The transient electromagnetic response of a resistive sheet: straightforward but not trivial

Thin conductive sheets are often used to model base metal deposits for mineral exploration. In a similar manner, thin resistive sheets can be used as the building blocks of oil, gas or gas hydrate reservoir models. One would expect that the calculation of the electromagnetic response of a resistive sheet using an integral equation method should follow trivially from the well-studied solution methods for a conductive sheet. The only physical difference between the two situations is the fact that the conductive solution relies on the continuity of the electric field tangential to the sheet surface whereas the resistive solution requires continuity of the normal current density. The authors started to develop the building blocks for a practical tool which would be useful in marine controlled-source electromagnetic projects. However, progress proved slow. It was eventually realized that the style of the approximations used in the conductive calculation resulted in solutions in the resistive case that failed surprisingly to converge. It turns out that the resistive problem is far more subtle than one might expect, not only for the full 3-D case, but also for the simplified 2-D version. This paper derives and examines the quasi-analytical solution for the response of a 2-D resistive sheet buried in a double half-space and excited by a 2-D inline dipole-dipole system. Non-trivial differences between the resistive and conductive solution techniques are illuminated, and a deeper understanding of the underlying physics behind the resulting response is gained. Results show that a large resistive sheet of finite transverse impedance behaves in the same way as a layer with corresponding thickness and resistivity, a well-known result in the resistivity method. The response of a finite sheet shows characteristics similar to those observed in full numerical modelling.