The forward problem of electromagnetic induction: Accurate finite-difference approximations for two-dimensional discrete boundaries with arbitrary geometry

Abstract

We describe finite-difference approximations to the equations of 2-D electromagnetic induction that permit discrete boundaries to have arbitrary geometrical relationships to the nodes. This allows finite-difference modelling with the flexibility normally ascribed to finite-element modelling. Accuracy is demonstrated by comparison with finite-element computations. We also show that related approximations lead to substantially improved accuracy in regions of steep, but not discontinuous, conductivity gradient.