Mathematical Problems in Engineering
Volume 2004 (2004), Issue 1, Pages 63-77

Direct current electric potential in an anisotropic half-space with vertical contact containing a conductive 3D body

Ping Li and Frank Stagnitti

School of Ecology and Environment, Centre for Applied Dynamical Systems and Environmental Modelling, Deakin University, P.O. Box 423, Warrnambool, Victoria 3280, Australia

Received 17 January 2002

Copyright © 2004 Ping Li and Frank Stagnitti. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Detailed studies of anomalous conductors in otherwise homogeneous media have been modelled. Vertical contacts form common geometries in galvanic studies when describing geological formations with different electrical conductivities on either side. However, previous studies of vertical discontinuities have been mainly concerned with isotropic environments. In this paper, we deal with the effect on the electric potentials, such as mise-à-la-masse anomalies, due to a conductor near a vertical contact between two anisotropic regions. We also demonstrate the interactive effects when the conductive body is placed across the vertical contact. This problem is normally very difficult to solve by the traditional numerical methods. The integral equations for the electric potential in anisotropic half-spaces are established. Green's function is obtained using the reflection and transmission image method in which five images are needed to fit the boundary conditions on the vertical interface and the air-earth surface. The effects of the anisotropy of the environments and the conductive body on the electric potential are illustrated with the aid of several numerical examples.