An integral‐equation solution for transient electromagnetic (TEM) scattering by prisms in layered half‐spaces is formulated to provide meaningful results when the prisms are in highly resistive layers. A prism is replaced with an unknown scattering current, which is approximated with pulse and divergence‐free basis functions in the frequency domain. Divergence‐free basis functions model eddy currents that exist in confined bodies in a very resistive host and hence simulate the inductive responses of the prisms. A Galerkin solution for the scattering current is obtained where the dominant charge operator is eliminated from part of the solution by integrating the tensor Green’s function around rectangular paths. After the scattering current is determined, the electric and magnetic fields scattered by the prisms are calculated; and the corresponding TEM responses are obtained by inverse Fourier transformation. The resulting solution provides meaningful results over a wide range of resistivities in layered hosts including the case of free space. The masking effect of a conductive overburden delays and suppresses the three‐dimensional TEM response of a conductor. The overburden response must be removed for the conductor’s response to be fully interpretable. An interpretation of the conductor with free‐space models is a poor approximation when the basement rock is conductive. Instead of an exponential decay at late times, the conductor’s response decays in an inverse power relationship. When the basement resistivity is increased, the conductor exhibits an exponential decay at late times. For a thin dike, the time constant estimated from this decay is identical to that for a thin plate in free space. However, the response of the dike buried beneath the overburden is larger than the response of the dike in free space. This increase in the response of the dike will bias modeling it in free space with thin plates. We have used the solution to gain insight regarding the lateral resolution of two vertical conductors for the fixed‐loop and central‐loop survey configurations. The results suggest that resolution of multiple conductors is very poor in a fixed‐loop survey; but in a central‐loop survey, the resolution is much better, provided the data are interpreted at early times. At later times, multiple conductors may not be resolvable and interpretational ambiguities could arise.
The minimal support discrete divergence free basis functions for a mini-element
