Mathematical Problems in Engineering
Volume 2004 (2004), Issue 1, Pages 63-77
doi:10.1155/S1024123X04201016
Direct current electric potential in an anisotropic half-space with vertical contact containing a conductive 3D body
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.
Abstract
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.