Mise‐à‐la‐masse interpretation using a perfect conductor in a piecewise uniform earth

Abstract

A useful analysis of the mise‐à‐la‐masse problem can be made by considering a perfectly conducting orebody in a piecewise uniform conducting earth. While the use of a perfect conductor is clearly an idealization of the true geological conditions it provides several advantages for the present purpose. The electric field associated with the above model can be expressed in terms of a surface integral of the normal potential gradient over the boundary of the conductor, where the normal gradient satisfies a well‐posed Fredholm integral equation of the first kind. This integral equation formulation remains unchanged when the conductor is arbitrarily located in the conducting earth, including the important case when it crosses surfaces of conductivity discontinuity. Moreover, it is readily specialized to the important case of a thin, perfectly conductive lamina. Consideration of the boundary value problem relevant to a conductive body fed by a stationary current source suggests that under certain circumstances, equivalent mise‐à‐la‐masse responses will result from any perfect conductor confined by the equipotential surfaces of the original problem. This type of equivalence can only be reduced by extending the potential measurements into or on to the conductor itself. This ambiguity in the interpretation of mise‐à‐la‐masse surveys suggests a simple if approximate integral solution to the mise‐à‐la‐masse problem. The solution is suitable for modelling the responses of perfect conductors and could possibly be used as the basis of a direct inversion scheme for mise‐à‐la‐masse data.

Research Note: A simple method of image solution for a sphere of constant electrical potential in a conducting half‐space: implications for the applied potential method

“…Scurtu (), Singh and Espindola (), and Singh () presented a method of image solutions for the case of point current sources at the ground surface with perfectly conducting spheres in the subsurface, a situation that is relevant to surface resistivity surveys. The approximation of a perfectly conducting anomaly was also made in the theoretical investigations of Furness () and Eloranta () and is expected to be valid provided that the conductor is at least 100 times more conductive than the background, which is common (Eloranta ).…”