A method for reconstructing the electrical conductivity profile of a contrasting object in an embedding medium is applied to the problem of induction logging as it is known in the oil industry. The conductivity of the formation and the unknown electromagnetic fields are simultaneously reconstructed in an iterative way using a conjugate gradient type of algorithm. In the algorithm it is assumed that the conductivity is a positive quantity. This fact, together with the knowledge that the contrasting domain is constrained in some test domain, constitutes the only a priori information about the configuration that is needed. Results of a number of numerical examples are presented which demonstrate the robustness of the present inversion scheme and show that an artificial regularization technique is not needed.