Application of potential theory in the numerical solution of the inverse problem of gravimetry

This article discusses the results of a study in solving the inverse problem of gravimetry. It is shown that the solution of the inverse problem should be conducted in two stages. At the first step, the contour of the area occupied by gravitation masses is determined using the Laplace equation. At the second step, a generalization of the Poisson equation is used to determine the density distribution of the masses that fill the area, whose contour is determined at the first step. In this case, when setting the problem of analytic continuation, the provisions of potential theory are applied. The results of numerical calculations are presented on a model example with the determination of unknown values of density and values of the gravitational field inside a region filled with gravitation masses.