Computer synthesis of acoustic wave fields in laminated and fractured media

Abstract

Frequency‐wavenumber integration is used to compute time‐domain sonic waveforms at any point in a stratified medium. The source is either a point force, or a point dislocation, at any depth. The medium consists of welded homogeneous layers with all 21 elastic constants varying independently from layer to layer. Currently, a free‐surface boundary condition at the top of the medium and a radiation condition at the bottom is used, but these boundary conditions can be easily changed. Although final results are in the time domain, the basic calculations are carried out in the frequency domain so anelastic effects are incorporated by use of complex elastic constants. (Usually, instead of directly specifying the elastic constants in each layer, Schoenberg algorithms were used to “fracture” a layer or to “construct” a layer from many thin microlayers of simpler material. These algorithms have a group property [Schoenberg and Muir, 1988] which makes it easy to generate fractured laminates.) For elastic materials with azimuthal anisotropy, two wavenumber integrations are required. If the medium is many wavelengths thick, and the source and receiver(s) are many wavelengths apart, then several hours of Cray CPU time are needed to generate a complete response. [Work supported by Geo‐Pacific Corporation.]