Journal of Geodesy

, Volume 75, Issue 1, pp 1–11 | Cite as

The solution of the general geodetic boundary value problem by least squares

  • M. van Gelderen
  • R. Rummel


 A general scheme is given for the solution in a least-squares sense of the geodetic boundary value problem in a spherical, constant-radius approximation, both uniquely and overdetermined, for a large class of observations. The only conditions are that the relation of the observations to the disturbing potential is such that a diagonalization in the spectrum can be found and that the error-covariance function of the observations is isotropic and homogeneous. Most types of observations used in physical geodesy can be adjusted to fit into this approach. Examples are gravity anomalies, deflections of the vertical and the second derivatives of the gravity potential.

Key words: Geodetic boundary value problem Geoid 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • M. van Gelderen
    • 1
  • R. Rummel
    • 2
  1. 1. Oude Delft 43B, 2611 BC Delft, The Netherlands, e-mail:; Tel.: +3115 2142125NL
  2. 2. Institut für Astronomische und Physikalische Geodäsie, Technische Universität München, Arcisstrasse 21, D-80290 Munich, Germany e-mail:; Tel.: +49 89 289 23189; Fax: +49 89 289 23178DE

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