Time focusing of electromagnetic sounding in conductive media using similarities between wave and diffusion propagation

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 the diffusive and the 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 s². Three alternative implementations are developed and their use is demonstrated. The first implementation is based on substitution s² for the Laplace transform variable s using forward and inverse numerical Laplace transform. 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 advantages of the techniques are their simple implementation. Other advantages and limitations of the method and each of the implementations are discussed. Application of common techniques used in processing of seismic radar for processing and EM sounding in conductive media are discussed