Bulletin géodésique

, 67:10 | Cite as

Geoid determination in Turkey (TG-91)

  • M. Emin Ayhan
Article

Abstract

It is considered that precise geoid determination is one of the main current geodetic problems in Turkey since GPS defined coordinates require geoidal heights in practice. In order to determine the geoid by least squares collocation (LSC) the area covering Turkey was divided into 114 blocks of size 1° × 1°. LSC approximation to the geoid based upon the tailored geopotential model GPM2-T1 is constructed within each block. The model GPM2-T1 complete to degree and order 200 has been developed by tailoring of the model GPM2 to mean free-air anomalies and mean heights of one degree blocks in Turkey. Terrain effect reduced point gravity data spaced 5′ × 5′ within each block which the sides extended 0°.5 were used in LSC. Residual terrain model (RTM) depends on point heights at 15″×20″ griding and 5′×5′ and 15′×15′ mean heights has been carried out in terrain effect reduction. Indirect effect of RTM on geoid is also taken into account. The geoid, called Turkish Geoid 1991 (TG-91), referenced to GRS-80 ellipsoid has been computed at 3′ × 3′ griding nodes within each block. The quality of the TG-91 is also evaluated by comparing computed and GPS derived geoidal height differences, and 2.1 – 2.6 ppm accuracy for average baseline lenght of 45 km is obtained.

Keywords

Global Position System Geoidal Height Gravimetric Geoid Little Square Collocation Geoid Determination 

References

  1. Andrews, D.F., P.J. Bickel, F.R. Hampel, P.J. Huber, W.H. Rogers, J.W. Tukey (1972): Robust estimates of Location. Princeton University Press, Princeton, New Jersey.Google Scholar
  2. Arabelos, D., (1989): Gravity field approximation in the area of Greece with emphasis on local characteristics. Bull. Geod. Vol. 63. No.1, pp. 69–84.CrossRefGoogle Scholar
  3. Arabelos, D., P.Knudsen, C.C.Tscherning (1987): Covariance and bias treatment when combining gravimetry, altimeter and gradiometer data by collocation. XIX General Assembly IUGG, Vancouver.Google Scholar
  4. Ayan, T.(1976): Astrogeodatische Geoidberechnung für das Gebiet der Turkei. Karlsruhe.Google Scholar
  5. Ayhan, E. (1991): Local geoid determination by least squares collocation. Harita Dergisi, No. 106, pp. 91–110 (In Turkish).Google Scholar
  6. Ayhan, E. E. Bank, O. Lenk, A. Jeker (1987): South-Western Anatolia (Aegean Region) Doppler geoid. Bolletino di Geod. e Sci. Aff. Anno XLVI, No. 4, pp.293–308.Google Scholar
  7. Denker, H., W.Torge, H.-G. Wenzel, D. Lelgeman, G. Weber (1986): Strategies and requirements for a new European geoid computations. Proc. of the Int. Syp. on the Definition of the Geoid, May 26–30, Florence.Google Scholar
  8. Denker, H., H.-G. Wenzel (1987): Local geoid determination and comparison with GPS results. Bull. Geod., Vol.61, No.4, pp.349–366.CrossRefGoogle Scholar
  9. Engelis, T., R.H. Rapp, C.C. Tscherning (1984): The precise computations of geoid undulation differences with comparison to results obtained from the global positioning system. Geophy. Res. Lett., Vol.11, No.9, pp. 821–824.CrossRefGoogle Scholar
  10. Engelis, T., R.H.Rapp, Y.Bock (1985): Measuring orthometric height differences with GPS and gravity data. Manuscripta Geodaetica, Vol.10, No.3, pp. 187–194.Google Scholar
  11. Forsberg, R.(1984): A study of terrain reductions, density anomalies and geophysical inversion methods in gravity field modelling. OSU, Dept. of Geod. Sci., Rept. No. 355, Columbus.Google Scholar
  12. Forsberg, R., F.Madsen (1981): Geoid prediction in nothern Greenland using collocation and digital terrain models. Anns. Geophys., Vol. 37, No.1, pp.31–36.Google Scholar
  13. Forsberg, R., C.C.Tscherning (1981): The use of height data in gravity field approximation by collocation. JGR, Vol. 86, No. 89, pp. 7843–7854.CrossRefGoogle Scholar
  14. Forsberg, R., F.Madsen (1990): High-precision geoid heights for GPS levelling. Presented at GPS-90 Sym., Ottawa.Google Scholar
  15. Forsberg R., A.H.W. Kearsley (1990): Precise gravimetric geoid computations over large regions. (In: Developments in Four — Dimensional Geodesy. Eds. F.K. Brunner, C. Rizos, Springer Verlag).Google Scholar
  16. Goad, C.C., M.M. Chin, C.C. Tscherning (1984): Gravity empirical covariance values for the continental United States. JGR, Vol.89, No. 89, pp. 7962–7968.CrossRefGoogle Scholar
  17. Gürkan, O. (1978): Astrogeodetic network distortions and Turkish first order triangulation network. KT, Trabzon (In Turkish).Google Scholar
  18. Kearsley, A.H.W., (1988): Tests on the recovery of precise geoid height differences from gravimetry. JGR, Vol. 93, No. 86, pp.6559–6570.CrossRefGoogle Scholar
  19. Kearsley, A.H.W., M.G. Sideris, J.Krynski, R.Forsberg, K.P.Schwarz (1985): White sands revisited. A comparison of techniques to predict deflections of the vertical. UCSE, Rept. No. 3007, Calgary.Google Scholar
  20. Kearsley, A.H.W., R. Forsberg (1990): Tailored geopotential models applications and shortcomings. Manuscripta Geodaetica, Vol. 15, No.3, pp.151–158.Google Scholar
  21. Knudsen, P. (1987): Estimation and modelling of the local empirical covariance function using gravity and satellite altimeter data. Bull. Geod., Vol. 61, No. 2, pp 145–160.CrossRefGoogle Scholar
  22. Knudsen, P. (1989): Determination of local empirical covariance functions from residual terrain reduced altimeter data. OSU, Dept. of Geod. Sci., Rept. No. 395, Columbus.Google Scholar
  23. Lachapelle, G., C.C. Tscherning (1978): Use of collocation for predicting geoid undulations and related quantities over large areas. Proc. of the Int. Sym. on the geoid in Europe and Mediterranean Area, Ancona, pp. 133–152.Google Scholar
  24. Moritz, H. (1980): Advanced physical geodesy. Herbert Wichmann Verlag, Karlsruhe.Google Scholar
  25. Rapp, R.H. (1986): Global potential solutions. (In: Mathematical and numerical techniques in physical geodesy. Ed.H.Sünkel, Springer Verlag, pp.365–415).Google Scholar
  26. Rapp. R.H., M.Kadir (1988): A preliminary geoid for the state of Tennesse. Surveying and Mapping. Vol. 48, No.4, pp.251–260.Google Scholar
  27. Schwarz, K.P. (1985): Data types and their spectral properties. (In: Local gravity field approximation. Ed.K.P. Schwarz, UCSE, Pub. 60003, pp.1–66).Google Scholar
  28. Schwarz, K.P, G.Lachapelle (1980): Local characteristic of the gravity anomaly covariance function. Bull. Geod., Vol. 54, No.1, pp.21–26.CrossRefGoogle Scholar
  29. Schwarz,K.P, M.G. Sideris (1985): Precise geoid heights and their use in GPS-interferometry. Geodetic survey of Canada, Dept.of Energy, Mines and Resources, Ottowa.Google Scholar
  30. Schwarz, K.P., M.G.Sideris, R.Forsberg (1987): Orthometric heights without levelling Jour. of Surv. Eng., Vol. 113, No.1, pp. 28–40.CrossRefGoogle Scholar
  31. Sideris, M.G., K.P.Schwarz (1986): Improvements of medium and short wavelength features of geopotential solutions by local data. Proc. of the Int. Syp. on the Definition of the Geoid, 26–30 May, Florence.Google Scholar
  32. Sünkel, H. (1979): A covariance approximation procedure. OSU, Dept. of Geod. Sci., Rept. No. 286, Columbus.Google Scholar
  33. Sünkel, H., N.Bartelme, H.Fuchs. M.Hanafy, W. D.Schuh, M.Wieser (1987): The gravity field in Austria. IUGG XIX General Assembly, Proc. of the IAG Sym. Vol.2, pp. 475–503.Google Scholar
  34. Torge, W., T.Basic, H.Denker, I.Dolift, H.- G.Wenzel(1989): Long range geoid control throught the Europen GPS traverse. DGK, Reihe B, Heft Nr.290.Google Scholar
  35. Tscherning, C.C. (1974): A Fortran IV program for the determination of the anomalous potential using stepwise least squares collocation. OSU, Dept. of Geod. Sci., Rept. No. 212, Columbus.Google Scholar
  36. Tscherning, C.C. (1981): Comparison of some methods for the detailed representation of the Earths gravity field. Rev. Geophys. Space Phys., Vol. 19, No.1, pp.213–221.CrossRefGoogle Scholar
  37. Tscherning, C.C. (1982): Geoid determination for the Nordic Countries using collocation. Proc. of the IAG General Meeting, Tokyo, pp. 472-483.Google Scholar
  38. Tscherning, C.C. (1985): Local approximation of the gravity potantial by least squares collocation (In: Local gravity field approximation. Ed. by K.P. Schwarz, UCSE, Pub. 60003, pp. 277–261).Google Scholar
  39. Tscherning, C.C., R.H. Rapp (1974): Closed covariance expressions for gravity anomalies, geoid undulations, and deflections of the vertical implied by anomaly degree variance models. OSU, Dept. of Geod. Sci. Rept. No. 208, Columbus.Google Scholar
  40. Tscherning, C.C., R.Forsberg (1987): Geoid determination in the Nordic Countries from gravity and height data. Boll. Sci. Aff., 46, No. 1, pp. 21–43.Google Scholar
  41. Tziavos, I.N. (1987): Determination of geoidal heights and deflections of the vertical for the Hellenic area using heterogenous data. Bull. Geod. Vol. 61, No.2, pp.177–197.CrossRefGoogle Scholar
  42. Vanicek, P., A.Klausberg (1987): The Canadian geoid Stokesian approach. Manuscripta Geodaetica, Vol.12, No.2, pp.86–98.Google Scholar
  43. Weber, G., H.Zomorrodian (1988): Regional geopotantial model improvement for the Iranian geoid determination. Bull. Geod. Vol. 62, No.2, pp.125–145.CrossRefGoogle Scholar
  44. Wenzel, H.-G. (1985): Hochauflπsende Kugelfunktionsinodelle für das Gravitationspotantial der Erde. Wiss. Arb. Der Fachrichtung Vermessungwesen der Universitat Hannover, No. 137, Hannover.Google Scholar

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • M. Emin Ayhan
    • 1
  1. 1.Geodetic DepartmentGeneral Command of MappingCebeciTurkey

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