Scattering theory for the elastic surface waves

本文研究的问题是：在弹性介质边界上传播的表面波是否可以用散射理论来处理。本文对适用于分析表面波的数学散射理论的公式问题，得到了如下结果：（1）可以构造Lax和菲利普斯型散射理论的公式;（2）可以发现体波散射理论与表面波散射理论的区别;（3）对于双曲问题的散射理论公式，已知有两种不同的类型（Wilcox型和Lax-Phillips型）。我们可以用一个抽象的框架来证明这两种类型是等价的，从这些结果中我们可以比较研究中得到的散射理论和以前的散射理论，我们接下来要关心的是澄清散射表面波的性质。为此，我们得到了下列结果：（4）对于在平坦边界上传播的表面波，表面波的能量如何传播;（5）扰动边界上驻波的低频分析这些结果可望为进一步研究表面波的性质奠定基础

The subject of the research is to clarify whether the surface waves propagating on boundaries of elastic medium can be regarded in the framework of the scattering theory or not. We obtain the following results on the problems about formulations of mathematical scattering theory suitable to analyzing the surface waves(1) We can construct a formulation of the scattering theory of Lax and Phillips type(2) We can find the diffences of scattering phenomena between the one for body waves and the one for surface waves(3) For formulations of scattering theories with respect to hyprebolic problems, it was known that there were two differnt types (Wilcox type and Lax-Phillips type). We can show that those two types are equivalent each other using an abstract frameworkFrom those results we can compair the scatteing theories obtained in the research and the previous onesOur next concern is to clarify the properties of the scattered surface waves. For the purpose, we obtain the following results(4) For surface waves propagating on the flat boundaries, How energies of them propagate(5) A low frequency analysis of stationary waves on perturbed boundaryThese results are expected to a basis on the further study of the properties of the surface waves