波动方程的逆散射与迭代线性化反演

Inverse scattering of wave equation and iterative linearized inversion

地矿部物化探研究所, 廊坊102849

Institute of Geophysical and Geochemical Exploration, MGMR, Langfang 102849

本文讨论的是非线性地球物理反演中目前最重要的方法．即逆散射与线性化这代算法相结合而形成的解析类反演方法。首先应用标量波动方程的逆散射理论推导出反射波场与波慢平方扰动之间满足的非线性积分方程, 并阐明波慢平方扰动与反射体之间的关系。然后介绍迭代线性化反演算法的理论和具体计算公式, 并专门对泛函求导的公式进行详细的推导。最后, 讨论了这一类反演方法的计算技术及参数选择问题。

The inverse scattering and the iterativc lincarized int-ersion are comblned into an analytic-typeof inversion method which is now the most important in geophysical nonlinear inversions' In thispaper, the inverse scattering theoty of scalar waxi equation is used to derivc the nonlinear integralequation satisfied with both the reflection wave field and the square slowness disturbance, therclationship betwecn the square slowncss disturbances and the reflectors is clearly described.Then. the theory and formula of the iterative lincarized inrersion algorithm are given. with theformula for functional deritution being deduccd in detail. Finally. the computational techniques andparameter selection are discussed in this kind of inversion methods.