Inverse problem of magnetometric resistivity response from exponentially varying conductive ground

Abstract

Abstract Magnetometric resistivity is an electromagnetic exploration method that has been used successfully to investigate electrical conductivity structures within the earth. We derive an analytical solution of the steady state magnetic field due to a direct current semi-infinite source on a multilayered earth with a layer having exponentially varying conductivity. Our variation in conductivity is realistic and can be generalized to all cases of exponential profiles. The Hankel transform is introduced to our problem and analytical result is obtained. Our solution is achieved by solving a boundary value problem in the wave number domain and then transforming the solution back to the spatial domain. An inverse problem via the use of the Levenberg-Marquardt optimization technique is introduced for finding the conductivity parameters of the ground. The optimal result of our model is close to the true value with percentage errors of our two conductivity parameters less than 2.6% and 3.6% after using only 3 iterations.