earthquake and tsunami raised significant social concern regarding tsunamis. Tsunami causes include earthquakes, volcanic activity, and landslides. Current tsunami numerical calculations often predict vertical seabed displacement caused by earthquakes using fault models, which is then applied directly as vertical displacement at the ocean surface. However, horizontal movement of the water mass, including divergence and convergence, should mitigate the vertical displacement of the sea surface, and considering horizontal water movement is more realistic for modeling actual phenomena.This study organizes the concept of evaluating lateral water movement based on the time variation of vertical seabed displacement. It investigates the changes in initial tsunami waveforms and their propagation characteristics in response to different seabed topography changes, as well as the validity and adaptability of the calculation method. 
The tsunami wave generation method used in this study is derived from the nonlinear long-wave equation for incompressible fluid flow.To verify the validity of this method, the research by Kakinuma et al. was used as a benchmark. Kakinuma et al. conducted analyses and experiments focusing on water surface fluctuations using the Volume of Fluid (VOF) method. Time-series waveforms were verified by comparing the water surface response to seabed displacement at three deformation velocities, confirming sufficient accuracy. When the results from this method were compared to Kakinuma’s results, they were found to be consistent for all three deformation velocities, confirming the validity of the method.
Following validation, the study tested water surface fluctuations for 11 different seabed deformation cases. All results were confirmed through videos, and comparisons between static and dynamic analyses showed that initial waveforms and propagation processes had higher water levels in the static case. Additionally, tsunami arrival times were faster in the static case compared to the dynamic case. Comparing results across the 11 cases revealed that for seabed topography with strong unidirectional uplift or subsidence, water levels were lower compared to other topographies. Furthermore, for topography with strong uplift or subsidence on the right (landward) side, tsunami arrival times were shorter than for other cases.
This study suggests that static analysis may overestimate tsunami impacts compared to dynamic analysis. The calculation method used in this study is capable of handling various initial and seabed conditions.