Topographic Corrections

Methods for calculation of mass effect of  topography; cartesian and spherical coordinates

Orlando Alvarez , Niels Köther

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Categories

1. Topographic Correction

1.2. Cartesian Coordinates (Rectangular approximation)

1.3. Spherical Coordinates (Spherical approximation)

2. Databases

3. Softwares

3.1. Rectangular Approximation

3.2. Spherical Approximation

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1. Topographic Correction

Molodensky, M.S., Eremeev, V.F. & Yurkina, M.I., 1962. Methods for study of the external gravity field and figure of the earth, Israel Program of Scientific Translations, Jerusalem (Russian original 1960)

Heiskanen, W.A. & Moritz, H., 1967. Physical Geodesy, W.H. Freeman and Company, San Fransisco.

Parker, R. L. 1972. The rapid calculation of potential anomalies. Geophysical Journal of the Royal Astronomical Society, 31, 447- 455.

Anderson, E.G., 1976. The effect of topography on solutions of Stokes’ problem, Unisurv S-14, Rep, School of Surveying, University of New South Wales, Kensington.25

Forsberg, R., 1984. A study of terrain reductions, density anomalies and geophysical inversion methods in gravity field modeling. Rep. No. 355 of the Dept. of Geodetic Science and Surveying. The Ohio State Univ. Columbus.

Blakely, R.J., 1995. Potential theory in gravity and magnetic applications, Cambridge University Press, New York.

Forsberg, R. & Tscherning, C.C., 1997. Topographic effects in gravity modeling for BVP. In: Sansò, F., Rummel, R., (eds): Geodetic boundary value problems in view of the one centimeter geoid, Springer-Verlag, Berlin, Lecture Notes of Earth Science, 65, 241–272.

Torge, W., 2001. Geodesy, 3rd edn., pp. 95-260, W. de Gruyter, Berlin – New York. Tscherning, C.C., 1976. Computation of the second-order derivatives of the normal potential based on the representation by a Legendre series, Manuscripta Geodaetica, 1(1), 71-92.

Hofmann-Wellenhof, B. & Moritz, H., 2006. Physical Geodesy, 2nd edn., Springer, Wien New York, 286pp.

Bouman, J., Ebbing, J., Fuchs, M., 2013. Reference frame transformation of satellite gravity gradients and topographic mass reduction. Journal of Geophysical Research: Solid Earth, 118(2), 759-774. DOI: 10.1029/2012JB009747

 

 1.2. Cartesian Coordinates (Rectangular aproximation)

Nagy, D., 1966. The gravitational attraction of a right rectangular prism, Geophysics, 31(2), 362-371.

Nagy, D., Papp, G. & Benedek, J., 2000. The gravitational potential and its derivatives for the prism, Journal of Geodesy, 74(7-8), 552-560, doi:10.1007/s001900000116.

 

1.3. Spherical Coordinates (Spherical approximation)

Novák, P. & Grafarend, E.W., 2005. Ellipsoidal representation of the topographical potential and its vertical gradient,Journal of Geodesy, 78(11-12), 691-706, doi:10.1007/s00190-005-0435-4.

Asgharzadeh, M.F., Von Frese, R.R.B., Kim, H.R., Leftwich, T.E. & Kim, J.W., 2006. Spherical prism gravity effects by Gauss-Legendre quadrature integration, Geophysical Journal International, 169, 1-11.

Heck, B. & Seitz, K., 2007. A comparison of the tesseroid, prism and point mass approaches for mass reductions in gravity field modeling, Journal of Geodesy, 81(2), 121-136. doi:10.1007/s00190-006-0094-0.

Wild-Pfeiffer, F., 2008. A comparison of different mass element for use in gravity gradiometry, Journal of Geodesy, 82, 637-653. doi 10.1007/s00190-008-0219-8.

Barthelmes, F., 2009. Definition of functionals of the geopotential and their calculation from spherical harmonic models theory and formulas used by the calculation service of the International Centre for Global Earth Models (ICGEM), Scientific Technical Report STR09/02, GFZ German Research Centre for Geosciences, Postdam, Germany, March 2009, http://icgem.gfz-postdam.de

Grombein, T., Heck, B., Seitz, K., 2010. Untersuchungen zur effizienten Berechnung topographischer Effekte auf den Gradiententensor am Fallbeispiel der Satellitengradiometriemission GOCE, Karlsruhe Institute of Technology, KIT Scientific Reports 7547, ISBN 978-3-86644-510-9, pp. 1-94

Grombein, T., Heck, B., Seitz, K., 2013. Optimized formulas for the gravitational field of a tesseroid. Journal of Geodesy, 87, 645-600.

 

2. Databases

Amante, C. & Eakins, B.W., 2008. ETOPO1 1 Arc-Minute Global Relief Model: Procedures, Data Sources and Analysis, National Geophysical Data Center, NESDIS, NOAA, U.S. Department of Commerce, Boulder, CO, August 2008.

Divins, D. L. 2003. Total Sediment Thickness of the World’s Oceans & Marginal Seas. NOAA National Geophysical Data Center, Boulder, CO,.

Whittaker, J., Goncharov, A., Williams, S., Dietmar Müller,R., Leitchenkov, G., 2013. Global sediment thickness dataset updated for the Australian-Antarctic Southern Ocean, Geochemistry, Geophysics, Geosystems. DOI: 10.1002/ggge.20181

 

3. Softwares

3.1. Rectangular Approximation

Forsberg, R., 1984. A study of terrain reductions, density anomalies and geophysical inversion methods in gravity field modeling. Rep. No. 355 of the Dept. of Geodetic Science and Surveying. The Ohio State Univ. Columbus.

3.2. Spherical Approximation

Uieda, L., Ussami, N. & Braitenberg, C.F., 2010. Computation of the gravity gradient tensor due to topographic masses using tesseroids, Eos Trans. AGU, 91(26), Meet. Am. Suppl., Abstract G22A-04. http://leouieda.github.io/tesseroids/