Advertisement

The Integral-Equation-Based Approaches for Modelling the Local Gravity Field in the Remove–Restore Scheme

  • A. Abdalla
  • R. Tenzer
Conference paper
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 139)

Abstract

We study the accuracy of local gravity field modelling using four different types of the integral-equation-based approaches, namely the Poisson integral, Green integral, point-mass, and radial multipole approaches. We investigate how these four discretised integral equations perform when the gravity data are corrected for the residual terrain model (RTM-correction) and for the reference gravity field (remove–restore scheme). All integral equations are discretised below data points at the chosen constant depth relative to the Bjerhammar sphere. The choice of the optimal depth of discretization is done based on minimising the RMS fit between the observed and predicted gravity data. In all four approaches the number of unknown parameters is identical to the number of input gravity data and the systems of discretised integral equations are solved using Jacobi iteration. The regularisation is not applied. The study area in New Zealand comprises a rough part of the Southern Alps in the South Island with flat coastal regions including offshore areas. The results of numerical experiments are presented and discussed. We demonstrate that the application of the RTM-correction to gravity data significantly improves the accuracy of the gravity field approximation when using the Green integral approach.

Keywords

Integral equation Local gravity Point mass Radial multipole Reference field Remove–restore technique Residual terrain model 

References

  1. Abdalla A, Tenzer R (2011) The evaluation of the New Zealand’s geoid model using the KTH method. Geod Cartogr 37(1):5–14CrossRefGoogle Scholar
  2. Andersen OB, Knudsen P, Berry P (2009) The DNSC08GRA global marine gravity field from double retraced satellite altimetry. J Geod 84:191–199CrossRefGoogle Scholar
  3. Alberts B, Klees R (2004) A comparison of methods for the inversion of airborne gravity data. J Geod 78:55–65CrossRefGoogle Scholar
  4. Bjerhammar A (1962) Gravity reductions to a spherical surface. Royal Institute of Technology, Division of Geodesy, StockholmGoogle Scholar
  5. Bjerhammar A (1987) Discrete physical geodesy. Report 380. Department of Geodetic Science and Surveying, The Ohio State University, ColumbusGoogle Scholar
  6. Columbus J, Sirguey P, Tenzer R (2011) A free, fully assessed 15-m DEM for New Zealand. Surv Q 66:16–19Google Scholar
  7. Forsberg R, Tscherning CC (1997) Topographic effects in gravity modelling for BVP. In: Sanso F, Rummel R (eds) Geodetic boundary value problems in view of the one centimeter geoid. Lecture notes in Earth sciences, vol 65. Springer, Berlin, pp 241–272Google Scholar
  8. Marchenko AN (1998) Parameterization of the Earth’s gravity field: point and line singularities. Lviv Astronomical and Geodetical Society, LvivGoogle Scholar
  9. Martinec Z (1996) Stability investigations of a discrete downward continuation problem for geoid determination in the Canadian Rocky mountains. J Geod 70:805–828CrossRefGoogle Scholar
  10. Novák P (2003) Geoid determination using one-step integration. J Geod 77:193–206CrossRefGoogle Scholar
  11. Novák P, Kern M, Schwarz KP, Sideris MG, Heck B, Ferguson S, Hammada Y, Wei M (2003) On geoid determination from airborne gravity. J Geod 76:510–522CrossRefGoogle Scholar
  12. Reigber C, Schmidt R, Flechtner F, Konig R, Meyer U, Neumaye KH, Schwintzer P, Zhu SY (2004) An Earth gravity field model complete to degree and order 150 from GRACE: EIGEN-GRACE02S. J Geodyn 39(1):1–10CrossRefGoogle Scholar
  13. Sjöberg LE (2003) A general model of modifying Stokes formula and its least squares solution. J Geod 77:459–464CrossRefGoogle Scholar
  14. Tenzer R, Klees R (2008) The choice of the spherical radial basis functions in local gravity field modelling. Stud Geophys Geod 52:287–304CrossRefGoogle Scholar
  15. Tenzer R, Klees R, Prutkin I (2012) A comparison of different integral-equation-based approaches for local gravity field modelling – Case study for the Canadian Rocky Mountains. In: Kenyon S, Christina. Pacino M, Marti. Urs (eds) Geodesy for planet Earth: Proceedings of the 2009 IAG symposium, Buenos Aires, 31 August–4 September 2009. IAG symposia, vol 136. Springer, Berlin (WOS), pp 381–388. doi: 10.1007/978-3-642-20338-1_46. ISBN 978-3-642-20337-4
  16. Young D (1971) Iterative solutions of large linear systems. Academic, New YorkGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • A. Abdalla
    • 1
  • R. Tenzer
    • 1
  1. 1.Faculty of Sciences, National School of SurveyingUniversity of OtagoDunedinNew Zealand

Personalised recommendations