Three-Dimensional Gravity Modeling In All Space

We review available analytical algorithms for the gravity effect and gravity gradients especially the vertical gravity gradient due to a right rectangular prism, a right polygonal prism, and a polyhedron. The emphasis is placed on an investigation of validity, consistency, and especially singularities of different algorithms, which have been traditionally proposed for calculation of the gravity effect on ground (or outside anomalous bodies), when they are applied to all points in space. The rounding error due to the computer floating point precision is estimated. The gravity effect and vertical gradient of gravity in three dimensions caused by a cubic model are calculated by different types of algorithms. The reliability of algorithms for the calculation of gravity of a right polygonal prismand a polyhedron is further verified by using a regular polygonal prism approximating a vertical cylinder and a regular polyhedron approximating a sphere, respectively. By highlighting Haáz-Jung- Plouff and Okabe-Steiner-Zilahi-Sebess’ formulae for a right rectangular prism, Plouff’s algorithm for a right polygonal prism, and Götze and Lahmeyer’s algorithm for a polyhedron and removing their singularities, we demonstrate that these formulae and algorithms can be used to model the gravity anomaly and its vertical gradient at all possible computation positions.