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

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.