Three-dimensional simulation and characterization of airborne transient electromagnetic response in rough media

Abstract

In fractal, porous, and cranny rough media, the diffusion of the electromagnetic (EM) field differs from that in piecewise smooth media. This phenomenon is known as anomalous diffusion. To study the influence of anomalous diffusion on EM signals, we use the fractional time derivative and derive a governing equation describing the subdiffusion process of electric fields in rough media. Three-dimensional forward modeling of the time-domain airborne EM is performed using the finite-difference method and frequency-time transformation. We verify the accuracy of our forward-modeling method by comparing it with semianalytical solutions for a layered earth model. The numerical results indicate that as the conductivity of rough media decreases with time, the amplitude of the EM field decreases during the early periods but increases during subsequent periods compared with nonrough media. The EM field does not diffuse in the classical mode of the “smoke ring,” but instead demonstrates a “trailing pattern,” meaning that it maintains its maximum value at positions close to the source and diffuses outward and attenuates until it vanishes.