某些各向异性粘弹性格林函数
Some Anisotropic Viscoelastic Green Functions
摘要：
本文计算了三种简单各向异性粘弹性介质的弹性动力学格林函数的封闭形式表达式。我们遵循Burridge等人[Proc. Royal Soc. of London. 440（1910）：（1993）]利用与介质有关的Christoffel张量的谱分解，将未知格林函数表示为三个标量函数$ϕ_i$。格林函数的计算问题归结为求解$ϕ_i$所满足的三个标量波动方程以及以$ϕ_i$为源项的后续方程。为了描述粘性效应，我们选择了经验幂律模型，该模型成为众所周知的二次频率损耗的Voigt模型。
英文摘要：
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 $ϕ_i$, 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 $ϕ_i$, and subsequent equations with $ϕ_i$ 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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