轴对称二维非均匀介质的快速反演方法

首先采用变分原理和非线性积分方程推导出反演方程，然后利用玻恩迭代法对轴对称二维非均匀介质分布进行了反演。通过计算实例表明，该方法的收敛速度比玻恩迭代法快得多，在迭代前期与变形玻恩迭代法相当，而在迭代后期比变形玻恩迭代法的收敛速度更快；同时，每次迭代所需时间虽然多于玻恩迭代法，但明显少于变形玻恩迭代法。该方法同时具备了玻恩和变形玻恩迭代法两者的优点。

An Efficient Inversion Method of Two-dimensional Axisymmetric Inhomogeneous Medium

In this paper, inversion equation is derived by the variation principle and nonlinear integral equation, then the Born Iterative Method (BIM) is applied to deal with the nonlinear inversion problem of the conductivity distribution in a two-dimensional axisymmetric medium. The numerical analysis is made to compare the method in this paper with the BIM and the Distorted Born Iterative Method (DBIM). It shows that the speed of the solution convergence of the method in this paper is faster than that of the BIM, and in the later iteration also faster than that of the DBIM. The computational time in each iteration is less than that of the DBIM apparently.