Abstract
A new finite‐difference form is developed for simulating the distortion of telluric fields by 3-D azimuthally symmetric structures. The technique involves a sequence of local integrations of the electric current density crossing closed surfaces surrounding each mesh node. The resulting expressions, which are accurate to second degree everywhere, correctly describe first‐order discontinuities in the electric field normal to electrical discontinuities in the interior of the model. Moreover, the new form (a nine‐point finite‐difference operator) accounts for cross‐derivative (e.g., [Formula: see text]) effects in the region about each node, which can lead to significantly improved accuracy near sharp, localized discontinuities where the anomalous field decays as [Formula: see text] or [Formula: see text] with distance. Numerical simulations are compared with analytical solutions for two simple models: (1) a circular disk‐shaped heterogeneity in a thin sheet; and (2) a sphere imbedded in a homogeneous, infinite medium. The comparison between the analytical and numerical results for both of these models indicates that an accuracy of better than a few percent is not exceptional.
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