Criteria for discretization of seafloor bathymetry when using a stairstep approximation: Application to computation of T-phase seismograms

Acoustic solutions for numerical models in which an overly coarse discretization of a stairstep boundary is employed to simulate smoothly varying bathymetry are degraded in a way that simulates scattering. Geometrical optics approximations are used to derive discretization criteria for simulating a smoothly sloping interface for the case of a source embedded in either an acoustic or an elastic seafloor, and applied to modeling T-phases. A finite difference time-domain modeling approach is used to synthesize T-phases for both smoothly sloping and rough seafloor boundaries. It is shown that scattering at a rough seafloor boundary yields ocean-borne acoustic phases with velocities near those of observed T-phase, while smooth seafloor models yield T-phases with slower horizontal velocities. The long duration of the computed T-phases for both the rough acoustic and elastic models is consistent with energy being scattered into the sound channel both as it transits the ocean/crust boundary, as well as at several subsequent seafloor reflections. However, comparison between the elastic and acoustic modeling solutions indicates that the T-phase wavetrain duration decreases with decreasing impedence contrast between the ocean and seafloor.