Modified Kadomtsev–Petviashvili equation for tsunami over irregular seabed

Abstract

We derive an asymptotic equation governing the trans-ocean propagation of tsunami from source to the continental shelf. Focus is on disturbances originated from a slender fault of finite length. The variable sea depth is assumed to consist of a slowly varying mean and random fluctuations. The method of multiple scales is used to derive a Kadomtsev–Petviashvili equation with variable coefficients. Modifications by one- and two-dimensional random irregularities are shown to affect the wave speed, dissipation and additional dispersion. The result can be used to facilitate physical insight with modest numerical efforts.