Some Anisotropic Viscoelastic Green Functions

In this paper, we compute the closed form expressions of elastodynamic 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 φi, 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 φi, and subsequent equations with φi as source terms. To describe viscosity effects, we choose an empirical power law model which becomes well known Voigt model for quadratic frequency losses.