Some Anisotropic Viscoelastic Green Functions

Details Some Anisotropic Viscoelastic Green Functions Some Anisotropic Viscoelastic Green Functions

2011-02-19

arxiv.org/abs/1102.4017v1

Mathematics

Analysis of PDEs

Scientific paper

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.

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