Abstract
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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Ardalan, A.A. and E.W.Grafarend: Ellipsoidal geoid undulations (ellipsoidal Bruns formulae): case studies. Journal of Geodesy, Vol. 75, pp. 544–552, 2001.
Heiskanen, W.A. and H. Moritz: Physical Geodesy. W.H. Freeman & Co, San Francisco, 1967.
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.
Torge, W.: Geodesy. 3. Ed., de Gruyter, 2001.
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.
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.
Wenzel, H.G.: Ultra hochaufloesende
Kugelfunktionsmodelle GMP98A und GMP98B des Erdschwerefeldes. Proceedings Geodaetische Woche, Kauserslautern, 1998.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Tscherning, C.C. (2004). A discussion of the use of spherical approximation or no approximation in gravity field modeling with emphasis on unsolved problems in Least-Squares Collocation. In: Sansò, F. (eds) V Hotine-Marussi Symposium on Mathematical Geodesy. International Association of Geodesy Symposia, vol 127. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-10735-5_25
Download citation
DOI: https://doi.org/10.1007/978-3-662-10735-5_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-06028-1
Online ISBN: 978-3-662-10735-5
eBook Packages: Springer Book Archive