Numerical properties of staggered finite‐difference solutions of Maxwell's equations for ground‐penetrating radar modeling

Abstract

Accurate modeling of electromagnetic wave propagation in conducting media is important for the further development of ground‐penetrating radar technologies. Numerical stability and dispersion criteria are derived here for two common 1‐D finite‐difference solutions of Maxwell's equations. In one finite‐difference scheme one‐sided differences are used to approximate the conducting term and in the other centered differences are employed. Stability is governed by the well‐known Courant criterion. In addition there is a stability condition controlling the diffusive aspects of wave propagation for the one‐sided difference scheme. It is found that the centered difference approximation has significantly better stability and dispersion characteristics. For the centered scheme, the well‐known spatial sampling criteria for the non‐conducting case are found to be valid for conducting media. The results are tested and illustrated using 1‐D synthetic radargrams.