Geodetic Boundary Value Problem

Geodetic Boundary Value Problem: the Equivalence between Molodensky’s and Helmert’s Solutions

This book offers a new approach to interpreting the geodetic boundary value problem, successfully obtaining the solutions of the Molodensky and Stokes boundary value problems (BVPs) with the help of downward continuation (DC) based methods. Although DC is known to be an improperly posed operation, classical methods seem to provide numerically sensible results, and therefore it can be concluded that such classical methods must in fact be manifestations of different, mathematically sound approaches. Here, the authors first prove the equivalence of Molodensky’s and Stoke's approaches with Helmert’s reduction in terms of both BVP formulation and BVP solutions by means of the DC method. They then go on to show that this is not merely a downward continuation operation, and provide more rigorous interpretations of the DC approach as a change of boundary approach and as a pseudo BVP solution approach.

The Geodetic Boundary Value Problem and the Coordinate Choice Problem

Geodetic Boundary Value Problems in View of the One Centimeter Geoid

The precise determination of the figure of the earth and its exterior gravitational field requires the solution of the geodetic boundary value problem (GBVP). Recently, a whole series of new measurement techniques has became available, in particular air- and spaceborne methods. They will make its solution much more complete and accurate and will contribute to a better understanding of ocean circulation and of the earth's interior. The book consists of contributions from leading scientists presented at an international summer school. It covers all aspects of the solution of the GBVP, from a mathematical basis via geodetic modeling to its relationship with advanced measurements. It provides three foundations to determine the geoid at a 1-cm precision level.