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.

Shows for the first time the theoretical equivalence of the various geodetic boundary value problems, with and without terrain reductions Offers a rigorous, alternative interpretation of the usual downward continuation approach as a change of boundary approach Provides the theoretical foundations for why the improperly posed downward continuation method has produced reasonable results in many practical applications of geoid/quasi-geoid determination Includes supplementary material: sn.pub/extras