2015 volcanic tsunami earthquake near Torishima Island: Ray tracing analysis of dispersive tsunami wave

An abnormal volcanic earthquake occurred at the Smith caldera, a submarine volcano along the Izu-Bonin arc. The earthquake has a CLVD-type focal mechanism and generated larger tsunami waves compared to its magnitude (M5.7), with heights as large as 60 cm at Hachijo Island, 180 km to the north of the epicenter. Therefore the earthquake may be regarded as a "volcanic tsunami earthquake." Tsunami waves were recorded by a dense array of ocean bottom pressure gauges, 100 km to the NNE from the epicenter, with arrival-time delay of high-frequency waves due to the dispersion effect. It is notable that the measured slowness direction of wavefront deviates from the great circle path and varies as a function of frequency. We develop a new ray tracing method considering the dispersion effect. First, we transform 2-D bathymetry data into frequency-dependent velocity data using a recursive algorithm to solve iteratively the formula of dispersion relation of the linear gravity wave. Then ray paths with different frequencies are traced on the frequency-dependent velocity fields by integrating ray equations for seismic surface waves. Ray paths and travel times significantly depend on its frequency due to the dispersion effect. In particular, lower-frequency waves are more affected by large-scale bathymetric changes, while higher-frequency waves are less affected. Simulated slowness direction and arrival time at the array change as a function of frequency, which is consistent with our observations. By minimizing the misfit between observation and simulation, the tsunami source can be constrained within the Smith caldera with a diameter of about 10 km. Thus, our ray tracing method including the dispersion effect allows us to examine different ray paths depending on frequency and to constrain a tsunami source location from limited azimuthal coverage of observations.