The Distorted Born Iterative Method（DBIM） is applied to deal with the nonlinear inversionproblem of the conductivity distribution in a two-dimensional axisymmetric medium. It is well known that the inversion of such transverse magnetic（TM） measurements is much more nonlinear than that Of transverse electric（TE） measurements. Tikhonov’s regUlarization method is used tO overcome ill-condition feature Of the mathe equation resulted from discretizing the nonlinear interal eqUation. Then the conjugate-gradient（CG） method isused to solve the matrix equation. In each iteration of foe DBIM

an efficient half analytical-half numericalmethod is used to solve the forward problem. This method provides a semianalytic expression for the Green’sfunction and its partial derivatives required in the inversion

and then deduces a semianalytic expression of theintegration in the nonlinear integral equation. Therefore

the efficiency and accuracy are improved dramatically.