Abstract. We derive analytical solutions of the steady state magnetic field due to a direct current source on three types of heterogeneous earth structures whose conductivities vary exponentially, linearly and binomially with depth. The Hankel transform is introduced to our problems and analytical results are obtained. Our solutions are 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 2.5% and 4.3% after using only 9 iterations.

Received: October 9, 2013

AMS Subject Classification: 86A25

Key Words and Phrases: inverse problem, magnetic field, direct current, Hankel transform

Download paper from here.