Abstract
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.
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References
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Bosch, W., Koch, K.R. The geopotential from gravity measurements, levelling data and satellite results. Bull. Geodesique 54, 73–79 (1980). https://doi.org/10.1007/BF02521098
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DOI: https://doi.org/10.1007/BF02521098