Skip to main content
SpringerLink
Log in

Global ellipsoid-referenced topographic, bathymetric and stripping corrections to gravity disturbance

  • Published:
Studia Geophysica et Geodaetica Aims and scope Submit manuscript

Abstract

This paper revisits several aspects of defining and computing the anomalous gravity data for purposes of gravimetric inversion/interpretation. Attention is paid to evaluation of a refined global topographic correction to the gravity disturbance based on the reference ellipsoid (RE) and constant reference density for solid topography onshore and sea water density for liquid topography offshore. The global bathymetric correction is discussed. Two issues associated with compilation and inversion of bathymetrically and topographically corrected gravity disturbances in regions of negative ellipsoidal (geodetic) heights are pointed out: the evaluation of normal gravity and the harmonic continuation of the gravity data. Stripping, the removal of an effect of a known density contrast, is considered also for additional geological elements such as lakes, glaciers, sedimentary basins, isostatic mountain roots, etc. The stripping corrections are discussed in the context of the gravimetric inverse problem.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Blakely R.J., 1995. Potential Theory in Gravity and Magnetic Applications. Cambridge University Press, New York.

    Google Scholar 

  • Chapman M.E. and Bodine J.H., 1979. Considerations of the indirect effect in marine gravity modelling. J. Geophys. Res., 84, 3889–3892.

    Article  Google Scholar 

  • Forsberg R., 1984. A Study of Terrain Reductions, Density Anomalies and Geophysical Inversion Methods in Gravity Field Modelling. Report No. 355, Department of Geodetic Science, The Ohio State University, Columbus.

    Google Scholar 

  • Forsberg R., 1985. Gravity field terrain effect computations by FFT. Bull. Géod., 59, 342–360.

    Article  Google Scholar 

  • Hackney R.I. and Featherstone W.E., 2003. Geodetic versus geophysical perspectives of the ‘gravity anomaly’. Geophys. J. Int., 154, 35–43, doi: 10.1046/j.1365-246X.2003.01941.x.

    Article  Google Scholar 

  • Hackney R.I. and Featherstone W.E., 2006. Corrigendum to Geodetic versus geophysical perspectives of the ‘gravity anomaly’. Geophys. J. Int., 167, 585–585, doi: 10.1111/j.1365-246X.2006. 03035.x.

    Article  Google Scholar 

  • Heck B. and Seitz K., 2007. A comparison of the tesseroid, prism and point-mass approaches for mass reductions in gravity field modelling. J. Geodesy, 81, 121–136, doi: 10.1007/s00190-006-0094-0.

    Article  Google Scholar 

  • Heiskanen W.A. and Moritz H., 1967. Physical Geodesy. Freeman and Co., San Francisco.

    Google Scholar 

  • Hinze W.J., Aiken C., Brozena J., Coakley B., Dater D., Flanagan G., Forsberg R., Hildenbrand Th., Keller G.R., Kellogg J., Kucks R., Li X., Mainville A., Morin R., Pilkington M., Plouff D., Ravat D., Roman D., Urrutia-Fucugauchi J., Véronneau M., Webring M. and Winester D., 2005. New standards for reducing gravity data: The North American gravity database. Geophysics, 70, J25–J32, doi: 10.1190/1.1988183.

    Article  Google Scholar 

  • Hofmann-Wellenhof B. and Moritz H., 2006. Physical Geodesy, Second Edition. Springer Verlag, Wien, NewYork.

    Google Scholar 

  • Ivan M., 1994. Upward continuation of potential fields from a polyhedral surface. Geophys. Prospect., 42, 391–404.

    Article  Google Scholar 

  • Ivan M., 1996. Polyhedral approximations in physical geodesy. J. Geodesy, 70, 755–767.

    Google Scholar 

  • Jekeli C. and Serpas J.G., 2003. Review and numerical assessment of the direct topographical reduction in geoid determination. J. Geodesy, 77, 226–239, doi: 10.1007/s00190-003-0320-y.

    Article  Google Scholar 

  • Jung W.Y. and Rabinowitz P.D., 1988. Application of the indirect effect on regional gravity fields in the North Atlantic Ocean. Marine Geodesy, 12, 127–133.

    Article  Google Scholar 

  • Klose U. and Ilk K.H., 1993. A solution to the singularity problem occurring in the terrain correction formula. Manuscr. Geod., 18, 263–279.

    Google Scholar 

  • Lemoine F.G., Kenyon S.C., Factor J.K., Trimmer R.G., Pavlis N.K., Chinn D.S., Cox C.M., Klosko S.M., Luthcke S.B., Torrence M.H., Wang Y.M., Williamson R.G., Pavlis E.C., Rapp R.H. and Olson T.R., 1998. The Development of the Joint NASE GSFC and the National Imagery and Mapping Agency (NIMA) Geopotential Model EGM96. National Aeronautics and Space Administration, Goddard Space Flight Center, Greenbelt, Maryland, USA.

    Google Scholar 

  • Li Y.C. and Sideris M.G., 1994. Improved gravimetric terrain corrections. Geophys J. Int., 119, 740–752.

    Article  Google Scholar 

  • Li X. and Götze H.J., 2001. Ellipsoid, geoid, gravity, geodesy and geophysics. Geophysics, 66, 1660–1668, doi: 10.1190/1.1487109.

    Article  Google Scholar 

  • Martinec Z., 1998. Boundary value problems for gravimetric determination of a precise geoid. Lecture Notes in Earth Sciences, Vol. 73. Springer Verlag, Berlin, Heidelberg, New York.

    Google Scholar 

  • Meurers B., 1992. Untersuchungen zur Bestimmung und Analyse des Schwerefeldes im Hochgebirge am Beispiel der Ostalpen. Österr. Beitr. Met. Geoph., 6, 146 pp.

    Google Scholar 

  • Meurers B. and Vajda P., 2006. Some aspects of Bouguer gravity determination-revisited. Contributions to Geophysics and Geodesy, 36, 99–112.

    Google Scholar 

  • Mikuška J., Pašteka R. and Marušiak I., 2006. Estimation of distant relief effect in gravimetry. Geophysics, 71, J59–J69, doi: 10.1190/1.2338333.

    Article  Google Scholar 

  • Moritz H., 1968. Density Distributions for the Equipotential Ellipsoid. Report 115, Department of Geodetic Science, The Ohio State University, Columbus, Ohio.

    Google Scholar 

  • Moritz H., 1973. Ellipsoidal Mass Distributions. Report No. 206, Department of Geodetic Science, The Ohio State University, Columbus, Ohio.

    Google Scholar 

  • Moritz H., 1980. Advanced Physical Geodesy. Abacus Press, Tunbridge Wells.

    Google Scholar 

  • Moritz H., 1990. The Figure of the Earth. Wichmann Verlag, Karlsruhe, Germany.

    Google Scholar 

  • Nagy D., 1966. The gravitational attraction of a right rectangular prism. Geophysics, 31, 362–371.

    Article  Google Scholar 

  • Nagy D., Papp G. and Benedek J., 2000. The gravitational potential and its derivatives for the prism. J. Geodesy, 74, 552–560, doi: 10.1007/s001900000116.

    Article  Google Scholar 

  • Nagy D., Papp G. and Benedek J., 2002. Corrections to “The gravitational potential and its derivatives for the prism”. J. Geodesy, 76, 475, doi: 10.1007/s00190-002-0264-7.

    Article  Google Scholar 

  • Nahavandchi H., 2000. The direct topographical correction in gravimetric geoid determination by the Stokes-Helmert method. J. Geodesy, 74, 488–496, doi: 10.1007/s001900000110.

    Article  Google Scholar 

  • Novák P., Vaníček P., Martinec Z. and Véronneau M., 2001. Effects of the spherical terrain on gravity and the geoid. J. Geodesy, 75, 491–504, doi: 10.1007/s001900100201.

    Article  Google Scholar 

  • Novák P. and Grafarend E.W., 2005. Ellipsoidal representation of the topographical potential and its vertical gradient. J. Geodesy, 78, 691–706, doi: 10.1007/s00190-005-0435-4.

    Article  Google Scholar 

  • Nowell D.A.G., 1999. Gravity terrain corrections-an overview. J. Appl. Geophys., 42, 117–134.

    Article  Google Scholar 

  • Paul M.K., 1974. The gravity effect of a homogeneous polyhedron for three-dimensional interpretation. Pure Appl. Geophys., 112, 553–561.

    Article  Google Scholar 

  • Petrović S., 1996. Determination of the potential of homogeneous polyhedral bodies using line integrals. J. Geodesy, 71, 44–52, doi: 10.1007/s001900050074.

    Article  Google Scholar 

  • Pohánka V., 1998. Optimum expression for computation of the gravity field of a polyhedral body with linearly increasing density. Geophys. Prospect., 46, 391–404.

    Article  Google Scholar 

  • Sideris M.G., 1985. A fast Fourier transform method for computing terrain corrections. Manuscr. Geod., 10, 66–73.

    Google Scholar 

  • Sjöberg L.E., 1994. On the Total Terrain Effects in Geoid and Quasigeoid Determinations Using Helmert Second Condensation Method. Report 36, Division of Geodesy, Royal Institute of Technology, Stockholm, Sweden.

    Google Scholar 

  • Smith D.A., 2000. The gravitational attraction of any polygonally shaped vertical prism with inclined top and bottom faces. J. Geodesy, 74, 414–420, doi: 10.1007/s001900000102.

    Article  Google Scholar 

  • Smith D.A., 2002. Computing components of the gravity field induced by distant topographic masses and condensed masses over the entire Earth using the 1-D FFT approach. J. Geodesy, 76, 150–168, doi: 10.1007/s00190-001-0227-4.

    Article  Google Scholar 

  • Smith D.A., Robertson D.S. and Milbert D.G., 2001. Gravitational attraction of local crustal masses in spherical coordinates. J. Geodesy, 74, 783–795, doi: 10.1007/s001900000142.

    Article  Google Scholar 

  • Sun W., 2002. A formula for gravimetric terrain corrections using powers of topographic height. J. Geodesy, 76, 399–406, doi: 10.1007/s00190-002-0270-9.

    Article  Google Scholar 

  • Talwani M. and Ewing M., 1960. Rapid computation of gravitational attraction of three-dimensional bodies of arbitrary shape. Geophysics, 25, 203–225.

    Article  Google Scholar 

  • Talwani M., 1998. Errors in the total Bouguer reduction. Geophysics, 63, 1125–1130, doi: 10.1190/1.1444412.

    Article  Google Scholar 

  • Tscherning C.C. and Sünkel H., 1981. A method for the construction of spheroidal mass distributions consistent with the harmonic part of the Earth’s gravity potential. Manuscr. Geod., 6, 131–156.

    Google Scholar 

  • Tsoulis D., 2001. Terrain correction computations for a densely sampled DTM in the Bavarian Alps, J. Geodesy, 75, 291–307, doi: 10.1007/s001900100176.

    Article  Google Scholar 

  • Tsoulis D., 2003. Terrain modeling in forward gravimetric problems: a case study on local terrain effects. J. Appl. Geophys., 54, 145–160.

    Article  Google Scholar 

  • Tsoulis D., Wziontek H. and Petrović S., 2003. A bilinear approximation of the surface relief in terrain correction computations. J. Geodesy, 77, 338–344, doi: 10.1007/s00190-003-0332-7.

    Article  Google Scholar 

  • Vajda P., Vaníček P., Novák P. and Meurers B., 2004. On evaluation of Newton integrals in geodetic coordinates: Exact formulation and spherical approximation. Contributions to Geophysics and Geodesy, 34(4), 289–314.

    Google Scholar 

  • Vajda P., Vaníček P. and Meurers B., 2006. A new physical foundation for anomalous gravity. Stud. Geophys. Geod., 50, 189–216, doi: 10.1007/s11200-006-0012-1.

    Article  Google Scholar 

  • Vajda P., Vaníček P., Novák P., Tenzer R. and Ellmann A., 2007. Secondary indirect effects in gravity anomaly data inversion or interpretation, J. Geophys. Res., 112, B06411, doi: 10.1029/2006JB004470.

    Article  Google Scholar 

  • Vajda P., Ellmann A., Meurers B., Vaníček P., Novák P. and Tenzer R., 2008. Gravity disturbances in regions of negative heights: A reference quasi-ellipsoid approach. Stud. Geophys. Geod., 52, 35–52.

    Article  Google Scholar 

  • Vogel A., 1982. Synthesis instead of reductions-New approaches to gravity interpretations. Earth Evolution Sciences, 2 Vieweg, Braunschweig, 117–120.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Geophysical Institute, Slovak Academy of Sciences, Dúbravská cesta 9, Bratislava, 845 28, Slovak Republic

    P. Vajda

  2. Department of Civil Engineering, Tallinn University of Technology, Ehitajate tee 5, 19086, Tallinn, Estonia

    A. Ellmann

  3. Institute of Meteorology and Geophysics, University of Vienna, Althanstrasse 14, 1090, Vienna, Austria

    B. Meurers

  4. Department of Geodesy and Geomatics Engineering, University of New Brunswick, P.O. Box 4400, Fredericton, N.B., E3B 5A3, Canada

    P. Vaníček

  5. Research Institute of Geodesy, Topography and Cartography, Ondřejov, 244, 251 65, Czech Republic

    P. Novák

  6. Department of Mathematics, University of Western Bohemia, Univerzitní 8, 306 14, Plzeň, Czech Republic

    P. Novák

  7. Faculty of Aerospace Engineering, Physical and Space Geodesy (PSG), Kluyverweg 1, 2629 HS, Delft, The Netherlands

    R. Tenzer

Authors
  1. P. Vajda
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Ellmann
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. B. Meurers
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. P. Vaníček
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. P. Novák
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. R. Tenzer
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to P. Vajda.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vajda, P., Ellmann, A., Meurers, B. et al. Global ellipsoid-referenced topographic, bathymetric and stripping corrections to gravity disturbance. Stud Geophys Geod 52, 19–34 (2008). https://doi.org/10.1007/s11200-008-0003-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11200-008-0003-5

Keywords

Search

Navigation