Simple interpretation of time‐domain electromagnetic sounding using similarities between wave and diffusion propagation

Abstract

By using similarities between EM sounding in dielectric and conductive media, it is shown that one can transform between solutions in one type of propagation to the other. The method is based on the similarities of the Laplace transform between diffusive and nondiffusive cases. In the diffusive case, the equation involves the Laplace variable s in the first power, while for the nondiffusive cases, similar equations occur with [Formula: see text]. Three alternative implementations are developed, and their use is demonstrated. The first implementation is based on substituting [Formula: see text] for the Laplace transform variable s using forward and inverse numerical Laplace transforms. The second implementation is based on expanding the diffusive time response on an exponential time base and replacing it with its image function in the wave case, namely, a sinusoidal function. The third implementation is based on direct transformation in the time domain using exponential time interval sampling. The performance of the techniques on synthetic data is demonstrated. Besides the advantage of simple implementation of these techniques, other advantages and limitations of the method and each of the implementations are discussed. A case history is presented. The application of common techniques used in the processing of seismic and radar for processing and EM sounding in conductive media is discussed. The use of the Poynting vector as a means of determining distance and direction is demonstrated.