Wave propagation simulation in a linear viscoacoustic medium

Abstract

A new approach for viscoacoustic wave propagation is developed. The Boltzmann's superposition principle based on the general standard linear solid rheology is implemented in the equation of motion by the introduction of memory variables. This approach replaces the conventional convolutional rheological relation, and thus the complete time history of the material is no longer required, and the equations of motion become a coupled first‐order linear system in time. The propagation in time is done by a direct expansion of the evolution operator by a Chebycheff polynomial series. The resulting method is highly accurate and effects such as the numerical dispersion often encountered in time‐stepping methods are avoided. The numerical algorithm is tested in the problem of wave propagation in a homogeneous viscoacoustic medium. For this purpose the 1‐D and 2‐D viscoacoustic analytical solutions were derived using the correspondence principle. Copyright © 1988, Wiley Blackwell. All rights reserved