A Novel Method of Computing the EM Response of a Conductive Plate in a Conductive Medium

Abstract

This thesis describes the development of a novel, simple, and robust integral equation technique to compute the electromagnetic response of a three dimensional plate-like conductor embedded in a conductive host. Thin sheet or plate-like conductors are mathematical models of many base metal mineral deposits, including mineralized veins, shears, and dipping strat. Solutions for the thin sheet models are usually formulated using the integral equation technique with the electric field as the variable. The appeal in this approach is its simplicity in derivation and the ease in interpretation of solutions. However, many of the approximate computer algorithms derived directly from the exact theory have suffered to some extent from the defect that the solutions fail to generate strong vortex and tend to become unstable when the host conductivity becomes too small. The determination of the scattered electric field within the plate requires the solution of an integral equation in which inductive and channeling terms couple together. The magnitudes of the terms vary with the selection of parameters. They can differ by many orders of magnitude particularly for very resistive hosts. The accuracy with which the terms can be derived numerically depends on the selection of appropriate basis functions. A small set of functions which can describe accurately both the current flows is difficult to find. There are several powerful techniques to circumvent the problem, but these methods usually result in complicated and costly software. Our approach to resolve the problem is to deform the thin plate so as to create an equivalent network model for which the channeling and vortex currents can be described equally well by one simple set of unknowns. The new model uses a set of basis functions with a spatial representation bearing a strong resemblance to a lattice composed of many thin conductive strips, called elements, arranged to look like a bottle-box with the top and base removed. It has finite length, width, and thickness, and consists of m x n basic square loops. In order to check our formulation, the EM responses of the new model in a conductive whole space are compared with equivalent responses of a thin disk derived by West and Edwards (1985) for a wide range of induction and channeling response parameters. Other tests of the lattice plate have shown that the solutions are accurate, stable, and robust, and the algorithm is efficient. The lattice plate is used in forward modeling to study the responses of plate-like conductors in the earth and in the sea floor to various Controlled Source Electromagnetic sounding systems.