2011/02/19 by Elie Bretin, Abdul Wahab, Bretin, Elie +1
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.AP #math.MP
paper · pdf · doi:10.48550/arxiv.1102.4017
arxiv created 2011/02/19 · arxiv updated 2011/02/23
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 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.