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

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.

Electric Potential and Fréchet Derivatives for a Uniform Anisotropic Medium with a Tilted Axis of Symmetry

“…In another paper (LI and UREN, 1998) they applied image theory to derive the solution for the potential from a buried current source in an arbitrary anisotropic half space, and showed how the image source is laterally displaced from the true source horizontal position. LI and STAGNITTI (2000) studied the problem of direct current electric potential in an anisotropic halfspace with a vertical contact and containing a conductive 3-D body. The analytic solution for the potential in a stack of layers, each having arbitrary anisotropy, was derived by PERVAGO et al (2006) by applying a set of Hankel transforms of integer order.…”