Approximate computation of radial gravity profiles for sources with circular symmetry

Abstract

Computation of the radial gravity profile due to a source body with circular symmetry about a vertical axis is normally accomplished by a complex computational evaluation of elliptic integrals or lambda functions. To solve this problem, an alternative method is proposed which first obtains the easily computed gravity values at points on the axis of the source body and then finds an appropriate linear combination of these values which approximates the gravity value at a given point on the radial profile to an acceptable degree of accuracy. Sets of coefficients in the linear relationship for each point of computation on the radial profile need be evaluated only once and then can be used repeatedly for different assumptions on the shape and size of the source body and its density distribution. A simple iterative scheme allows selection of a small set of equidistant points on the vertical axis, consistent with a desired accuracy for the computed values along the radial profile. In the two examples given, errors in the computed anomalies are everywhere less than 0.01 percent of the true peak anomaly values.