The modelling of direct current electric potential in an arbitrarily anisotropic half-space containing a conductive 3-D body

Abstract

A new approach to the computation of the D.C. potentials in an arbitrarily anisotropic half-space in which there is embedded a 3-D equipotential (perfect) conductor is presented. With the aid of a Fredholm's integral equation of the first kind developed for the potential, the problem is formulated in which the unknown function is the normal component of the current density on the surfaces of the conductor and it is solved numerically by means of a method of subareas. A Green's function for the point source potential in the arbitrarily anisotropic half-space is the kernel of the integral equation, which is developed by a new method. The integrated Green's function defined for the integral calculation of the subareas can be calculated using a one dimension analytical method followed by another multi-dimensional numerical approach when the body is represented by the cube cell accumulation method, in which the cell surfaces are parallel to the Cartesian coordinate system. The effects of the arbitrary anisotropy and the conductive body on the electric potential are illustrated with the aid of several numerical examples, where the point current source is located at different positions in the half-space. Forward modelling of the nature shown in this paper is valuable as an interpretation aid. An extension of this work to the cases of typical field survey geometries is relatively straight forward.