Analytical solution of magnetic field from a DC source buried in a conductive layered space

Abstract

An analytical solution of the steady state magnetic field due to a direct current source is derived for the problem of a buried current source and a buried receiver. The model is developed for source and receiver electrodes arbitrarily located in a horizontally stratified layered earth. The generalized Hankel transform is introduced to our problem and analytical result is obtained. Our solution is achieved by solving a boundary value problem in the wavenumber 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 method leads to very good result and has high speed of convergence.