Abstract
The computation of the vertical attraction due to the topographic masses, the so-called Terrain Correction, is a fundamental step in geodetic and geophysical applications: it is required in high-precision geoid estimation by means of the remove–restore technique and it is used to isolate the gravitational effect of anomalous masses in geophysical exploration. The increasing resolution of recently developed digital terrain models, the increasing number of observation points due to extensive use of airborne gravimetry in geophysical exploration and the increasing accuracy of gravity data represents nowadays major issues for the terrain correction computation. Classical methods such as prism or point masses approximations are indeed too slow while Fourier based techniques are usually too approximate for the required accuracy. In this work a new software, called Gravity Terrain Effects (GTE), developed to guarantee high accuracy and fast computation of terrain corrections is presented. GTE has been thought expressly for geophysical applications allowing the computation not only of the effect of topographic and bathymetric masses but also those due to sedimentary layers or to the Earth crust-mantle discontinuity (the so-called Moho). In the present contribution, after recalling the main classical algorithms for the computation of the terrain correction we summarize the basic theory of the software and its practical implementation. Some tests to prove its performances are also described showing GTE capability to compute high accurate terrain corrections in a very short time: results obtained for a real airborne survey with GTE ranges between few hours and few minutes, according to the GTE profile used, with differences with respect to both planar and spherical computations (performed by prism and tesseroid respectively) of the order of 0.02 mGal even when using fastest profiles.
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References
Alvarez O., Gimenez M.E., Martinez M.P., LinceKlinger F., and Braitenberg C., New insights into the Andean crustal structure between 32 degree and 34 degree S from GOCE satellite gravity data and EGM08 model. Gelogical Society, London, Special Publications, 399, 183–202 (2014).
Andreu M.A., and Simo C., Determination del geoide UB91 a Catalunya, Institut Cartografic de Catalunya, Monografies tecniques, Num. 1 (1992).
Arabelos D., and Tziavos I.N., Combination of ERS-1 and TOPEX altimetry for precise geoid and gravity recovery in the Mediterranean Sea, Geophys J Int, 125(1), 285-302 (1996).
Asgharzadeh M.F., von Frese R.R.B., Kim H.R., Leftwich T.E., and Kim J.W., Spherical prism gravity effects by Gauss-Legendre quadrature integration, Geophys J Int, 169(1), 1–11 (2007).
Ayhan M.E., Geoid determination in Turkey (TG-91), Bulletin Geodesique, 67(1), 10-22 (1993).
Benciolini B., Mussio L., Sansò F., Gasperini P., and Zerbini S., Geoid Computation in the Italian Area, Boll. di Geodesia e Sc. Affini, XLIII(3), 213-244 (1984).
Biagi L., and Sansò F., TC Light: a New Technique for Fast RTC Computation, International Association of Geodesy Symposia, 123, 61-66 (2000).
Blais J.A., and Ferland R., Optimization in gravimetric terrain corrections. Can J Heart Sci 21, 505–515 (1983).
Braitenberg C., Mariani P., and De Min A., The European Alps and nearby orogenic belts sensed by GOCE, B Geofis Teor Appl, 54(4), 321–334 (2013).
Department of primary industries, Victoria, Gippsland Nearshore Airborne Gravity Survey - Data Package, (2012).
Dodson A.H., and Gerrard S., A relative geoid for the UK, International Association of Geodesy Symposia, 104, 47–52 (1990).
Forsberg R., Kaminskis J., and Solheim D., Geoid of the Nordic and Baltic region from gravimetry and satellite altimetry, International Association of Geodesy Symposia, 117, 540-547 (1997).
Forsberg R., Study of terrain reductions, density anomalies and geophysical inversion methods in gravity field modelling, Reports of the Department of Geodetic Science and Surveying, 355, The Ohio State University, Columbus, Ohio (1984).
Forsberg R., Gravity field terrain effect computations by FFT, Bullettin Geodesique, 59, 342–360 (1985).
Götze H-J., and Lahmeyer B., Application of three-dimensional interactive modeling in gravity and magnetics, Geophysics, 53, 1096–1108 (1988).
Hansen R.O., An analytical expression for the gravity field of a polyhedral body with linearly varying density, Geophysics, 64, 75–77 (1999).
Hinze W.J., Aiken C., Brozena J., Coakley B., Dater D., Flanagan G., Forsberg R., Hildenbrand T., Keller G.R., Kellogg J.N., Kucks R., Li X., Mainville A., Morin R., Pilkington M., Plouff D., Ravat D., Roman D., Urrutia-Fucugauchi J., Veronneau M., Webring M., and Winester D., New standards for reducing gravity data: The North American gravity database, Geophysics, 70(4), J25–J32 (2005).
Holstein H., and Ketteridge B., Gravimetric analysis of uniform polyhedra, Geophysics, 61, 357–364 (1996).
Klose U., and Ilk K.H., A solution to the singularity problem occurring in the terrain correction formula, Manuscripte Geodaetica, 18, 263–279 (1993).
MacMillan W.D., Theoretical Mechanics, vol. 2: The Theory of The Potential. MacGraw-Hill, NewYork (1930). Reprinted by Dover Publications, New York (1958).
Nagy D., The gravitational attraction of a right rectangular prism, Geophysics, 31, 362–371 (1966).
Nagy D., Papp G., and Benedek J., The gravitational potential and its derivatives for the prism. J. Geodesy, 74, 552–560 (2000).
Paul M.K., The gravity effect of a homogeneous polyhedron for three-dimensional interpretation, Pure Appl. Geophys, 112, 553-561 (1974).
Parker R.L., The rapid calculation of potential anomalies, Geophys J R Astr Soc, 31, 447–455 (1972).
Petrovic S., Determination of the potential of homogeneous polyhedral bodies using line integrals, J. Geodesy, 71, 44–52 (1996).
Pivetta T., and Braitenberg C., Laser-scan and gravity joint investigation for subsurface cavity exploration - The Grotta Gigante benchmark, Geophysics, 80(4), B83 - B94 (2015).
Sampietro D., Sona G., and Venuti G., Residual Terrain Correction on the Sphere by an FFT algorithm, Proceedings of the 1st International Symposium on international gravity field service, 306–311 (2007).
Sansò F., Sideris M.G., Geoid determination: theory and methods, 734. Springer Science & Business Media, London (2013).
Sideris M.G., Computation of gravimetric terrain correction using Fast Fourier Transform techniques, Department of Geomatics Engineering, University of Calgary, 20007, (1984).
Strang van Hees G., Stokes formula using fast Fourier techniques, Manusc Geodaet, 15, 235–239 (1990).
Szwillus W., Koether N., and Göetze H., Calculation of gravitational terrain effects using robust, adaptive and exact algorithms, AGU Fall Meeting Abstracts, 1 (2012).
Talwani M., and Ewing M., Rapid computation of gravitational attraction of three-dimensional bodies of arbitrary shape, Geophysics, 25, 203–225 (1960).
Tscherning C.C., Forsberg R., and Knudsen P., The GRAVSOFT package for geoid determination.Proceedings of the 1st Continental Workshop on the geoid in Europe, Research Institute of Geodesy, Topography and Cartography, Prague, 327-334 (1992).
Tscherning C.C., and Forsberg R., Geoid determination in the Nordic countries from gravity and height data. Bollettino di geodesia e scienze affini, 46(1), 21-43 (1987).
Tsoulis D., 1999, Analytical and numerical methods in gravity field modeling of ideal and real masses, Deutsche Geodatisch\(\ddot{e}\)nchen Germany (1999).
Tsoulis D., and Petrovic S., On the singularities of the gravity field of a homogeneous polyhedral body, Geophysics, 66, 535–539 (2001).
Tsiavos I.N., Sideris M.G., and Sunkel H., The effect of surface density variation on terrain modeling - A case study in Austria, Proceedings, Session G7, “Techniques for local geoid determination”, European Geophysical Society XXI General Assembly, The Hague, 99–110 (1996).
Uieda L., Bomfim E.P., Braitenberg C., and Molina E., Optimal forward calculation method of the Marussi tensor due to a geologic structure at GOCE height, Proceedings of the 4th International GOCE User Workshop, (2011).
Whiteway T.G., Australian Bathymetry and Topography Grid, Geoscience Australia Record, 21, (2009).
Acknowledgments
The authors would like to thank the management of Eni Upstream and Technical Services for the permission to present this work. We are grateful to Dr. A. Gatti for useful conversations and important suggestions which helped improving the GTE C software.
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Sampietro, D., Capponi, M., Triglione, D. et al. GTE: a new software for gravitational terrain effect computation: theory and performances. Pure Appl. Geophys. 173, 2435–2453 (2016). https://doi.org/10.1007/s00024-016-1265-4
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DOI: https://doi.org/10.1007/s00024-016-1265-4