介质参数反演的广义射线近似方法

GENERALIZED RAY APPROXIMATE METHOD TO INVERSE MEDIA PARAMETERS

在对无粘性介质参数反演问题进行的研究中，引入一种全波场广义射线近似形式，提出一种新的反演参数的方法．文中，首先对由弹性波动方程演变成的声波方程进行分析，引入背景场量和扰动量，并结合Ｇｒｅｅｎ函数理论，得到了介质参数的积分方程；然后结合前人对非均匀介质中波函数局部理论的定性分析，引入一种全波场广义射线近似形式，把问题归结为一个第一类Ｆｒｅｄｈｏｌｍ积分方程；最后对半空间问题层状介质模型进行了反演．算例结果表明，当介质参数扰动比近于０．５时，此方法也能有效地反演其变化规律，明显优于传统的Ｂｏｒｎ弱散射近似方法的反演结果．

In this paper,the inverse problem of the media parameters in inhomogeneous media is studied,and a generalized ray approximate form of toeal wave field is introduced.First the acoustic wave equation derived from the elastic wave equation is studied,and the reference and perturbance values is introduced,and the integral equation of the media perturbance parameters is obtained.Then from the point of view of the local principle of wave function in inhomogeneous media,a generalized ray approximate form of toeal wave field in inhomogeneous media is introduced,and the inverse problem is concentrated on the Fredholm integral equation of the first kind.Finally,the media parameters in half-plane is inversed.Numerical examples show when the media parameter perturbances are about 0.5,this method can effectively inverse its varistion.Apparently,thismethod is prior to the conventional Born weak scattering approximation.