非均匀介质中弹性波动方程的参数摄动法

本文通过对非均匀介质弹性波动方程中的介质参数引入背景场量和摄动量，得到以摄动项为次生源的均匀介质中的波动方程，利用Green函数理论化微分方程为积分方程；然后把均匀介质中的位移波场做为第一次迭代结果，代入积分方程进行位移波场的求解；当扰动量达50%时，此方法仍然有效，分析数值结果，从而对一般非均匀介质中的波场性质有了一个定性了解，结果与一般非均匀介质中的声波局部理论基本一致．

The Parameter Perturbation Method on Elastic Wave Equation in inhomogeneous Medium

In this paper, the medium parameters of the elastic wave equation in inhomogeneous medium are rewritten by introducing the referential Yariables and the perturbational variables, and the wave squation whose sources are the medium paremeter perturbatioal term in homogeneous medium is obtained. By using the Green function theory, the integral equation of the pertrubational parameters is obtained. Then the displacement field in homogeneous medium is considered the result of the first iteration,and the displacement field is solved by this integral equation. When the perturbations of medium parameters are about 50 percent, this method can solve the displacement field effectively. From the analysis of the numerical resultes, the characteristics of ways field in inhomogeneous medium are obtained. The results conform with the local principles of wave function in inhomogeneous medium.