Simplified frequency‐domain expressions for potential fields of arbitrary three‐dimensional bodies

Abstract

Models based on homogeneous polyhedral bodies offer great flexibility in representing the potential fields of complex geologic sources. However, existing expressions for the gravity and magnetic fields of such bodies suffer from two disadvantages. First, the surface of the body must be specified as a set of triangular facets, which makes input to a modeling program rather awkward. Second, each facet of the body must be rotated into a special position, which generates substantial computational overhead and makes the analytic expressions difficult to interpret. In this paper, Pedersen’s Fourier transform expressions for the potential fields due to homogeneous polyhedral bodies are recast in a simpler, coordinate‐invariant form. The resulting expressions are then rewritten as a sum of contributions from each vertex of the body. This greatly simplified form is used as the basis for a modeling program that is substantially faster and more straightforward than existing programs. Furthermore, the analytic expressions promise to be useful for further investigation of an inverse method based on polyhedral‐body models.