Comparison of gravimetric formulas for uniform polyhedra

Abstract

The gravitational anomaly of a polyhedral target of uniform density is amenable to analytical solution and has received wide attention. We analyze a number of apparently dissimilar solutions for consistency and comment on their suitability for numeric computation. Consistency is determined by evaluating a method over a special contour for which all methods must agree. Numerical performance is assessed through operation counts and algorithm classification into vertex, line, or surface type, each type having a known accuracy bound for a given floating‐point precision. We verify performance predictions through model calculations. In particular, we demonstrate the effectiveness of revised vertex and line algorithms and of a new analytical surface method. Our scheme of analysis and classification has general application. It provides criteria by which existing and novel solutions may be examined for consistency and numerical performance.