Abstract
A precise gravimetric geoid model is determined by using Stokes formula assuming that there is no topography above the geoid. Then, the geoid model is simply corrected by considering the constant crustal density of 2670 kg m−3 for topographical mass. In fact, the actual density of topographical mass differs about ±20% from the constant value. Recently a global crustal density model within 30″ resolution has been released by the University of New Brunswick in Canada. The paper is devoted to the study of the effect of using this model on the accuracy of gravimetric geoid in a mountainous region in Turkey. Numerical results prove that the differences in the geoid height due to this model may reach up to several decimetres, which should not be ignored in a precise geoid modelling with 1-cm geoid. Thus, it is concluded that the effect of topographical density variations, contained in this model, is significant and should be taken into account in precise geoid determination, particularly in mountainous regions.
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Abbak R.A. and Ustun A., 2015. A software package for computing a regional gravimetric geoid model by the KTH method. Earth Sci. Inform., 8, 255–265.
Abbak R.A., Erol B. and Ustun A., 2012a. Comparison of the KTH and remove-compute-restore techniques to geoid modelling in a mountainous area. Comput. Geosci, 48, 31–40.
Abbak R.A., Sjöberg L.E., Ellmann A. and Ustun A., 2012b. A precise gravimetric geoid model in mountainous areas with scarce gravity data: A case study in central Turkey. Stud. Geophys. Geod., 56, 909–927.
Ågren J., Sjöberg L.E. and Kiamehr R., 2009. The new gravimetric quasigeoid model KTH08 over Sweden. J Appl. Geodesy, 3, 143–159.
Akyilmaz O., Ustun A., Aydin C., Arslan N., Doganalp S., Guney C., Mercan H., Uygur S.O., Uz M. and Yagci O., 2016. High Resolution Gravity Field Modelling and Tracking Regional Mass by Means of Low Earth Orbit Satellites. Technical Report, Project No. 113Y155, Technical University of Istanbul, Istanbul, Turkey.
Amante C. and Eakins B., 2009. ETOPO1: 1 Arc-Minute Global Relief Model: Procedures, Data Sources and Analysis. NOAA Technical Memorandum NESDIS NGDC-24, National Geophysical Data Center, https://www.ngdc.noaa.gov/mgg/global/.
Bildirici I.O. and Abbak R.A., 2017. Comparison of ASTER and SRTM digital elevation models at one-arc-second resolution over Turkey. Selcuk Univ. J. Eng. Sci. Technol, 5, 16–25.
Bildirici I.O., Ustun A., Selvi H.Z., Abbak R.A. and Bugdayci I., 2009. Assessment of shuttle radar topography mission elevation data based on topographic maps in Turkey. Cartogr. Geogr. Inf. Sci., 36, 95–104.
Ellmann A. and Sjöberg L.E., 2004. Ellipsoidal correction for the modified Stokes formula. Boll. Geod. Sci. Affin., 63, 153–172.
Farahani H.H., Slobbe D.C., Klees R. and Seitz K., 2017. Impact of accounting for coloured noise in radar altimetry data on a regional quasigeoid model. J. Geodesy, 91, 97–112.
Farr T.G., Rosen P.A., Caro E., Crippen R., Duren R., Hensley S., Kobrick M., Paller M., Rodriguez E., Roth L., Seal D., Shaffer S Shimada J., Umland J., Werner M., Oskin M., Burbank D. and Alsdorf D., 2007. The Shuttle Radar Topography Mission. Rev. Geophys., 45, RG2004, doi:10.1029/2005RG000183.
Featherstone W.E., Lyon T.J. and Mccubbine J.C., 2019. Potentially misleading GPS leveling-based assessment of gravimetric geoid or quasigeoid models due to vertical land motion and different GPS processing software. J. Surv. Eng.-ASCE, 145, 04019015.
Foroughi I., Vaníček P., Kingdon R.W., Goli M., Sheng M., Afrasteh Y., Novák P. and Santos M.C., 2019. Sub-centimetre geoid. J. Geodesy, 93, 849–868.
Harkness W., 2012. The Solar Parallax and Its Related Constants: Including the Figure and Density of the Earth. Nabu Press, Charleston, SC.
Hofmann-Wellenhof B. and Moritz H., 2005. Physical Geodesy. Springer-Verlag, Wien, Austria.
Huang J., Vaníček P., Pagiatakis S.D. and Brink W., 2001. Effect of topographical density on geoid in the Canadian Rocky Mountains. J. Geodesy, 74, 805–815.
Kiamehr R., 2006a. A strategy for determining the regional geoid by combining limited ground data with satellite-based global geopotential and topographical models: a case study of Iran. J. Geodesy, 79, 602–612.
Kiamehr R., 2006b. The impact of lateral density variation model in the determination of precise gravimetric geoid in mountainous areas: a case study of Iran. Geophys. J. Int., 167, 521–527.
Kotsakis C. and Sideris M.G., 1999. On the adjustment of combined GPS/levelling/geoid networks. J. Geodesy, 73, 412–421.
Kuhn M., 2003. Geoid determination with density hypotheses from isostatic models and geological information. J. Geodesy, 77, 50–65.
Laske G., Masters G., Ma Z. and Pasyanos M., 2012. CRUST 1.0: An updated global model of Earth’s crust. Geophysical Research Abstracts, 14, EGU2012-3743-1.
Laske G., Ma Z., Masters G. and Pasyanos M., 2013a. CRUST 1.0: A new global crustal model at 1 × 1 degree. https://igppweb.ucsd.edu/gabi/crust1.html.
Laske G., Ma Z. Masters G. and Pasyanos M., 2013b. CRUST 2.0: A new global crustal model at 2 × 2 degree.https://igppweb.ucsd.edu/gabi/crust2.html.
Laske G., Ma Z., Masters G. and Pasyanos M., 2013c. CRUST 5.1: A new global crustal model at 5 × 5 degree. https://igppweb.ucsd.edu/gabi/crust.html.
Martinec Z., 1993. Effect of Lateral Density Variations of Topographical Masses in Improving Geoid Model Accuracy over Canada. Technical Report. Project No. 23244-2-4356, University of New Brunswick, Canada.
Sheng M.B., Shaw C., Vaníček P., Kingdon R.W., Santos M. and Foroughi I., 2019. Formulation and validation of a global laterally varying topographical density model. Tectonophysics, 762, 45–60.
Sjöberg L.E., 1984. Least Squares Modification of Stokes and Vening-Meinesz Formulas by Accounting for Errors of Truncation, Potential Coefficients and Gravity Data. Technical Report. Department of Geodesy, Institute of Geophysics, University of Uppsala, Sweden.
Sjöberg L.E., 1991. Refined least squares modification of Stokes’ formula. Manuscripta Geodaetica, 16, 367–375.
Sjöberg L.E., 1999. The IAG approach to the atmospheric geoid correction in Stokes’ formula and a new strategy. J. Geodesy, 73, 362–366.
Sjöberg L.E., 2003a. A general model of modifying Stokes’ formula and its least squares solution. J. Geodesy, 77, 790–804.
Sjöberg L.E., 2003b. A solution to the downward continuation effect on the geoid determination by Stokes’ formula. J. Geodesy, 77, 94–100.
Sjöberg L.E., 2004. The effect on the geoid of lateral topographic density variations. J. Geodesy, 78, 34–39.
Sjöberg L.E., 2007. The topographic bias by analytical continuation in physical geodesy. J. Geodesy, 81, 345–350.
Sloss P.W., 1988. ETOPO 5: A new global topography model at 5 × 5 arc-mins. https://www.ngdc.noaa.gov/mgg/global/etopo5.html.
Stokes G.G., 1849. On the variations of gravity on the surface of the Earth. Trans. Cambridge Phil. Soc., 8, 672–695.
Ustun A. and Abbak R.A., 2010. On global and regional spectral evaluation of global geopotential models. J. Geophys. Eng., 7, 369–370.
Yildiz H., Forsberg R., Ågren J., Tscherning C.C. and Sjöberg L.E., 2012. Comparison of remove-compute-restore and least squares modification of Stokes’ formula techniques to quasi-geoid determination over the Auvergne test area. J. Geod. Sci., 2, 53–64.
Acknowledgments
The author thanks to Assoc. Prof. Dr. Rahmi Aksoy at Geology Department at Konya Technical University for his beneficial discussion during the compilation of the manuscript. The gravity and GNSS-levelling data were provided by two projects funded by the Research Fund of Selcuk University in Turkey under grants 09-101-009 and 17-401-084.
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Computer code availability: The software exploited in the present study was developed in C programming language, which is freely available under the license of GNU public. Interested readers can obtain the software with experimental data from the author. In order to learn how it works, please see Abbak and Ustun (2015). Inquiries and bug reports about the software are welcome to the author.
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Abbak, R.A. Effect of a high-resolution global crustal model on gravimetric geoid determination: a case study in a mountainous region. Stud Geophys Geod 64, 436–451 (2020). https://doi.org/10.1007/s11200-020-1023-z
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DOI: https://doi.org/10.1007/s11200-020-1023-z