曲线坐标在弹性波散射研究中的应用──SH波对不等深度凹陷地形的散射

APPLICATIONS OF CURVILINEAR COORDINATES TO SCATTERING OF ELASTIC WAVES──SCATTERING OF SH-WAVES BY CANYONS WITH VARIABLE DEPTH-TO-WIDTH RATIO

本文利用曲线坐标的分析方法研究ＳＨ波对凹陷地形散射的边值问题。首先给出了在曲线坐标系中波动方程解的逼近函数序列，并使此解满足由曲线坐标所描述的具有不同深度的凹陷地形上的边界条件，最后将待解的问题归结为对一组无穷代数方程组的求解．本文提供的方法有如下的特点：（１）可将通常求解凹陷地形对ＳＨ波散射的波动方程的混合边值问题（指在不同边界区域上给出不同的应力分量的边界条件）化为一应力边值问题；（２）本文所使用的曲线坐标，可描述具有不同深度与宽度比的拟半圆形凹陷地形散射问题，并给出一般解；（３）本文方法可推广用于求解Ｐ（－ＳＶ）波对凹陷地形的散射问题。作为算例，本文给出了ＳＨ波对具有不同深度与宽度比的凹陷地形散射的数值结果，并进行了分析比较。

he scattering of plane SH-waves by canyon topography with variable depth-to-width ratio is studied by means of curvilinear coordinates method in this paper. The complete function series of solution of wave propagation equation in curvilinear coordinates is firstly made out by using complex function method. Then the series solution is forced to satisfy the boundary conditions on the conyons with variable depth-to-width ratio described by the curvilinear coordinate. Finally, the problem to be solved is translated into the solution of a set of infinite algebraic equations. As examples, the computational results of scattering of SH-waves by different canyons are given, and part of the results are compared with anylitic results.There are some distinguished features in this paper: (1) In the solving of scattering of SH-waves by canyon topography, the mixed boundary model, which means that there are boundary conditions of different stress components in different areas, is reasonably simplified as a unitary boundary model. (2) The curvilinear coordinates used in this paper can describe canyons with variable depth-to-width ratio, and the scattering solution in general use is given. (3) The method used in this paper can be extended to solve the scattering of P(-SV)- waves by canyons with variable depth-to-width ratio.