EXPLICIT ASYMPTOTICS FOR TSUNAMI WAVES IN FRAMEWORK OF THE PISTON MODEL

Abstract

An asymptotically numerical description of tsunami waves propagation in a basin with non-uniform depth in a neighborhood of wavefronts that can have caustics is proposed. The piston model and the long wave approximation are used. It is assumed that the size of the area of the initial disturbance is small in comparison both with the characteristic length of interval of the varying of the bottom depth and the distance from the observation point. The description is based on a generalization of asymptotic approach known as the Maslov canonical operator. We find formulas that are relatively simple and can be transformed in a computer program for fast calculating wave profiles. Some features of the tsunami waves propagation in basins of non-uniform depth are illustrated by graphics.