Uncertainty in tsunami wave heights and arrival times caused by the rupture velocity in the strike direction of large earthquakes

In tsunami risk assessments, understanding the uncertainties involved in numerical simulations of tsunami wave heights and arrival times is important. However, few studies have been conducted to determine the effects of dynamic parameters (i.e., rupture velocity and rise time) in the simulation of tsunami wave heights and arrival times, although numerous studies have been conducted on the uncertainties that result from static parameters (i.e., top depth, strike, dip, rake, and fault slip). In this study, we calculated the variability in tsunami wave heights and their arrival times as a result of the uncertainties in the along-strike rupture velocity of faults. Specifically, numerical simulations of tsunamis were conducted with various rupture velocities and starting points within a large fault. The numerical analyses considered hypothetical bathymetry and dynamic effects and indicated that the uncertainties in the maximum wave height and its arrival time are greater as the water depth increases. The number of sub-faults affected the wave heights and suggested that we should consider these effects in numerical simulations of tsunamis. The results of the numerical analyses using the actual bathymetry of the Tohoku region in Japan showed that the spatial uncertainty in the maximum wave height at a 50 m depth had a 0.04 log-normal standard deviation based on a distribution of ratios between the calculated wave heights from numerical simulations with and without considering dynamic effects. The results of this study are practical for probabilistic tsunami hazard assessments for which we must evaluate the quantitative value of the spatial uncertainty in wave heights. This study is a basis for similar research in terms of offering a technique for evaluating wave height uncertainty due to the rupture velocity.