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Corrections in Geoid Determination

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Abstract

The original, as well as any type of modified Stokes’ formula, requires a number of corrections as Stokes’ integral allows no masses outside the sphere of integration . The corrections include direct topographic, atmospheric and ellipsoidal effects and a downward continuation (DWC) effect on the surface gravity anomaly to be applied prior to Stokes’ integration. After integration, indirect effects are applied to the potential for restoration of masses as well as for corrections to the potential on the reference ellipsoid (rather than the sphere of integration). These are the classical corrections that are used more or less also in the modern remove-restore technique. The KTH method for geoid determination uses “additive corrections” to the preliminary geoid heights computed directly from the surface gravity anomalies. These corrections are therefore combinations of direct and indirect effects on potential/geoid height , implying several advantages. For example, the numerical solution to the DWC effect on the potential is much more stable than the corresponding effect on the gravity anomaly.

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References

  • Ågren J (2004a) The analytical continuation bias in the geoid determination using potential coefficients and terrestrial gravity data. J Geod 78:314–332

    Article  Google Scholar 

  • Ågren J (2004b) Regional geoid determination methods for the era of satellite gravimetry, numerical investigations using synthetic Earth gravity models. Doctoral thesis in Geodesy, Royal Institute of Technology, Stockholm, Sweden

    Google Scholar 

  • Ågren J, Sjöberg LE, Kiamehr R (2009) The new gravimetric quasigeoid model KTH08 over Sweden. J Appl Geod 3(3):143–153

    Google Scholar 

  • Cruz JY (1986) Ellipsoidal corrections to potential coefficients obtained from gravity anomaly data on the ellipsoid. Rep 371, Department of Geodetic Science and Surveying, Ohio State University, Columbus

    Google Scholar 

  • Ellmann A, Sjöberg LE (2004) Ellipsoidal correction for the modified Stokes formula. Boll Geod Sci Aff 63:153–172

    Google Scholar 

  • Fei ZL, Sideris MG (2000) A new method for computing the ellipsoidal correction for Stokes’s formula. J Geod 74:223–231

    Article  Google Scholar 

  • Heiskanen WA, Moritz H (1967) Physical Geodesy. W H Freeman and Co., San Francisco and London

    Google Scholar 

  • Huang J, Véronneau M, Pagiatakis SD (2003) On the ellipsoidal correction to the spherical Stokes solution of the gravimetric geoid. J Geodesy 77(3–4):171–181

    Article  Google Scholar 

  • Jekeli C (1981) The downward continuation to the earth’s surface of truncated spherical and ellipsoidal harmonic series of the gravity height anomaly. Rep 323, Department of Geodetic Science and Surveying, OSU, OH

    Google Scholar 

  • Martinec Z (1998a) Boundary-value problems for gravimetric determination of a precise geoid. Lecture notes in earth sciences. Springer, Berlin

    Google Scholar 

  • Martinec Z (1998b) Construction of Green’s function for the Stokes boundary-value problem with ellipsoidal corrections in the boundary condition. J Geodesy 72:460–472

    Article  Google Scholar 

  • Martinec Z, Grafarend EW (1997) Solution to the Stokes boundary-value problem on an ellipsoid of revolution. Stud Geophys Geod 41:103–129

    Article  Google Scholar 

  • Molodenskii MS, Eremeev VF, Yurkina MI (1962) Methods for study of the external gravitation field and figure of the earth. Translated from Russian (1960), Israel Program for Scientific Translations, Jerusalem

    Google Scholar 

  • Moritz H (1980) Advanced physical geodesy. Herbert Wichmann Verlag, Karlsruhe

    Google Scholar 

  • Moritz H (2003) The strange behavior of asymptotic series in mathematics, celestial mechanics and physical geodesy. In: Grafarend EW, Krumm FW, Schwarze VS (eds) Geodesy: the challenge of the third millennium. Springer, Berlin, pp 371–377 (in the Internet: Google-Suchenach “asymptotic series”)

    Google Scholar 

  • Sjöberg LE (1977) On the errors of spherical harmonic developments of gravity at the surface of the earth, Department of Geodetic Science Rep No. 257, The OSU, Columbus, OH

    Google Scholar 

  • Sjöberg LE (1999) The IAG approach to the atmospheric geoid correction in Stokes formula and a new strategy. J Geodesy 73(7):362–366

    Article  Google Scholar 

  • Sjöberg LE (2000) On the topographic effects by the Stokes-Helmert method of geoid and quasigeoid determinations. J Geod 74(2):255–268

    Article  Google Scholar 

  • Sjöberg LE (2001) Topographic and atmospheric corrections of the gravimetric geoid determination with special emphasis of the effects of degrees zero and one. J Geod 75:283–290

    Article  Google Scholar 

  • Sjöberg LE (2003a) A computational scheme to model the geoid by the modified Stokes’s formula without gravity reductions. J Geod 77(2003):423–432

    Article  Google Scholar 

  • Sjöberg LE (2003b) A solution to the downward continuation effect on the geoid determined by Stokes’ formula. J. Geod 77:94–100

    Article  Google Scholar 

  • Sjöberg LE (2003c) The ellipsoidal corrections to order e2 of geopotential coefficients and Stokes’ formula. J Geod 77:139–147

    Article  Google Scholar 

  • Sjöberg LE (2003d) The correction to the modified Stokes formula for an ellipsoidal Earth. In Santos M (ed) Honoring the academic life of Petr Vanicek, UNB Technical Report No. 218, New Brunswick, pp 99–110

    Google Scholar 

  • Sjöberg LE (2004a) The effect on the geoid of lateral topographic density variations. J Geod 78:34–39

    Google Scholar 

  • Sjöberg LE (2004b) A spherical harmonic representation of the ellipsoidal correction to the modified Stokes formula. J Geod 78(2004):180–186

    Article  Google Scholar 

  • Sjöberg LE (2005) Discussion on the approximations made in the practical implementation of the remove-compute-restore technique in regional geoid modelling. J Geod 78:645–653

    Article  Google Scholar 

  • Sjöberg LE (2007) The topographic bias by analytical continuation in physical geodesy. J Geod 81:345–350

    Article  Google Scholar 

  • Sjöberg LE (2008) Answers to the comments by M. Vermeer on L.E. Sjöberg (2007) “The topographic bias in physical geodesy”. J Geod 81:345–350. doi:10.1007/s00190-006-0112-2

    Article  Google Scholar 

  • Sjöberg LE (2009a) The terrain correction in gravimetric geoid determination—is it needed? Geophys J Int 176:14–18

    Article  Google Scholar 

  • Sjöberg LE (2009b) On the topographic bias in geoid determination by the external gravity field. J Geod 83:967–972

    Article  Google Scholar 

  • Sjöberg LE (2009c) Solving the topographic bias as an initial value problem. Art Sat 44(3):77–84

    Google Scholar 

  • Sjöberg LE (2014) On the topographic effects by Stokes’ formula. J Geod Sci 4:130–135

    Google Scholar 

  • Sjöberg LE (2015a) The secondary indirect topographic effect in physical geodesy. Stud Geophys Geod 59:173–187

    Article  Google Scholar 

  • Sjöberg LE (2015b) The topographic bias in Stokes’ formula vs. the error of analytical continuation by an earth gravitational model—are they the same? J Geod Sci 5:171–179

    Google Scholar 

  • Sjöberg LE, Nahavandchi H (2000) The atmospheric geoid effects in Stokes’s formula. Geophys J Int 140:95–100

    Article  Google Scholar 

  • Vermeer M (2008) Comments on L. E. Sjöberg (2007) “The topographic bias by analytical continuation in physical geodesy”. J Geod 81:345–350

    Google Scholar 

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Authors and Affiliations

  1. Division of Geodesy and Satellite Positioning, Royal Institute of Technology, Stockholm, Sweden

    Lars E. Sjöberg & Mohammad Bagherbandi

  2. Department of Industrial Development, IT and Land Management, University of Gävle, Gävle, Sweden

    Mohammad Bagherbandi

Authors
  1. Lars E. Sjöberg
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  2. Mohammad Bagherbandi
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Correspondence to Lars E. Sjöberg .

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Sjöberg, L.E., Bagherbandi, M. (2017). Corrections in Geoid Determination. In: Gravity Inversion and Integration. Springer, Cham. https://doi.org/10.1007/978-3-319-50298-4_5

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