Gravity Anomaly of Polyhedral Bodies Having a Polynomial Density Contrast

We analytically evaluate the gravity anomaly associated with a polyhedral body having an arbitrary geometrical shape and a polynomial density contrast in both the horizontal and vertical directions. The gravity anomaly is evaluated at an arbitrary point that does not necessarily coincide with the origin of the reference frame in which the density function is assigned. Density contrast is assumed to be a third-order polynomial as a maximum but the general approach exploited in the paper can be easily extended to higher-order polynomial functions. Invoking recent results of potential theory, the solution derived in the paper is shown to be singularity-free and is expressed as a sum of algebraic quantities that only depend upon the 3D coordinates of the polyhedron vertices and upon the polynomial density function. The accuracy, robustness and effectiveness of the proposed approach are illustrated by numerical comparisons with examples derived from the existing literature.