Advertisement

Pure and Applied Geophysics

, Volume 173, Issue 7, pp 2435–2453 | Cite as

GTE: a new software for gravitational terrain effect computation: theory and performances

  • D. SampietroEmail author
  • M. Capponi
  • D. Triglione
  • A. H. Mansi
  • P. Marchetti
  • F. Sansò
Article

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.

Keywords

Terrain correction gravity FFT airborne gravimetry 

Notes

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.

References

  1. 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).Google Scholar
  2. Andreu M.A., and Simo C., Determination del geoide UB91 a Catalunya, Institut Cartografic de Catalunya, Monografies tecniques, Num. 1 (1992).Google Scholar
  3. 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).Google Scholar
  4. 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).Google Scholar
  5. Ayhan M.E., Geoid determination in Turkey (TG-91), Bulletin Geodesique, 67(1), 10-22 (1993).Google Scholar
  6. 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).Google Scholar
  7. Biagi L., and Sansò F., TC Light: a New Technique for Fast RTC Computation, International Association of Geodesy Symposia, 123, 61-66 (2000).Google Scholar
  8. Blais J.A., and Ferland R., Optimization in gravimetric terrain corrections. Can J Heart Sci 21, 505–515 (1983).Google Scholar
  9. 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).Google Scholar
  10. Department of primary industries, Victoria, Gippsland Nearshore Airborne Gravity Survey - Data Package, (2012).Google Scholar
  11. Dodson A.H., and Gerrard S., A relative geoid for the UK, International Association of Geodesy Symposia, 104, 47–52 (1990).Google Scholar
  12. 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).Google Scholar
  13. 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).Google Scholar
  14. Forsberg R., Gravity field terrain effect computations by FFT, Bullettin Geodesique, 59, 342–360 (1985).Google Scholar
  15. Götze H-J., and Lahmeyer B., Application of three-dimensional interactive modeling in gravity and magnetics, Geophysics, 53, 1096–1108 (1988).Google Scholar
  16. Hansen R.O., An analytical expression for the gravity field of a polyhedral body with linearly varying density, Geophysics, 64, 75–77 (1999).Google Scholar
  17. 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).Google Scholar
  18. Holstein H., and Ketteridge B., Gravimetric analysis of uniform polyhedra, Geophysics, 61, 357–364 (1996).Google Scholar
  19. Klose U., and Ilk K.H., A solution to the singularity problem occurring in the terrain correction formula, Manuscripte Geodaetica, 18, 263–279 (1993).Google Scholar
  20. MacMillan W.D., Theoretical Mechanics, vol. 2: The Theory of The Potential. MacGraw-Hill, NewYork (1930). Reprinted by Dover Publications, New York (1958).Google Scholar
  21. Nagy D., The gravitational attraction of a right rectangular prism, Geophysics, 31, 362–371 (1966).Google Scholar
  22. Nagy D., Papp G., and Benedek J., The gravitational potential and its derivatives for the prism. J. Geodesy, 74, 552–560 (2000).Google Scholar
  23. Paul M.K., The gravity effect of a homogeneous polyhedron for three-dimensional interpretation, Pure Appl. Geophys, 112, 553-561 (1974).Google Scholar
  24. Parker R.L., The rapid calculation of potential anomalies, Geophys J R Astr Soc, 31, 447–455 (1972).Google Scholar
  25. Petrovic S., Determination of the potential of homogeneous polyhedral bodies using line integrals, J. Geodesy, 71, 44–52 (1996).Google Scholar
  26. 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).Google Scholar
  27. 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).Google Scholar
  28. Sansò F., Sideris M.G., Geoid determination: theory and methods, 734. Springer Science & Business Media, London (2013).Google Scholar
  29. Sideris M.G., Computation of gravimetric terrain correction using Fast Fourier Transform techniques, Department of Geomatics Engineering, University of Calgary, 20007, (1984).Google Scholar
  30. Strang van Hees G., Stokes formula using fast Fourier techniques, Manusc Geodaet, 15, 235–239 (1990).Google Scholar
  31. Szwillus W., Koether N., and Göetze H., Calculation of gravitational terrain effects using robust, adaptive and exact algorithms, AGU Fall Meeting Abstracts, 1 (2012).Google Scholar
  32. Talwani M., and Ewing M., Rapid computation of gravitational attraction of three-dimensional bodies of arbitrary shape, Geophysics, 25, 203–225 (1960).Google Scholar
  33. 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).Google Scholar
  34. 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).Google Scholar
  35. Tsoulis D., 1999, Analytical and numerical methods in gravity field modeling of ideal and real masses, Deutsche Geodatisch\(\ddot{e}\)nchen Germany (1999).Google Scholar
  36. Tsoulis D., and Petrovic S., On the singularities of the gravity field of a homogeneous polyhedral body, Geophysics, 66, 535–539 (2001).Google Scholar
  37. 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).Google Scholar
  38. 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).Google Scholar
  39. Whiteway T.G., Australian Bathymetry and Topography Grid, Geoscience Australia Record, 21, (2009).Google Scholar

Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  • D. Sampietro
    • 1
    Email author
  • M. Capponi
    • 2
  • D. Triglione
    • 2
  • A. H. Mansi
    • 2
  • P. Marchetti
    • 3
  • F. Sansò
    • 1
  1. 1.GReD s.r.l. c/o ComoNExTLomazzoItaly
  2. 2.DICA, Politecnico di MilanoMilanItaly
  3. 3.Eni s.p.aSan Donato MilaneseItaly

Personalised recommendations