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本文将变形玻恩迭代方法用于处理轴对称二维非均匀介质分布的电导率反演问题众所周知，横磁场的反演比横电场的反演的非线性程度更高．本文选用了收敛速度快而效果好的变形波恩迭代反演方法．而离散非线性积分方程所得矩阵方程的病态特性用古洪诺夫正则化方法来克服，再用共轭梯度方法求解在每次选代过程中采用了快速的半解析半数值的高效正演方法，本文用它半解析地表达出反演中所需计算的格林函数的偏导数；并在此基础上半解析地求出了反演的非线性积分方程中的积分运算，从而大大提高了反演速度和精度
In this paper, the modified Born iteration method is used to deal with the inversion problem of axial symmetric two-dimensional inhomogeneous medium distribution. It is well known that the inversion of transverse magnetic field is more nonlinear than the inversion of transverse electric field. In this paper, the modified Bonn iterative inversion method with fast convergence and good effect is selected. However, the ill-posed characteristics of the matrix equation obtained by the discrete nonlinear integral equation are overcome by the method of Gullness Regularization, and then the conjugate gradient method is used to solve the problem of using the fast semi-analytical semi-numerical high-efficient forward method in each iteration In this paper, we use it to semi-analytically express the partial derivative of the Green’s function required for the inversion. On the basis of this, we can obtain the integral operation in the inverse nonlinear integral equation semi-analytically, thus greatly improving the anti- Play speed and accuracy