A discussion of the use of spherical approximation or no approximation in gravity field modeling with emphasis on unsolved problems in Least-Squares Collocation
Spherical approximation is widely used in gravity field modeling, but it causes errors of the order of the flattening. Different methods for avoiding using this approximation when linearizing observation functionals are possible due to our improved knowledge of the gravity field and of the surface of the Earth. However a number of problems are not solved today, such as those related to the use of a Bjerhammar sphere in Least-Squares Collocation (LSC). If this concept is used, the associated homogeneous /isotropic kernels in genera] use will be strongly non-homogeneous on the ellipsoid. A possible solution is to use a “Bjerhammar” ellipsoid inside the Earth.
KeywordsGravity Anomaly Gravity Vector Spherical Approximation Gravity Field Modeling Geoid Undulation
Unable to display preview. Download preview PDF.
- Heiskanen, W.A. and H. Moritz: Physical Geodesy. W.H. Freeman & Co, San Francisco, 1967.Google Scholar
- Lemoine, F.G., S.C. Kenyon, J.K. Factor, R.G. Trimmer, N.K. Pavlis, D.S. Chinn, C.M. Cox, S.M. Klosko, S.B. Luthcke, M.H. Torrence, Y.M. Wang, R G Williamson, E.C. Pavlis, R.H. Rapp, and T.R. Olson, The Development of the Joint NASA GSFC and the National Imagery and Mapping Agency (NIMA) Geopotential Model EGM96, NASA/TP-1998–206861, Goddard Space Flight Center, Greenbelt, MD, July, 1998.Google Scholar
- Torge, W.: Geodesy. 3. Ed., de Gruyter, 2001.Google Scholar
- Tscherning, C.C., R.Forsberg and P.Knudsen: The GRAVSOFT package for geoid determination. Proc. 1. Continental Workshop on the Geoid in Europe, Prague, May 1992, pp. 327–334, Research Institute of Geodesy, Topography and Cartography, Prague, 1992.Google Scholar
- Tscherning, C.C. and R.H.Rapp: Closed Covariance Expressions for Gravity Anomalies, Geoid Undulations, and Deflections of the Vertical Implied by Anomaly Degree-Variance Models. Reports of the Department of Geodetic Science No. 208, The Ohio State University, Columbus, Ohio, 1974.Google Scholar
- Wenzel, H.G.: Ultra hochaufloesendeGoogle Scholar
- Kugelfunktionsmodelle GMP98A und GMP98B des Erdschwerefeldes. Proceedings Geodaetische Woche, Kauserslautern, 1998.Google Scholar