Abstract
Solutions to the direct problem in gravimetric interpretation are well-known for wide class of source bodies with constant density contrast. On the other hand, sources with non-uniform density can lead to relatively complicated formalisms. This is probably why analytical solutions for this type of sources are rather rare although utilization of these bodies can sometimes be very effective in gravity modeling. I demonstrate an analytical solution to that problem for a spherical shell with radial polynomial density distribution, and illustrate this result when applied to a special case of 5th degree polynomial. As a practical example, attraction of the normal atmosphere is calculated.
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References
Cassinis G., Dore P. and Ballarin S., 1937. Fundamental tables for reducing gravity observed values. Tipografia Legatoria Mario Ponzio, 11–27.
Ecker E. and Mittermayer E., 1969. Gravity corrections for the influence of the atmosphere. Bolletino di Geofisica Teorica ed Applicata, 11, 41–42.
García-Abdeslem J., 2005. The gravitational attraction of a right rectangular prism with density varying with depth following a cubic polynomial. Geophysics, 70, 39–42.
Gradshteyn I.S. and Ryzhik I.M., 1980. Tables of Integrals, Series, and Products, Corrected and Enlarged 4th Edition. Academic Press, San Diego, CA, 1160 p.
Heck B. and Seitz K., 2007. A comparison of the tesseroid, prism and point-mass approaches for mass reductions in gravity field modeling. J. Geodesy, 81, 121–136.
Holstein H., 2003. Gravimagnetic anomaly formulas for polyhedra of spatially linear media. Geophysics, 68, 157–167.
Karcol R., 2010. The Contribution to the Direct Problem in Gravimetry. M.Sc. Thesis, Faculty of Natural Sciences, Comenius University, Bratislava, Slovakia (in Slovak).
Mikuška J. Pašteka R. and Marušiak I., 2006. Estimation of distant relief effect in gravimetry. Geophysics, 71, J59–J69.
Mikuška J., Marušiak I., Pašteka R., Karcol R. and Beňo J., 2008. The effect of topography in calculating the atmospheric correction in gravimetry. SEG Expanded Abstracts, 784–788.
NIMA Agency, 2000. Department of Defense World Geodetic System. National Imagery and Mapping Agency Technical Report TR8350.2, Third Edition, Amendment 1. January 3, 2000. Department of Defense, Washingtom, D.C.
NOAA, NASA and USAF, 1976. U.S. Standard Atmosphere. U.S. Government Printing Office, Washington, D.C, 227 pp. (http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19770009539_1977009539.pdf).
Talwani M., 1973. Computer usage in the computation of gravity anomalies. In: Bolt B.A. (Ed.), Geophysics: Methods in Ccomputation Physics 13. Academic Press Inc., 343–389.
Wenzel H., 1985. Hochauflösende Kugelfunktionsmodelle für das Gravitationspotential der Erde. Wissenschaftliche Arbeiten der Fachrichtung Vermessungswesen der Universität Hannover, Nr.137, 155 pp. (in German).
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Karcol, R. Gravitational attraction and potential of spherical shell with radially dependent density. Stud Geophys Geod 55, 21–34 (2011). https://doi.org/10.1007/s11200-011-0002-9
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DOI: https://doi.org/10.1007/s11200-011-0002-9