A precise gravimetric geoid model in a mountainous area with scarce gravity data: a case study in central Turkey
- 304 Downloads
In mountainous regions with scarce gravity data, gravimetric geoid determination is a difficult task that needs special attention to obtain reliable results satisfying the demands, e.g., of engineering applications. The present study investigates a procedure for combining a suitable global geopotential model and available terrestrial data in order to obtain a precise regional geoid model for Konya Closed Basin (KCB). The KCB is located in the central part of Turkey, where a very limited amount of terrestrial gravity data is available. Various data sources, such as the Turkish digital elevation model with 3 ″ × 3″ resolution, a recently published satellite-only global geopotential model from the Gravity Recovery and Climate Experiment satellite (GRACE) and the ground gravity observations, are combined in the least-squares sense by the modified Stokes’ formula. The new gravimetric geoid model is compared with Global Positioning System (GPS)/levelling at the control points, resulting in the Root Mean Square Error (RMS) differences of ±6.4 cm and 1.7 ppm in the absolute and relative senses, respectively. This regional geoid model appears to be more accurate than the Earth Gravitational Model 2008, which is the best global model over the target area, with the RMS differences of ±8.6 cm and 1.8 ppm in the absolute and relative senses, respectively. These results show that the accuracy of a regional gravimetric model can be augmented by the combination of a global geopotential model and local terrestrial data in mountainous areas even though the quality and resolution of the primary terrestrial data are not satisfactory to the geoid modelling procedure.
Keywordsgeoid KTH method Konya Closed Basin least-squares modification Stokes’ formula
Unable to display preview. Download preview PDF.
- Ayhan M.E., Demir C., Lenk O., Kılıçoğlu A., Aktug B., Acikgoz M., Firat O., Sengun Y.S., Cingoz A., Gurdal M.A., Kurt A.I., Ocak M., Turkezer A., Yildiz H., Bayazit N., Ata M., Caglar Y. and Ozerkan A., 2002. Turkish National Fundamental GPS Network; 1999A (TUTGA-99A), Turkish Journal of Mapping (Harita Dergisi), Special Issue 16, (in Turkish).Google Scholar
- Bildirici I.O., Ustun A., Ulugtekin N., Selvi H.Z., Abbak R.A., Bugdayci I. and Dogru A.O., 2009. Compilation of digital elevation model for Turkey in 3-arc-second resolution by using SRTM data supported with local elevation data. In: Gartner G. and Ortag F. (Eds.), Cartography in Central and Eastern Europe. Lecture Notes in Geoinformation and Cartography. Springer-Verlag, Heidelberg, Germany, 63–76.CrossRefGoogle Scholar
- Ellmann A., 2004. The Geoid for the Baltic Countries Determined by the Least Squares Modification of Stokes Formula. Ph.D. Thesis, Royal Institute of Technology (KTH), Division of Geodesy, Stockholm, Sweden.Google Scholar
- Ellmann A. and Sjöberg L.E., 2004. Ellipsoidal correction for the modified Stokes’ formula. Boll. Geod. Sci. Aff., 63, 153–172.Google Scholar
- Flechtner F., Dahle C., Neumayer K.H., König R. and Förste C., 2010. The Release 04 CHAMP and GRACE EIGEN gravity field models. In: Flechtner F.M., Gruber Th., Güntner A., Mandea M., Rothacher M., Schöne T. and Wickert J. (Eds.), System Earth via Geodetic-Geophysical Space Techniques. Advanced Technologies in Earth Sciences. Springer-Verlag, Heidelber, Germany, 41–58, ISBN 978-3-642-10227-1, DOI 978-3-642-10228-8.CrossRefGoogle Scholar
- Heiskanen W.A. and Moritz H., 1967. Physical Geodesy. W.H. Freeman and Co., London, U.K.Google Scholar
- Kiamehr R., 2006. Precise Gravimetric Geoid Model for Iran Based on GRACE and SRTM Data and the Least Squares Modification of the Stokes’ Formula with Some Geodynamic Interpretations. Ph.D. Thesis. Royal Institute of Technology (KTH), Department of Transport and Economics, Stockholm, Sweden.Google Scholar
- Kiamehr R., 2007. Qualification and refinement of the gravity database based on cross-validation approach. A case study of Iran. Acta Geod. Geophys. Hung., 42, 195–195.Google Scholar
- Krige D.G., 1951. A statistical approach to some basic mine valuation problems on the Witwatersrand. J. Chem. Metall. Min. Soc. S. Afr., 52(6), 119–139, DOI: 10.2307/3006914.Google Scholar
- Martinec Z., 1998. Boundary-Value Problems for Gravimetric Determination of a Precise Geoid. Springer-Verlag, Berlin, Germany.Google Scholar
- Mayer-Guerr T., Kurtenbach E. and Eicker A., 2010. ITG-Grace2010 Gravity Field Model. http://www.igg.uni-bonn.de/apmg/index.php?id=itg-grace2010.
- Meissl P., 1971. A Study of Covariance Functions from Discrete Mean Value. Report No.151, Department of Geodetic Sciences, Ohio State University, Columbus, USA.Google Scholar
- Molodensky M.S., Yeremeev V.F. and Yurkina M.I., 1960. Methods for study of the external gravitational field and figure of the Earth. TRUDY Ts NIIGAiK, 131, Geodezizdat, Moscow (English translat.: Israel Program for Scientific Translation, Jerusalem 1962).Google Scholar
- Pavlis N.K., Holmes S.A., Kenyon S.C. and Factor J.K., 2008. An Earth Gravitational Model to Degree 2160: EGM2008. Geophysical Research Abstracts, 10, 2-2-2008. Full version released by National Geospatial-Intelligence Agency, Bethesda, MD, (http://www.dgfi.badw.de/typo3_mt/fileadmin/2kolloquium_muc/2008-10-08/Bosch/EGM2008.pdf).
- Sjöberg L.E., 1981. Least squares combination of satellite and terrestrial data in physical geodesy. Ann. Geophys., 37, 25–30.Google Scholar
- Sjöberg L.E., 1984. Least-Squares Modification of Stokes and Venning-Meinesz Formulas by Accounting for Errors of Truncation, Potential Coeffcients and Gravity Data. Technical Report, Department of Geodesy, Institute of Geophysics, University of Uppsala, Uppsala, Sweden.Google Scholar
- Sjöberg L.E., 1991. Refined least squares modification of Stokes formula. Manuscripta Geodaetica, 16, 367–375.Google Scholar
- Sjöberg L.E., 2003b. A general model of modifying Stokes formula and its least squares solution. J. Geodesy, 77, 790–804.Google Scholar
- SRTM, 2010. http://www2.jpl.nasa.gov/srtm.
- TRDEM3, 2008. http://www.tsym3.selcuk.edu.tr.
- Ulotu P.E., 2009. Geoid Model of Tanzania from Sparse and Varying Gravity Data Density by the KTH Method. Ph.D. Thesis. Division of Transport and Economics, Royal Institute of Technology (KTH), Stockholm, Sweden.Google Scholar
- Vaníček P. and Kleusberg A., 1987. The Canadian geoid — Stokes approach. Manuscripta Geodaetica, 12, 86–98.Google Scholar
- Vincent S. and Marsch J., 1974. Gravimetric global geoid. In: Veis G. (Ed.), Proceedings of International Symposium on the Use of Artificial Satellites for Geodesy and Geodynamics. National Technical University, Athens, Greece.Google Scholar