Some Anisotropic Viscoelastic Green Functions

TL;DR

This paper derives explicit elastodynamic Green functions for three types of anisotropic viscoelastic media using spectral decomposition, simplifying the problem to scalar wave equations with viscosity modeled by a power law.

Contribution

It provides closed-form expressions for Green functions in anisotropic viscoelastic media, extending previous work by incorporating empirical viscosity models.

Findings

Closed-form Green functions for three anisotropic viscoelastic media.

Reduction of the problem to scalar wave equations with viscosity effects.

Application of a power law model to describe viscoelastic behavior.

Abstract

In this paper, we compute the closed form expressions of elastody- namic Green functions for three different viscoelastic media with simple type of anisotropy. We follow Burridge et al. [Proc. Royal Soc. of London. 440(1910): (1993)] to express unknown Green function in terms of three scalar functions $\phi_i$, by using the spectral decomposition of the Christoffel tensor associated with the medium. The problem of computing Green function is, thus reduced to the resolution of three scalar wave equations satisfied by $\phi_i$, and subsequent equations with $\phi_i$ as source terms. To describe viscosity effects, we choose an empirical power law model which becomes well known Voigt model for quadratic frequency losses.