On the combination of terrestrial gravity data with satellite gradiometry and airborne gravimetry treated in terms of boundary-value problems

Abstract

The unprecedented progress in satellite, but also airborne and terrestrial measurements is associated with new possibilities for refined studies on Earth gravity field. At the same time, however, these advances open a number of new problems of theoretical nature. The purpose of this paper is to study the synthesis of satellite, airborne and terrestrial measurements and to show that it brings impulses for the formulation of boundary-value problems which together with some optimization concepts may offer a reasonable way for the combination of the mentioned data. In a sense the approach offers a generalization or modification of the problems, their importance is well-know in physical geodesy. Mathematical properties and the solution of these problems are discussed. The apparatus of spherical harmonics is applied and it illustrates the synthesis in a spectral domain. The optimization procedure enables to treat the fact that the problems are overdetermined by nature. © Springer-Verlag Berlin Heidelberg 2007.