Abstract
In this paper we are concerned with the simple Molodensky problem and the linearized fixed-boundary gravimetric boundary-value problem in spherical approximation. We find a series solution for these problems from a variational approach using the Molodensky shrinking These series are compared with the solution by analytical continuation and the change of boundary method.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Auz A, Otero J (2002) Gradient solution of the GPSgravimetric boundary problem (in Spanish). In: Proc III Spanish-Portuguese Assembly on Geodesy and Geophysics, in print
Brovar VV (1964) On the solutions of Molodensky’s boundary value problem. Bulletin Géodésique 72: 167–173
Dautrey R, Lions JL (1990) Mathematical analysis and numerical methods for science and technology. Volume 1: Physical origins and classical methods. Springer, Berlin Heidelberg New York
Grafarend EW, Heck B, Knickmeyer EH (1985) The free versus fixed geodetic boundary value problem for different combinations of geodetic observables. Bulletin Géodésique 59: 11–32
Heiskanen WA, Moritz H (1967) Physical Geodesy. W.H. Freeman and Co., San Francisco Londres
Holota P (1985) Boundary value problems of physical geodesy: present state, boundary perturbation and the Green-Stokes representation. In: Proc 1st Hotine-Marussi Symposium on Mathematical Geodesy ( Rome ), Politecnico di Milano, pp 529–558
Holota P (1989) Higher order theories in the solution of boundary value problems of physical geodesy by means of successive approximations. In: Proc 2nd HotineMarussi Symposium on Mathematical Geodesy ( Pisa ), Politecnico di Milano, pp 471–505
Holota P (1997) Coerciveness of the linear gravimetric boundary-value problem. Journal of Geodesy 71: 640–651
Hotine M (1969) Mathematical geodesy. ESSA Mono- graph 2, U.S. Department of Commerce, Washington
Kautsky J (1962) Approximations of solutions of Dirichlet’s problem on nearly circular domains and their application in numerical methods. Aplikace Matematiky 7: 186–200
Koch KR, Pope AJ (1972) Uniqueness and existence for the geodetic boundary value problem using the known surface of the earth. Bulletin Géodésique 106: 467–476
Kuzmina RP (2000) Asymptotic methods for ordinary differential equations. Kluwer Academic Publishers, Dordrecht
Martinec Z, Grafarend EW (1997) Solution of the Stokes boundary-value problem on an ellipsoid of revolution. Studia Geoph. et Geod. 41: 103–129
Molodensky MS, Eremeev VF, Yurkina MI (1962) Methods for study of the external gravitational field and figure of the earth. Israel Program for Scientific Translations, Jerusalem
Moritz H (1980) Advanced physical geodesy. Herbert Wichmann and Abacus Press, Karlsruhe Tunbridge
Moritz H (2000) Molodensky’s theory and GPS. In: Moritz H, Yurkina MI (eds) M.S.Molodensky: In memoriam. Mitteilungen der geodätischen Institute der Technischen Universität Graz, Folge 88, Graz, pp 69–85
Rummel R (1988) Zur iterativen Lösung der Geodätischen Randwertaufgabe. In: Deutsche Geodätische Kommission Reihe B, Nr. 287, Munich, pp 175–181
Sacerdote F, Sansb F (1986) The scalar boundary value problem of physical geodesy. Manuscripta Geodaetica 11: 15–28
Sansò F (1993) Theory of geodetic B.V.P.s applied to the analysis of altimetric data. In: Rummel R, Sansò F (eds) Satellite altimetry in geodesy and oceanography. Lecture notes in Earth Sciences 50: 317–371, Springer, Berlin Heidelberg New York
Stock B (1983) A Molodenskii-type solution of the geodetic boundary value problem using the known surface of the earth. Manuscripta Geodaetica 8: 273–288
Sünkel H (1997) GBVP–Classical solutions and implementation. In: Sansò F, Rummel R (eds) Geodetic Boundary Value Problems in View of the One Centimeter Geoid. Lecture notes in Earth Sciences 65: 219–237, Springer, Berlin Heidelberg New York
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Otero, J., Auz, A. (2004). A formal comparison between Marych-Moritz’s series, Sansò’s change of boundary method and a variational approach for solving some linear geodetic boundary value problems. In: Sansò, F. (eds) V Hotine-Marussi Symposium on Mathematical Geodesy. International Association of Geodesy Symposia, vol 127. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-10735-5_29
Download citation
DOI: https://doi.org/10.1007/978-3-662-10735-5_29
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-06028-1
Online ISBN: 978-3-662-10735-5
eBook Packages: Springer Book Archive