Bulletin Géodésique

, Volume 54, Issue 1, pp 73–79 | Cite as

The geopotential from gravity measurements, levelling data and satellite results

  • W. Bosch
  • K. R. Koch


The geodetic boundary value problem is formulated which uses as boundary values the differences between the geopotential of points at the surface of the continents and the potential of the geoid. These differences are computed by gravity measurements and levelling data. In addition, the shape of the geoid over the oceans is assumed to be known from satellite altimetry and the shape of the continents from satellite results together with three-dimensional triangulation. The boundary value problem thus formulated is equivalent to Dirichlet's exterior problem except for the unknown potential of the geoid. This constant is determined by an integral equation for the normal derivative of the gravitational potential which results from the first derivative of Green's fundamental formula. The general solution, which exists, of the integral equation gives besides the potential of the geoid the solution of the geodetic boundary value problem. In addition approximate solutions for a spherical surface of the earth are derived.


Integral Equation Gravity Field Spherical Surface Normal Gravity Satellite Altimetry 
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.


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Copyright information

© Bureau Central de L’Association Internationale de Géodésie 1980

Authors and Affiliations

  • W. Bosch
    • 1
  • K. R. Koch
    • 1
  1. 1.Institut für Theoretische GeodäsieBonn 1Fed. Rep. of Germany

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