03127nam 22005295 450 991015044670332120220404215112.03-319-46358-610.1007/978-3-319-46358-2(CKB)3710000000943228(DE-He213)978-3-319-46358-2(MiAaPQ)EBC4738835(PPN)197139019(EXLCZ)99371000000094322820161109d2017 u| 0engurnn#008mamaatxtrdacontentcrdamediacrrdacarrierGeodetic boundary value problem: the equivalence between Molodensky’s and Helmert’s solutions /by Fernando Sansò, Michael G. Sideris1st ed. 2017.Cham :Springer International Publishing :Imprint: Springer,2017.1 online resource (V, 81 p. 13 illus., 2 illus. in color.)SpringerBriefs in Earth Sciences,2191-53693-319-46357-8 Includes bibliographical references at the end each chapters.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.SpringerBriefs in Earth Sciences,2191-5369GeophysicsMathematical physicsGeophysics/Geodesyhttps://scigraph.springernature.com/ontologies/product-market-codes/G18009Mathematical Applications in the Physical Scienceshttps://scigraph.springernature.com/ontologies/product-market-codes/M13120Geophysics and Environmental Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/P32000Geophysics.Mathematical physics.Geophysics/Geodesy.Mathematical Applications in the Physical Sciences.Geophysics and Environmental Physics.550526.1Sansò Fernandoauthttp://id.loc.gov/vocabulary/relators/aut422254Sideris Michael Gauthttp://id.loc.gov/vocabulary/relators/autBOOK9910150446703321Geodetic Boundary Value Problem: the Equivalence between Molodensky’s and Helmert’s Solutions2500549UNINA