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A high-precision digital astrogeodetic traverse in an area of steep geoid gradients close to the coast of Perth, Western Australia

  • P. Schack
  • C. Hirt
  • M. Hauk
  • W. E. Featherstone
  • T. J. Lyon
  • S. Guillaume
Original Article
  • 192 Downloads

Abstract

We present results from a new vertical deflection (VD) traverse observed in Perth, Western Australia, which is the first of its kind in the Southern Hemisphere. A digital astrogeodetic QDaedalus instrument was deployed to measure VDs with \({\sim }\)0.2\(''\) precision at 39 benchmarks with a \({{\sim }}1~\hbox {km}\) spacing. For the conversion of VDs to quasigeoid height differences, the method of astronomical–topographical levelling was applied, based on topographical information from the Shuttle Radar Topography Mission. The astronomical quasigeoid heights are in 20–30 mm (RMS) agreement with three independent gravimetric quasigeoid models, and the astrogeodetic VDs agree to 0.2–0.3\(''\) (north–south) and 0.6–0.9\(''\) (east–west) RMS. Tilt-like biases of \({\sim }1\,\,\hbox {mm}\) over \({\sim }1\,\,\hbox {km}\) are present for all quasigeoid models within \({\sim }20\,\,\hbox {km}\) of the coastline, suggesting inconsistencies in the coastal zone gravity data. The VD campaign in Perth was designed as a low-cost effort, possibly allowing replication in other Southern Hemisphere countries (e.g., Asia, Africa, South America and Antarctica), where VD data are particularly scarce.

Keywords

Vertical deflections Astronomical levelling Geoid validation Coastal zone geodesy 

Notes

Acknowledgements

We would like to thank: (1) DAAD (German Academic Exchange Service) and Universities Australia for funding this project, (2) Jo Jensen of C. R. Kennedy, Perth, for providing a back-up total station, (3) DFG (German Research Foundation) grant Hi1760/1, and (4) Scripps Institution of Oceanography (University of California), the US National Oceanographic and Atmospheric Administration and the National Geospatial-Intelligence Agency for permission to use the marine gravity anomalies from Sandwell et al. (2014).

References

  1. Bosch W, Wolf H (1974) Über die Wirkung von topographischen Lokal-Effekten bei profilweisen Lotabweichungs-Prädiktionen. Mitteilungen aus dem Institut für Theoretische Geodäsie der Universität Bonn Nr. 28Google Scholar
  2. Brown CG, Sarabandi K, Pierce LE (2005) Validation of the shuttle radar topography mission height data. IEEE Trans Geosci Remote Sens 43(8):1707–1715.  https://doi.org/10.1109/TGRS.2005.851789CrossRefGoogle Scholar
  3. Bürki B (1989) Integrale Schwerefeldbestimmung in der Ivrea-Zone und deren geophysikalische Interpretation. Geodätisch-geophysikalische Arbeiten in der Schweiz, Nr. 40, Schweizerische Geodätische KommissionGoogle Scholar
  4. Davidson WA (1995) Hydrogeology and groundwater resources of the Perth region, Western Australia. Ph.D. thesis, Curtin University of Technology, School of Applied GeologyGoogle Scholar
  5. Featherstone WE (1995) On the use of Australian geodetic datums in gravity field determination. Geomat Res Australas 62:17–36Google Scholar
  6. Featherstone WE, Lichti DD (2009) Fitting gravimetric geoid models to vertical deflections. J Geod 83(6):583–589.  https://doi.org/10.1007/s00190-008-0263-4CrossRefGoogle Scholar
  7. 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.  https://doi.org/10.1080/00050326.2000.10440341. [Erratum in The Australian Surveyor 47(1):7]  https://doi.org/10.1080/00050356.2002.10558836
  8. Featherstone WE, Kirby JF, Hirt C, Filmer MS, Claessens SJ, Brown NJ, Hu G, Johnston GM (2011) The AUSGeoid09 model of the Australian height datum. J Geod 85(3):133–150.  https://doi.org/10.1007/s00190-010-0422-2CrossRefGoogle Scholar
  9. Featherstone WE, McCubbine JC, Brown NJ, Claessens SJ, Filmer MS, Kirby JF (2017) The first Australian gravimetric quasigeoid model with location-specific uncertainty estimates. J Geod.  https://doi.org/10.1007/s00190-017-1053-7Google Scholar
  10. Fischer I, Slutsky M, Shirley FR, Wyatt PY III (1968) New pieces in the picture puzzle of an astrogeodetic geoid map of the world. Bull Géod 88(1):199–221.  https://doi.org/10.1007/BF02525661CrossRefGoogle Scholar
  11. Forsberg R (1984) A study of terrain reductions, density anomalies and geophysical inversion methods in gravity field modelling. Report 355, Department of Geodetic Science and Surveying, Ohio State University, Columbus, USAGoogle Scholar
  12. Fryer JG (1972) The Australian geoid. Aust Surv 24(4):203–214.  https://doi.org/10.1080/00050326.1972.10440630CrossRefGoogle Scholar
  13. Guillaume S (2015) Determination of a precise gravity field for the CLIC feasibility studies. Dissertation Nr. 22590, Eidgenössische Technische Hochschule ETH Zürich, Switzerland.  https://doi.org/10.3929/ethz-a-010549038
  14. Guillaume S, Bürki B, Griffet S, Mainaud-Durand H (2012) QDaedalus: augmentation of total stations by CCD sensor for automated contactless high-precision metrology. In: FIG Proceedings. https://www.fig.net/resources/proceedings/fig_proceedings/fig2012/papers/ts09i/TS09I_guillaume_buerki_et_al_6002.pdf
  15. Hauk M, Hirt C, Ackermann C (2017) Experiences with the QDaedalus system for astrogeodetic determination of deflections of the vertical. Surv Rev 49(355):294–301.  https://doi.org/10.1080/00396265.2016.1171960CrossRefGoogle Scholar
  16. Heiskanen WA, Moritz H (1967) Physical geodesy. W.H. Freeman, San FranciscoGoogle Scholar
  17. Helmert FR (1880/1884) Die mathematischen und physikalischen Theorien der höheren Geodäsie. Teubner, Leibzig (reprint Minerva, Frankfurt a.M. 1961)Google Scholar
  18. Hirt C (2006) Monitoring and analysis of anomalous refraction using a digital zenith camera system. Astron Astrophys 459(1):283–290.  https://doi.org/10.1051/0004-6361:20065485CrossRefGoogle Scholar
  19. Hirt C, Flury J (2008) Astronomical–topographic levelling using high-precision astrogeodetic vertical deflections and digital terrain model data. J Geod 82(4–5):231–248.  https://doi.org/10.1007/s00190-007-0173CrossRefGoogle Scholar
  20. Hirt C, Seeber G (2007) High-resolution local gravity field determination at the sub-millimeter level using a digital zenith camera system. In: Tregoning P, Rizos C (eds) Proc. Dynamic Planet, Cairns 2005, IAG Symposia, vol 130, pp 316–321Google Scholar
  21. 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.  https://doi.org/10.1007/s00190-007-0184-7CrossRefGoogle Scholar
  22. Hirt C, Denker H, Flury J, Lindau A, Seeber G (2007) Astrogeodetic validation of gravimetric quasigeoid models in the German Alps-first results. In: Proceedings of first international symposium of the international gravity field service, Istanbul, Turkey, 28 Aug, 01 Sept 2006, Harita Dergisi, vol 18, Ankara, pp 84–89Google Scholar
  23. Hirt C, Feldmann-Westendorff U, Denker H, Flury J, Jahn C-H, Lindau A, Seeber G, Voigt C (2008) Hochpräzise Bestimmung eines astrogeodätischen Quasigeoidprofils im Harz für die Validierung des Quasigeoidmodells GCG05. Zeitschrift für Vermessungswesen 133:108–119Google Scholar
  24. Hirt C, Bürki B, Somieski A, Seeber G (2010a) Modern determination of vertical deflections using digital zenith cameras. J Surv Eng 136(1):1–12.  https://doi.org/10.1061/_ASCE_SU.1943-5428.0000009CrossRefGoogle Scholar
  25. Hirt C, Marti U, Bürki B, Featherstone WE (2010b) Assessment of EGM2008 in Europe using accurate astrogeodetic vertical deflections and omission error estimates from SRTM/DTM2006.0 residual terrain model data. J Geophys Res Solid Earth 115(B10):B10404.  https://doi.org/10.1029/2009JB007057CrossRefGoogle Scholar
  26. Hirt C, Schmitz M, Feldmann-Westendorff U, Wübbena G, Jahn C-H, Seeber G (2011) Mutual validation of GNSS height measurements from high-precision geometric-astronomical levelling. GPS Solut 15(2):149–159.  https://doi.org/10.1007/s10291-010-0179-3CrossRefGoogle Scholar
  27. Hirt C, Claessens SJ, Fecher T, Kuhn M, Pail R, Rexer M (2013) New ultra-high resolution picture of Earth’s gravity field. Geophys Res Lett 40(16):4279–4283.  https://doi.org/10.1002/grl.50838CrossRefGoogle Scholar
  28. Jamil H, Kadir M, Forsberg R, Olesen A, Isa MN, Rasidi S, Mohamed A, Chihat Z, Nielsen E, Majid F, Talib K (2017) Airborne geoid mapping of land and sea areas of East Malaysia. J Geod Sci 7(1):84–93.  https://doi.org/10.1515/jogs-2017-0010Google Scholar
  29. Jekeli C (1999) An analysis of vertical deflections derived from high-degree spherical harmonic models. J Geod 73(1):10–22.  https://doi.org/10.1007/s001900050213CrossRefGoogle Scholar
  30. Kotsakis C (2009) A study on the reference frame consistency in recent Earth gravitational models. J Geod 83:31.  https://doi.org/10.1007/s00190-008-0227-8CrossRefGoogle Scholar
  31. Li X, Crowley JW, Holmes SA, Wang YM (2016) The contribution of the GRAV-D airborne gravity to geoid determination in the Great Lakes region. Geophys Res Lett 43(9):4358–4365.  https://doi.org/10.1002/2016GL068374CrossRefGoogle Scholar
  32. Marti U (1997) Geoid der Schweiz 1997. Geodätisch-geophysikalische Arbeiten in der Schweiz Nr. 56, Schweizerische Geodätische KommissionGoogle Scholar
  33. Middleton MF, Wilde SA, Evans BA, Long A, Dentith MC (1993) A preliminary interpretation of deep seismic reflection and other geophysical data from the Darling Fault zone, Western Australia. Explor Geophys 24(3–4):711–718.  https://doi.org/10.1071/EG993711CrossRefGoogle Scholar
  34. Moritz H (2000) Geodetic reference system 1980. J Geod 74(1):128–140.  https://doi.org/10.1007/s001900050278CrossRefGoogle Scholar
  35. Pavlis NK, Holmes SA, Kenyon SC, Factor JK (2012) The development and evaluation of the Earth Gravitational Model 2008 (EGM2008). J Geophys Res Solid Earth 117(B4):B04406.  https://doi.org/10.1029/2011JB008916CrossRefGoogle Scholar
  36. Pavlis NK, Holmes SA, Kenyon SC, Factor JK (2013) Correction to "The development and evaluation of the Earth Gravitational Model 2008 (EGM2008)". J Geophys Res Solid Earth 118(B5):2633.  https://doi.org/10.1002/jgrb.50167CrossRefGoogle Scholar
  37. Sandwell DT, Müller RD, Smith WHF, Garcia E, Francis R (2014) New global marine gravity model from CryoSat-2 and Jason-1 reveals buried tectonic structure. Science 346(6205):65–67.  https://doi.org/10.1126/science.1258213CrossRefGoogle Scholar
  38. Schwarz KP, Li YC (1996) What can airborne gravimetry contribute to geoid determination? J Geophys Res Solid Earth 101(8):17873–17881.  https://doi.org/10.1029/96JB00819CrossRefGoogle Scholar
  39. Smith DA, Holmes SA, Li X, Guillaume S, Wang YM, Bürki B, Roman DR, Damiani TM (2013) Confirming regional 1 cm differential geoid accuracy from airborne gravimetry: the geoid slope validation survey of 2011. J Geod 87(10–12):885–907.  https://doi.org/10.1007/s00190-013-0653-0CrossRefGoogle Scholar
  40. Torge W, Müller J (2012) Geodesy, 4th edn. De Gruyter, BerlinCrossRefGoogle Scholar
  41. Vignudelli S, Kostianoy A, Cipollini P, Benveniste J (eds) (2011) Coastal altimetry. Springer, Berlin, p 566.  https://doi.org/10.1007/978-3-642-12796-0Google Scholar
  42. Voigt C (2013) Astrogeodätische Lotabweichungen zur Validierung von Schwerefeldmodellen. Deutsche Geodätische Kommission C 702, MünchenGoogle Scholar
  43. Voigt C, Denker H (2013) Validation of second generation GOCE gravity field models by astrogeodetic vertical deflections. In: IAG Proceedings, vol 139, pp 291–296.  https://doi.org/10.1007/978-3-642-37222-3_38
  44. Voigt C, Denker H, Hirt C (2009) Regional astrogeodetic validation of GPS/levelling data and quasigeoid models. In: Sideris MG (ed) Observing our changing earth. Springer, Berlin, pp 413–420Google Scholar
  45. Wang YM, Becker C, Mader G, Martin D, Li X, Jiang T, Breidenbach S, Geoghegan C, Winester D, Guillaume S, Bürki B (2017) The geoid slope validation survey 2014 and GRAV-D airborne gravity enhanced geoid comparison results in Iowa. J Geod.  https://doi.org/10.1007/s00190-017-1022-1Google Scholar
  46. Watts AB (2001) Isostasy and flexure of the lithosphere. Cambridge University Press, CambridgeGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Astronomical and Physical GeodesyTechnical University of MunichMunichGermany
  2. 2.School of Earth and Planetary SciencesCurtin University of TechnologyPerthAustralia
  3. 3.Institute of Geodesy and PhotogrammetrySwiss Federal Institute of Technology ZurichZurichSwitzerland

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