Computation of wave fields in inhomogeneous media -- Gaussian beam approach

TLDR

An asymptotic procedure for computing wave fields in two‑dimensional laterally inhomogeneous media is proposed. The method simulates the wave field with a system of Gaussian beams, propagating each beam independently through arbitrary inhomogeneities and reconstructing the field at a receiver by integrating the beams in its vicinity. The resulting integral formula remains valid even in singular regions where the ray method fails, such as caustics and critical points, and numerical examples confirm its effectiveness.

Abstract

An asymptotic procedure for the computation of wave fields in two-dimensional laterally inhomogeneous media is proposed. It is based on the simulation of the wave field by a system of Gaussian beams. Each beam is continued independently through an arbitrary inhomogeneous structure. The complete wave field at a receiver is then obtained as an integral superposition of all Gaussian beams arriving in some neighbourhood of the receiver. The corresponding integral formula is valid even in various singular regions where the ray method fails (the vicinity of caustic, critical point, etc.). Numerical examples are given.