A method for computing the geoid height contribution of three‐dimensional bodies within a spherical earth

Abstract

A method is presented for calculating the geoid height associated with three‐dimensional bodies of arbitrary shape and anomalous density within a spherical earth. Each three‐dimensional body is specified by giving its shape and anomalous density at a number of successive depths. The method calculates the anomalous gravitational potential due to such bodies and then obtains the geoid height using Bruns’ formula. The calculation utilizes the portion of the density model that lies in a hemisphere centered at the observation point. The method is partly analytical and partly numerical, and it is designed for digital computation. Use of the method to compute the anomalous potential in the vicinity of an anomalous body of simple shape shows that the method can give very accurate results.