Gravimagnetic similarity in anomaly formulas for uniform polyhedra

Abstract

Gravitational and magnetic anomalies of an arbitrary target body are linked through Poisson's differential relation. For a uniform polyhedral target, Poisson's relation reduces to an algebraic link between gravity and magnetic anomaly formulas. The derivation is given in tensor form. It identifies for each target facet edge a vector function, in terms of which the gravitational and magnetic potential and field anomaly formulas are similarly expressed as appropriately weighted linear combinations. This similarity unifies the theory of uniform polyhedral anomalies. It benefits analysis and construction of software that naturally embraces all anomalies in a single code. The analysis is exemplified by a discussion of singularities and by the adaptation of three gravity‐field algorithms to the remaining gravitational and magnetic cases, while retaining the respective computational advantages of the former gravity‐field algorithms.