The profile of a two-dimensional axi-symmetric inhomogeneous medium is reconstructed by using the distorted Born iterative method and multi-grid technique.

A number of effective procedures for improving the distorted Born iterative method are proposed, including the accurate and efficient solution of the direct problem, second-difference regularization, weighted least-squares solution, estimation of the initial guess by using a priori information and multiple-frequency scheme.

A novel inverse iteration method, variational Born iteration method (VBIM), for the inversion and reconstruction of two-dimensional axisymmetic inhomogeneous media is described in this paper.

In this paper we present a new iteration method,namely,the variational Born iteration method (VBIM) to inverse the formation conductivity using measurement data from the array induction tool (AIT).