General elastic wave scattering problems using an impedance operator approach - I. Mathematical development

Abstract

General 3-D anisotropic wave scattering problems can be solved by using an impedance operator to decompose the wavefield by direction of energy flow. This decomposition exists and is well-defined for all wavefields. The impedance operator recasts the boundary value problem of the classical wave equation as two initial value problems: a Riccati equation for the impedance operator and a one-way wave equation for the particle velocity, each of which can be solved to high precision. A curvilinear coordinate transform ensures that the method is formulated entirely in terms of continuous wavefield variables and allows for a natural treatment of any form of topography. © 2004 RAS.