Determination of the excess density in a horizontal layered model

The inversion gravity problem formulated as follows is solved. The excess density in each layer of a fixed horizontal stratified model is a function of horizontal coordinates (σ(ξ, η)) approximated by a specially constructed function. The problem is to reconstruct the function σ = σ(ξ, η) from the external gravity field. If the geological model includes more than one layer, the problem is solved with the use of a set of reference points at which the sought function is given. Variations in a gravity anomaly with respect to the field at a fixed point are used in solving this problem.