Abstract
Newton’s integral can be evaluated either in the space domain by a direct integration approach or in the frequency domain by a spherical harmonic approach. In the first approach Newton’s integral is evaluated by a discretised numerical integration using the gravitational potential (or its derivatives) caused by regularly shaped bodies such as prisms or tesseroids (i.e., spherical or elliptical volume elements, respectively). The second approach expresses Newton’s integral by spherical harmonic expansions of height or density functions, which can be interpreted as the gravitational effect of different mass layers. This paper studies the theoretical and practical differences between both approaches. The gravitational effect of the global topographic masses, described here by equivalent rock heights, is evaluated using both approaches and the results compared. Numerical results for the gravitational potential are given for evaluation points located directly on the Earth’s surface and at different heights (e.g., flight levels) above it.
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References
Anderson EG (1976): The effect of topography on solutions of Stokes’s problem. UNISURV Report S14, University of New South Wales, Kensington, Australia, pp. 252.
Heiskanen WA, Moritz H (1967) Physical Geodesy, Freeman, San Francisco, 364 pp.
Hildebrand FB (1974) Introduction to numerical analysis. McGraw-Hill, New York (reprinted 1987 by Dover Publications, New York, 669 pp).
Holmes SA, Featherstone WE (2002) A unified approach to the Clenshaw summation and the recursive computation of very high degree and order normalised associated Legendre functions, J Geod 76: 279–299.
Kuhn M (2002) On the indirect effect of Helmert’s condensation methods. International Geoid Service Bulletin 13: 50–61.
Kuhn M, Featherstone WE (2003a) On the optimal spatial resolution of crustal mass distributions for forward gravity field modelling. In Tziavos IN (ed) Gravity and Geoid 2002, Proceedings of the 3rd meeting of the International Gravity and Geoid Commission, Thessaloniki, Greece, 195–200.
Kuhn M, Featherstone WE (2003b, this issue) Construction of a synthetic Earth gravity model by forward gravity modelling. Paper presented at the General Assembly of the International Union of Geodesy and Geophysics, June–July, 2003, Sapporo, Japan.
Lambeck K (1988) Geophysical Geodesy — The slow deformation of the Earth. Univ. Press, Oxford, 718 pp.
Lemoine FG and 14 other authors (1998) The development of the NASA GSFC and National Imaginary and Mapping Agency (NIMA) geopotential model EGM96. Rep. NASA/TP-1998-206861, National Aeronautics and Space Administration, Maryland, 575 pp.
Mader K (1951) Das Newtonsche Raumpotential prismatischer Körper und seine Ableitung bis zur written Ordnung. Österreichische Zeitschrift für Vermessungswesen, Sonderheft 11.
Nagy D (1966) The gravitational attraction of a right rectangular prism. Geophysics 31: 362–371.
Nagy D, Papp G, Benedek J (2000) The gravitational potential and its derivatives for the prism, J Geod 74: 552–560.
Nagy D, Papp G, Benedek J (2002) Corrections to "The gravitational potential and its derivatives for the prism", J Geod 76: 475.
Ramillen G (2002) Gravity/magnetic potential of uneven shell topography, J Geod 76: 139–149.
Seitz K, Heck B (2003) Efficient calculation of topographic reductions by the use of tesseroids. Presentation at the joint assembly of the EGS, AGU and EUG, Nice, France, 6–11 April 2003.
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© 2005 Springer-Verlag Berlin Heidelberg
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Kuhn, M., Seitz, K. (2005). Comparison of Newton’s Integral in the Space and Frequency Domains. In: Sansò, F. (eds) A Window on the Future of Geodesy. International Association of Geodesy Symposia, vol 128. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-27432-4_66
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DOI: https://doi.org/10.1007/3-540-27432-4_66
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24055-6
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