Anomalies of an external and internal gravitational field of upper Earth layers in square law approximation

Abstract

The explicit form for the quadratic contribution to the gravitational field from the dipole distributed anomalous masses is found. The anomalous masses are represented in the form of layers of variable height, arranged relative to the reference ellipsoid. The solution is reduced to the mathematical problem of finding an expression for the coefficients of expansion in terms of spherical harmonics of the square of any function that can be presented as a finite series of spherical harmonics, in terms of the coefficients of this initial series. The formulas have been calculated using mathematical modelling of symbol computation using computer algebra packages. The results obtained are illustrated using the example of the contribution from relief masses and density jumps on the Mohorovicic (Moho) discontinuity.