IGFS 2014 pp 161-168 | Cite as

Egyptian Geoid Using Best Estimated Response of the Earth’s Crust due to Topographic Loads

  • Hussein A. Abd-ElmotaalEmail author
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 144)


In this paper, the Egyptian gravimetric geoid is computed using the best estimated response of the earth’s crust due to the topographic loads. It has been proved that both the inverse isostasy approach and the direct isostasy approach (with Kelvin function \(\mathop{\mathrm{kei}}\nolimits x\)) give practically the same response of the earth’s crust due to topographic loads. The window remove-restore technique (Abd-Elmotaal and Kühtreiber, J Geod 77(1–2):77–85, 2003) has been used to avoid the double consideration of some of the topographic-isostatic masses in the neighbourhood of the computational point. The tailored geopotential model EGTGM2014 (Abd-Elmotaal, Egyptian geoid using ultra high-degree tailored geopotential model. Proceedings of the 25th international federation of surveyors FIG congress, 2014) has been used for the long wavelength contributions of the earth’s gravity field. The gravimetric geoid is computed for Egypt using Stokes’ integral in the frequency domain by 1-D FFT technique. For the sake of comparison, another geoid for Egypt using EGM2008 and Airy floating hypothesis has been computed. The computed geoids are scaled/fitted to the GPS-levelling derived geoid. The internal precision of the computed geoids is almost the same and it is at the level of 3 cm. The external accuracy of the geoid computed by the best estimated response of the earth’s crust is better by 4 dm.


Egypt Geoid Isostasy Kelvin function Tailored geopotential model 



This project was supported financially by the Science and Technology Development Fund (STDF), Egypt, Grant No. 366.


  1. Abd-Elmotaal HA (1991) Gravity anomalies based on the Vening Meinesz isostatic model and their statistical behaviour. Mitteilungen der geodätischen Institute der Technischen Universtät Graz 72Google Scholar
  2. Abd-Elmotaal HA (1993) Vening Meinesz Moho depths: traditional, exact and approximated. Manuscr Geodaet 18(4):171–181Google Scholar
  3. Abd-Elmotaal HA (1998) An alternative capable technique for the evaluation of geopotential from spherical harmonic expansions. Boll Geod Sci Affini 57(1):25–38Google Scholar
  4. Abd-Elmotaal HA (2003) Implementing seismic Moho depths in geoid computation. Surv Rev 37(289):235–245CrossRefGoogle Scholar
  5. Abd-Elmotaal HA (2004) Isostatic response of the earth’s crust derived by inverse isostasy. J Geodyn 37(2):139–153. doi:10.1016/j.jog.2004.01.002 CrossRefGoogle Scholar
  6. Abd-Elmotaal HA (2013) Behaviour of earth’s crust due to topographic loads derived by inverse and direct isostasy. NRIAG J Astron Geophys 2:196–202. doi:10.1016/j.nrjag.2013.12.005 CrossRefGoogle Scholar
  7. Abd-Elmotaal HA (2014) Egyptian geoid using ultra high-degree tailored geopotential model. In: Proceedings of the 25th international federation of surveyors FIG congress, Kuala Lumpur, 16–21 June 2014.
  8. Abd-Elmotaal HA, Abd-Elbakhy M, Ashry M (2013) 30 Meters digital height model for Egypt. In: VIII Hotine-Marussi symposium, Rome, 17–22 June 2013Google Scholar
  9. Abd-Elmotaal HA, Kühtreiber N (1999) Improving the geoid accuracy by adapting the reference field. Phys Chem Earth Pt A 24(1):53–59CrossRefGoogle Scholar
  10. Abd-Elmotaal HA, Kühtreiber N (2003) Geoid determination using adapted reference field, seismic Moho depths and variable density contrast. J Geod 77(1–2):77–85CrossRefGoogle Scholar
  11. Abramowitz M, Stegun IA (1965) Handbook of mathematical functions, with formulas, graphs, and mathematical tables. Dover Publications, New YorkGoogle Scholar
  12. Bechtel TD, Forsyth DW, Swain CJ (1987) Mechanisms of isostatic compensation in the vicinity of the east African rift, Kenya. Geophys J Roy Astron Soc 90:445–465CrossRefGoogle Scholar
  13. Brotchie JF, Silvester R (1969) On crustal flexure. J Geophys Res 74:5240–5252CrossRefGoogle Scholar
  14. Dorman LM, Lewis BTR (1970) Experimental isostasy: 1. Theory of the determination of the earth’s isostatic response to a concentrated load. J Geophys Res 75:3357–3365Google Scholar
  15. Forsberg R (1984) A study of terrain reductions, density anomalies and geophysical inversion methods in gravity field modelling. Ohio State University, Department of Geodetic Science and Surveying, Rep 355Google Scholar
  16. Haagmans R, de Min E, van Gelderen M (1993) Fast evaluation of convolution integrals on the sphere using 1D FFT, and a comparison with existing methods for Stokes’ integral. Manuscr Geodaet 18(4):227–241Google Scholar
  17. Hein GW, Eissfeller B, Ertel M, Hehl K, Jacoby W, Czerwek D (1989) On gravity prediction using density and seismic data. Institute of Astronomical and Physical Geodesy, University FAF MunichGoogle Scholar
  18. Lewis BTR, Dorman LM (1970) Experimental isostasy: 2. An isostatic model for the USA derived from gravity and topographic data. J Geophys Res 75:3367–3386Google Scholar
  19. Moritz H (1990) The figure of the Earth: theoretical geodesy and the Earth’s interior. Wichmann, KarlsruheGoogle Scholar
  20. Pavlis N, Holmes S, Kenyon S, Factor J (2012) The development and evaluation of the earth gravitational model 2008 (EGM2008). J Geophys Res 117(B04406). doi:10.1029/2011JB008916
  21. Rapp RH (1982) A Fortran program for the computation of gravimetric quantities from high degree spherical harmonic expansions. Ohio State University, Department of Geodetic Science, Rep 334Google Scholar
  22. Sideris MG, Li YC (1993) Gravity field convolutions without windowing and edge effects. Bull Geod 67(2):107–118. doi:10.1007/BF01371374 CrossRefGoogle Scholar
  23. Tscherning CC, Knudsen P, Forsberg R (1994) Description of the GRAVSOFT package. Geophysical Institute, University of Copenhagen, Technical ReportGoogle Scholar
  24. Turcotte DL, Schubert G (1982) Geodynamics: applications of continuum physics to geological problems. Wiley, New YorkGoogle Scholar
  25. Vening Meinesz FA (1940) Fundamental tables for regional isostatic reduction of gravity values. Publ Netherlands Acad Sci, sec 1 DI. 17(3):1–44Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Civil Engineering DepartmentFaculty of Engineering, Minia UniversityMiniaEgypt

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