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

  • J. Otero
  • A. Auz
Conference paper
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 127)


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.


Analytical Continuation Variational Approach Boundary Method Gravity Disturbance Gradient Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 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 printGoogle Scholar
  2. Brovar VV (1964) On the solutions of Molodensky’s boundary value problem. Bulletin Géodésique 72: 167–173CrossRefGoogle Scholar
  3. 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 YorkCrossRefGoogle Scholar
  4. Grafarend EW, Heck B, Knickmeyer EH (1985) The free versus fixed geodetic boundary value problem for different combinations of geodetic observables. Bulletin Géodésique 59: 11–32CrossRefGoogle Scholar
  5. Heiskanen WA, Moritz H (1967) Physical Geodesy. W.H. Freeman and Co., San Francisco LondresGoogle Scholar
  6. 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 529–558Google Scholar
  7. 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 471–505Google Scholar
  8. Holota P (1997) Coerciveness of the linear gravimetric boundary-value problem. Journal of Geodesy 71: 640–651CrossRefGoogle Scholar
  9. Hotine M (1969) Mathematical geodesy. ESSA Mono- graph 2, U.S. Department of Commerce, WashingtonGoogle Scholar
  10. Kautsky J (1962) Approximations of solutions of Dirichlet’s problem on nearly circular domains and their application in numerical methods. Aplikace Matematiky 7: 186–200Google Scholar
  11. Koch KR, Pope AJ (1972) Uniqueness and existence for the geodetic boundary value problem using the known surface of the earth. Bulletin Géodésique 106: 467–476CrossRefGoogle Scholar
  12. Kuzmina RP (2000) Asymptotic methods for ordinary differential equations. Kluwer Academic Publishers, DordrechtGoogle Scholar
  13. Martinec Z, Grafarend EW (1997) Solution of the Stokes boundary-value problem on an ellipsoid of revolution. Studia Geoph. et Geod. 41: 103–129CrossRefGoogle Scholar
  14. 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, JerusalemGoogle Scholar
  15. Moritz H (1980) Advanced physical geodesy. Herbert Wichmann and Abacus Press, Karlsruhe TunbridgeGoogle Scholar
  16. 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 69–85Google Scholar
  17. Rummel R (1988) Zur iterativen Lösung der Geodätischen Randwertaufgabe. In: Deutsche Geodätische Kommission Reihe B, Nr. 287, Munich, pp 175–181Google Scholar
  18. Sacerdote F, Sansb F (1986) The scalar boundary value problem of physical geodesy. Manuscripta Geodaetica 11: 15–28Google Scholar
  19. 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 YorkGoogle Scholar
  20. Stock B (1983) A Molodenskii-type solution of the geodetic boundary value problem using the known surface of the earth. Manuscripta Geodaetica 8: 273–288Google Scholar
  21. 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 YorkCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • J. Otero
    • 1
  • A. Auz
    • 2
  1. 1.Instituto de Astronomía y Geodesia (UCM-CSIC), Facultad de MatemáticasUniversidad ComplutenseMadridSpain
  2. 2.GMVTres Cantos MadridSpain

Personalised recommendations