Abstract
The method to determine the Geoid from the gravimetric data on the known physical surface of the earth and from the mass density model leads to the fixed gravimetric boundary value problem for both the exterior and interior domain of the earth. After linearization and spherical approximation the solution can be beautifully written in a closed form by Hotine’s function for the exterior domain and similarly for the interior domain.
In this paper a geometrically as well as physically better spheroidal approximation will be outlined. The corresponding Green’s functions will be derived from the Green’s function theory in series of the spheroidal harmonics, and represented in explicit forms up to the earth flattening. They are, in contrast to the spherical case, also dependent on the azimuth. The criterion for the continuous differentiability of the solutions will also be derived, smoothing the solutions however will not be dealt with in this study.
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Thông, N.C. (1991). The Geoid, Green’s Functions and the Gravimetric Boundary Value Problem for the Spheroid Earth. In: Rapp, R.H., Sansò, F. (eds) Determination of the Geoid. International Association of Geodesy Symposia, vol 106. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3104-2_43
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DOI: https://doi.org/10.1007/978-1-4612-3104-2_43
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