Journal of Geodesy

, Volume 83, Issue 6, pp 583–589 | Cite as

Fitting gravimetric geoid models to vertical deflections

Short Note

Abstract

Regional gravimetric geoid and quasigeoid models are now commonly fitted to GPS-levelling data, which simultaneously absorbs levelling, GPS and quasi/geoid errors due to their inseparability. We propose that independent vertical deflections are used instead, which are not affected by this inseparability problem. The formulation is set out for geoid slopes and changes in slopes. Application to 1,080 astrogeodetic deflections over Australia for the AUSGeoid98 model shows that it is feasible, but the poor quality of the historical astrogeodetic deflections led to some unrealistic values.

Keywords

Gravimetric geoid errors Vertical deflections Vertical datum errors 

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References

  1. Baarda W (1968) A testing procedure for use in geodetic networks, Publications on Geodesy, New Series, 2(5). Netherlands Geodetic Commission, DelftGoogle Scholar
  2. Bomford AG (1967) The geodetic adjustment of Australia 1963–66. Surv Rev 19(144): 52–71Google Scholar
  3. Bomford G (1980) Geodesy, 4th edn. Oxford University Press, OxfordGoogle Scholar
  4. Farin GE (2001) Curves and surfaces for CAGD: a practical guide, 5th edn. Morgan Kaufmann, San FranciscoGoogle Scholar
  5. Featherstone WE (1998) Do we need a gravimetric geoid or a model of the Australian height datum to transform GPS heights in Australia? Aust Surv 43(4): 273–280Google Scholar
  6. Featherstone WE (2001) Absolute and relative testing of gravimetric geoid models using global positioning system and orthometric height data. Comput Geosci 27(7):807–814. doi:10.1016/S0098-3004(00)00169-2 CrossRefGoogle Scholar
  7. Featherstone WE (2004) Evidence of a north–south trend between AUSGeoid98 and AHD in southwest Australia. Surv Rev 37(291): 334–343Google Scholar
  8. Featherstone WE (2006a) Yet more evidence for a north–south slope in the AHD. J Spat Sci 51(2):1–6; corrigendum in 52(1):65–68Google Scholar
  9. Featherstone WE (2006b) The pitfalls of using GPS and levelling data to test gravity field models. EGU general assembly, ViennaGoogle Scholar
  10. Featherstone WE, Kirby JF, Kearsley AHW, Gilliand JR, Johnston J, Steed R, Forsberg R, Sideris MG (2001) The AUSGeoid98 geoid model of Australia: data treatment, computations and comparisons with GPS/levelling data, J Geod 75(5–6):313–330. doi:10.1007/s001900100177 Google Scholar
  11. Featherstone WE, Rüeger JM (2000) The importance of using deviations of the vertical in the reduction of terrestrial survey data to a geocentric datum, Trans Tasman Surv 1(3):46–61 (erratum in Aust Surv 47(1):7)Google Scholar
  12. Featherstone WE, Sproule DM (2006) Fitting AUSGeoid98 to the Australian height datum using GPS data and least squares collocation: application of a cross validation technique. Surv Rev 38(301): 573–582Google Scholar
  13. Featherstone WE, Morgan L (2007) Validation of the AUSGeoid98 model in Western Australia using historic astrogeodetically observed deviations of the vertical. J R Soc West Aust 90(3): 143–149Google Scholar
  14. Forsberg R (1998) Geoid tailoring to GPS—with example of a 1-cm geoid of Denmark. Finnish Geodetic Institute Report 98(4): 191–198Google Scholar
  15. Fotopoulos G (2005) Calibration of geoid error models via a combined adjustment of ellipsoidal, orthometric and gravimetric geoid height data, J Geod 79(1–3):111–123. doi:10.1007/s00190-005-0449-y CrossRefGoogle Scholar
  16. Grafarend EW (1997) Field lines of gravity, their curvature and torsion, the Lagrange and the Hamilton equations of the plumbline. Ann Geophys 40(5): 1233–1247Google Scholar
  17. Heiskanen WA, Moritz H (1967) Physical geodesy. Freeman, San FranciscoGoogle Scholar
  18. Hirt C, Bürki B (2002) The digital zenith camera—a new high-precision and economic astrogeodetic observation system for real-time measurement of deflections of the vertical. In: Tziavos IN(eds) Gravity and geoid 2002. Department of Surveying and Geodesy, Aristotle University of Thessaloniki, pp 389–394Google Scholar
  19. Hirt C, Flury J (2007) Astronomical-topographic levelling using high-precision astrogeodetic vertical deflections and digital terrain model data. J Geod 82(4–5):231–248. doi:10.1007/s00190-007-0173-x Google Scholar
  20. Hirt C, Denker H, Flury J, Lindau A, Seeber G (2007) Astrogeodetic validation of gravimetric quasigeoid models in the German Alps– first results. In: Kiliçoğlu A, Forsberg R(eds) Gravity field of the earth. General command of mapping, AnkaraGoogle Scholar
  21. Hirt C, Seeber G (2007) High-resolution local gravity field determination at the sub-millimetre level using a digital zenith camera system. In: Tregoning P, Rizos C(eds) Dynamic planet. Springer, Berlin, pp 316–321CrossRefGoogle Scholar
  22. Hirt C, Seeber G (2008) Accuracy analysis of vertical deflection data observed with the Hannover digital zenith camera system TZK2-D. J Geod 82(6):347–356. doi:10.1007/s00190-007-0184-7 CrossRefGoogle Scholar
  23. Jekeli C (1999) An analysis of vertical deflections derived from high-degree spherical harmonic models. J Geod 73(1):10–22. doi:10.1007/s001900050213 CrossRefGoogle Scholar
  24. Jiang Z, Duquenne H (1996) On the combined adjustment of a gravimetrically determined geoid and GPS levelling stations. J Geod 70(8):505–514. doi:10.1007/s001900050039 Google Scholar
  25. Kearsley AHW (1976) The computation of deflections of the vertical from gravity anomalies, Unisurv Rep S15. School of Surveying, Univ of New South Wales, SydneyGoogle Scholar
  26. Kotsakis C (2008) Transforming ellipsoidal heights and geoid undulations between different geodetic reference frames. J Geod 82(4–5): 249–260. doi:10.1007/s00190-007-0174-9 CrossRefGoogle Scholar
  27. Kotsakis C, Sideris MG (1999) On the adjustment of combined GPS/levelling/geoid networks. J Geod 73(8):412–421. doi:10.1007/s001900050261 CrossRefGoogle Scholar
  28. Kuang S (1996) Geodetic network analysis and optimal design: concepts and applications. Ann Arbor Press, ChelseaGoogle Scholar
  29. Kühtreiber N (1999) Combining gravity anomalies and deflections of the vertical for a precise Austrian geoid. Bollettino di Geofisica Teorica ed Applicata 40(3–4): 545–553Google Scholar
  30. Kühtreiber N, Abd-Elmotaal HA (2007) Ideal combination of deflection components and gravity anomalies for precise geoid computation. In: Tregoning P, Rizos C(eds) Dynamic planet. Springer, Berlin, pp 259–265CrossRefGoogle Scholar
  31. Marti U (2007) Comparison of high precision geoid models in Switzerland. In: Tregoning P, Rizos C(eds) Dynamic planet. Springer, Berlin, pp 377–382CrossRefGoogle Scholar
  32. Mather RS (1970) The geodetic orientation vector for the Australian geodetic datum, Geophys J R Astron Soc 22(1):55–81. doi:10.1111/j.1365-246X.1971.tb03583.x Google Scholar
  33. Milbert DG (1995) Improvement of a high resolution geoid model in the United States by GPS height on NAVD88 benchmarks. Int Geoid Serv Bull 4: 13–36Google Scholar
  34. Moritz H (1980) Geodetic reference system 1980. Bull Géod 54(4): 395–405CrossRefGoogle Scholar
  35. Müller A, Bürki B, Kahle HG, Hirt C, Marti U (2007a) First results from new high-precision measurements of deflections of the vertical in Switzerland. In: Jekeli C, Bastos L, Fernandes J(eds) Gravity geoid and space missions. Springer, Berlin, pp 143–148Google Scholar
  36. Müller A, Bürki B, Limpach P, Kahle HG, Grigoriadis VN, Vergos GS, Tziavos IN (2007b) Validation of marine geoid models in the North Aegean Sea using satellite altimetry, marine GPS data and astrogeodetic measurements. In: Kiliçoğlu A, Forsberg R(eds) Gravity field of the earth. General command of mapping, AnkaraGoogle Scholar
  37. Pavlis NK, Holmes SA, Kenyon SC, Factor JK (2008) An earth gravitational model to degree 2160: EGM2008. EGU general assembly, ViennaGoogle Scholar
  38. Prutkin I, Klees R (2007) On the non-uniqueness of local quasi-geoids computed from terrestrial gravity anomalies. J Geod 82(3):147–156. doi:10.1007/s00190-007-0161-1 CrossRefGoogle Scholar
  39. Soltanpour A, Nahavandchi H, Featherstone WE (2006) The use of second-generation wavelets to combine a gravimetric geoid model with GPS-levelling data. J Geod 80(2):82–93. doi:10.1007/s00190-006-0033-0 CrossRefGoogle Scholar
  40. Tenzer R, Vaníček P, Santos M, Featherstone WE, Kuhn M (2005) The rigorous determination of orthometric heights. J Geod 79(1–3): 82–92. doi:10.1007/s00190-005-0445-2 CrossRefGoogle Scholar
  41. Torge W (2001) Geodesy, 3rd edn. de Gruyter, BerlinGoogle Scholar
  42. Wessel P, Smith WHF (1998) New, improved version of generic mapping tools released. EOS Trans AGU 79(47): 579CrossRefGoogle Scholar
  43. Zhong D (1997) Robust estimation and optimal selection of polynomial parameters for the interpolation of GPS geoid heights. J Geod 71(9):552–561. doi:10.1007/s001900050123 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Western Australian Centre for Geodesy, The Institute for Geoscience ResearchCurtin University of TechnologyPerthAustralia
  2. 2.Department of Geomatics Engineering, The Centre for Bioengineering Research and Education, Schulich School of EngineeringThe University of CalgaryCalgaryCanada

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