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

A useful analysis of the mise-a-la-masse problem can be made by considering a perfectly conducting orebody in a piecewise uniform conducting earth. Wh ile the use of a perfect conductor is clearly an idealization of the true g eological conditions it provides several advantages for the present purpose . The electric field associated with the above model can be expressed in term s 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 re mains unchanged when thp conductor is arbitrarily located in the conducting earth, including the important case when it crosses surfaces of conductivi ty 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 f ed by a stationary current source suggests that under certain circumstances , equivalent mise-a-la-masse responses will result from any perfect conduct or confined by the equipotential surfaces of the original problem. This type of equivalence can only be reduced by extending the potential mea surements into or on to the conductor itself. This ambiguity in the interpr etation of mise-a-la-masse surveys suggests a simple if approximate integra l solution to the mise-a-la-masse problem. The solution is suitable for mod elling the responses of perfect conductors and could possibly be used as th e basis of a direct inversion scheme for mise-a-la-masse data.