On the treatment of the geodetic boundary value problem by means of regular gravity space formulations

Abstract

The aim of this thesis is to present an alternative for the solution of a fundamental problem of geodesy. This problem, the so-called classical geodetic boundary value problem, comprises the determination of the figure of the Earth as well as the recovery of the Earths̉ gravity field in the exterior of the terrestrial masses. Already in 1849, G.G. Stokes addressed the problem of finding the Earths̉ gravity potential together with the physical shape of the Earth, i.e. the geoid. Later on in 1962, M.S. Molodensky proposed his famous theory for the direct gravimetric determination of the Earths̉ topographical surface along with the external gravity potential. Both approaches solve the initially nonlinear free boundary value problem, which implies considerable mathematical difficulties in the investigation of its existence and uniqueness properties, by means of a twofold linearization strategy. For this purpose, adequate approximations for the solution of the physical problem component, i.e. the determination of the gravity field, and for the geometrical part, i.e. the determination of the shape of the Earths̉ body, must be assumed. In detail, a normal potential to approximate the true potential as well as a reference surface for the geoid or the topography is required ...