Time evolution of the electric field: Part 1 — Using the rapid expansion method (REM) with pseudospectral evaluation of spatial derivatives

Abstract

We present a method for modeling transient EM data acquired on land or at sea. We use the rapid expansion method (REM) to develop the 3-component electric wave field time response from the spatial responses found using a pseudo-spectral method. The results are free of numerical dispersion and accurate to the Nyquist frequency in time and space. The resulting diffusive field is a weighted sum of Chebyshev polynomials, which exhibit a wave-like character and are very sensitive to small perturbations in the medium. The method is intrinsically parallel which leads to computational efficiency. Numerical results compare favorably with the analytic response and 1D methods even though the computations are intrinsically 3D.