Invariance in gravimagnetic anomaly formulas for uniform polyhedra

The anomaly formulas of gravitation and magnetics for uniform polyhedral targets are related by the gradient operation. The relationship enforces an invariance among subexpressions of the formulas. Knowledge of the invariance is not new. However, its role as a simplifier in an abstract calculus of anomaly functions is novel. This is exemplified by the derivation of anomaly formula variants of practical value. The gravitational potential V of a uniform polyhedral target allows compact expression to terms of certain vector functions bij, one associated with each edge j of every target facet i, as defined in Holstein (2002). The derivation requires integration of elementary volume and surface integrals associated with the Newtonian potential. Corresponding integrations of the derived integrands for the gravity field and gravity gradient tensor reveal anomaly formulas for ∇ V and ∇∇ V with reappearance of the same functions bij. This phenomenon is described as gravimagnetic similarity, extensions to the magnetic case being immediate on account of Poisson's relation.