Minimum Travel-time Path for Tsunamis

Abstract:

We propose a ray tracing method as a solution for a two-point boundary value problem for tsunamis based on the long wave theory. Until this study, only initial value problems (or shooting method) had been discussed in tsunami research.

Our method searches the shortest travel-time path between two given points. In the long wave theory, the tsunami wave velocity is proportional to the square root of water depth. The tsunami wave velocity field is converted by the well-known global bathymetric atlases. Our method computes the minimum travel times starting from each of the two given points and calculates the local ray direction to trace the minimum travel-time ray path. We utilize an explicit, non-iterative tracing scheme that exhibits efficient computation and robust results. Because the method does not rely on an initial ray path, we always obtain the global minimum travel time ray path.

We performed mild slope, steep slope, and diffraction tests and compared to the pseudo-bending method. Our method demonstrates stable results in various complex real bathymetries. The ray path with the minimum travel time is always derived. We also apply our method to real bathymetries. We analyze the tsunami ray paths of specific coasts from different directions. The results exhibit that the tsunami ray paths are significantly influenced by local bathymetry that can provide important tsunami information and be useful for tsunami forecast and hazard mitigation. Our tracing method also provides a new approach for tsunami research.