横观各向同性介质中弹性波的吸收边界条件

ABSORBING BOUNDAEY CONDITIONS FOR ELASTIC WAVES IN TRANSVERSELY ISOTROPIC MEDIA

在数值求解固体中的弹性波动问题时，常需引入吸收边界条件来限制大范围或无边界的求解区域，使数值计算得以顺利进行．本文通过合成简单的一阶偏微分算子，给出了横观各向同性介质中弹性波的吸收边界条件，其中每个单一的算子均可完全吸收沿某一角度出射的平面波．文中还基于弹性波的势函数理论，导出了准Ｐ波和准Ｓ波在吸收边界处的反射系数公式，用以检验其吸收能力．本文所给出的吸收条件，形式简单，且算例表明吸收效果良好，因而有推向实用的价值．

In the numerical simulating of elastic wave propagation in solid, it is often essential to introduce absorbing boundary conditions to limit the large or unbounded domain so that a numerical computation of solution is feasible. In this peper, the absorbing boundaries for transversely isotropic media are constructed by the composition of simple first-order partial differential operators, and each of the operators might perfectly absorb a plane wave outgoing at a certain angle. To test the absorbing ability, the formulas of reflected coefficient for quasi-P and quasiS wave on the absorbing boundaries arc derived based on the potential functions theory of elastic wave. The form of absorbing conditions given in this peper is simple, and the absorbing effect demonstrated by numerical examples is good. Therefore, it has practical prospects.