Modelling of resistivity and IP anomalies of a thin conductor with an integral equation

A method is presented for calculating the resistivity and IP anomalies of a thin conductor. The conductor is represented by a two-dimensional conductive surface, and consequently the electric charge on its boundaries can be described as a two-dimensional surface charge.

The potential on the surface is solved from an integrodifferential equation. For moderate conductivity values of the surface, the same equation can also be used in calculating the potential outside the conductor. For high conductivity, however, the charge density on the conductor is first solved with the aid of Coulomb's law, where the potential acts as primary term. The potential outside the conductor is then calculated from the known charge density by again applying the Coulomb's law. This procedure is valid over the whole conductivity range from zero to practically infinite values. For a perfect conductor, the potential can also be calculated directly by applying the equipotential condition of the conductor.

As an application, the potential and charge distributions of the model are considered as a function of the longitudinal conductance of the conductor.