Time-domain pressure and surface wave propagation over generic topography due to sea floor motion

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Abstract
The surface-gravity wave evolution, imitating tsunamis triggered by the ocean floor’s arbitrary temporal motion over a generic seafloor topography, is investigated using the linearised water-wave theory of a compressible ocean. The pressure wave bounce between the water surface and ocean floor, followed by the generation of acoustic-gravity wave (AGW) propagation away from the initial disturbance, is shown with unprecedented details. The computational novelty covers accurate pressure-wave-field computation using high-frequency AGW modes, unlike the dominant first AGW in surface waves. The mathematical problem is solved using the Fourier transformation and eigenfunction expansion techniques, following a multistep approximation of the arbitrarily deep sea. Test cases of two idealistic subsurface geometries (continental shelf and mountain range) using the ocean floor’s linear and parabolic temporal growth show elongation and shortening of the surface wavelength and changes in the propagation speed due to the variable seafloor topography through simulations. The mutual interaction of the pressure waves within the water column unravels depth-change-induced scattering. While high-frequency pressure at a shallower depth is dominant for the continental shelf, a significantly reduced amplitude across a mountain ridge is visualised with a corresponding lower impact of the acoustic-gravity wave on the surface wave. Substantial contrast in the pressure wave field triggered by a slight change in the rupture’s properties suggests its careful consideration when building tsunami prediction models. Since these AGWs are precursors to tsunamis, we believe their detection through an accurate pressure measurement will give very important information about the associated tsunami wave.

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