Domain Transformation, Boundary Problems and Optimization Concepts in the Combination of Terrestrial and Satellite Gravity Field Data

Abstract

The purpose of this paper is to further develop a method ofcombining terrestrial and satellite gravity field data, which in an optimal way exploits gravity field information contained in the solution of boundary problems in a close neighborhood of the Earth. The method is considerably generalized in this paper. In particular effects caused by the topography of the Earth are taken into account. The starting point is a transformation of the boundary problems considered under a small modification of curvilinear coordinates. In the new coordinates the boundary and also the boundary condition is simpler, but topography dependent coefficients appear in the structure of Laplace’s operator. Effects caused by the topography of the Earth are treated as perturbations and refinements of the solution are expressed as corrections constructed by means of successive approximations. As a consequence of the transformation a spherical mathematical apparatus may be applied at each iteration step. Especially Green’s function is constructed for the problem solved in a domain bounded by two concentric spheres. The structure of an iteration step connects the paper with earlier results. Within the iteration step they provide an applicable treatment. The continuation of the solution is discussed with a particular view to its harmonic branch and regularity at infinity. The reasoning leads to optimization concepts considered in the paper