弹性波慢度表面的计算

由声场本构方程导出速度场的波动方程，令本征矩阵的行列式为零，得到含参量的三次方程。弹性波慢度的计算涉及到张量运算、矩阵运算、公式化简等。对于一般的各向异性媒质，方程有三个互不相等的特征根：一个准纵波和两个准横波；对于各项同性媒质，方程有两个互不相等的特征根，其中一个为重根：一个纵波和一个横波。该文给出了弹性波慢度归一化后的空间分布图形。

Computation of Acoustic Wave's Slowness Surface

The problem of acoustic wave＇ s slowness surface is derived from the acoustic waves equation, parametric triple equation whose roots are characteristic slowness numbers is obtained after setting the determinant of eigen - matrix to zero. Acoustic wave＇ s slowness is involved with the calculations of the tensor computing, matrix opera- tions, formulaic simplification and so on. The general anisotropic media, there are three different characteristic roots in the equation： a prospective longitudinal wave and two prospective horizontal waves; to the isotropic media, there are two different characteristic roots, one of them is a same root： a longitudinal wave and a horizontal wave. In order to make the abstract concept more intuitive, give the acoustic wave＇ s slowness return of the spatial distribution of graphics.