Wave propagation simulation in a linear viscoelastic medium

Abstract

A new formulation for wave propagation in an anelastic medium is developed. The phenomenological theory of linear viscoelasticity provides the basis for describing the attenuation and dispersion of seismic waves. The concept of a spectrum of relaxation mechanisms represents a convenient description of the constitutive relation of linear viscoelastic solids; however, Boltzmann's superposition principle does not have a straightforward implementation in time-domain wave propagation methods. This problem is avoided by the introduction of memory variables which circumvent the convolutional relation between stress and strain. The formulae governing wave propagation are recast as a first-order differential equation in time, in the vector represented by the displacements and memory variables. The problem is solved numerically and tested against the solution of wave propagation in a homogeneous viscoelastic medium, obtained by using the correspondence principle.