弹性波逆散射微扰论

本文将普遍声逆散射微扰论应用于弹性波层析成像问题，在Born变换下推出了以旋转角为补偿参数的各阶微扰重建公式，实现了对非均匀各向同性散射体内3个参数（质量密度ρ和两个Lamé系数λ，μ）的同时重建. 对于层析成像问题，在弹性波的传播过程中P波与SV波有耦合，但它们不会和SH波发生耦合，于是可以得到3个形式相对简单的标量方程. 在Born变换下，在散射波中引入微扰参数，将散射体的3个参数分别按该微扰参数展开，然后利用二维自由空间的Green函数分别得到散射的P波、SV波和SH波的积分表示. 最后，经一维傅氏变换后，得到Born变换下散射体3个参数的各阶微扰重建公式.

Elastic wave inverse scattering perturbation theory

This paper presents an elastic wave inverse scattering perturbation theory with an isotropic inhomogeneous circular cylinder as scatterer and a monochromatic plane P，SV，or SH wave perpendicular to the cylinder, as incident wave. The mass density and two Lam coefficients, which vary only along a plan perpendicular to the cylinder, are imaged through three separate experiments. The complicated elastic vector wave equation can be reduced to three scalar wave equations, in which only the P and the SV waves are coupled. And then the two_dimensional free space Green function is employed to transform them into the Lippmann_Schwinger integral equations. Introducing a perturbation parameter into the scattered waves and setting expansion of all three imaging parameters in series of the perturbation parameter, the first_ and high_order perturbation approximation algorithms under Born transform are obtained.