半空间SH波方程非线性井间双参数反演

The Nonlinear CBP Inversion of Two parameter with SH Elastic Wave In Half space

以半空间的ＳＨ波方程出发，采用Ｂｏｒｎ迭代法求解半空间弹性介质中密度和剪切模量分布的非线性反演问题。首先，采用矩量法和正则化方法，给出井间反演积分方程的离散形式，然后应用Ｂｏｒｎ迭代法求解非线性反演问题。数值模拟计算表明，提出算法有较好的收敛性和反演精度。

In this paper, a Born iterative method is presented to solve the nonlinear inversion of SH wave equation in half space for the density and shear modulus configurations. First, the moment method is used to discrete the integral equation. Then in order to find an adequate solution of inverse problem, the regularization procedure is employed to circumvent the instability of the problem. In regulaization procedure, instead of solving the ill posed matrix equation directly, we can solve an optimization problem which minimizes the cost function. Last, we proposed a Born iterative method for solving the nonlinear problem. The numerical results for various cases show good accuracy and stability. The solution of nonlinear multiparameter inversion is quite effective.