Comparison of Different Approaches for Combining Gravity Field Wavelengths for Egypt

Abd-Elmotaal, Hussein; Ashry, Mostafa; Makhloof, Atef

doi:10.21608/jesaun.2023.246329.1283

Comparison of Different Approaches for Combining Gravity Field Wavelengths for Egypt

Document Type : Research Paper

Authors

¹ Professor, Civil Engineering Dept., Faculty of Engineering, Minia University, Minia, Egypt

² Lecturer, Civil Engineering Dept., Faculty of Engineering, Minia University, Minia, Egypt

³ Assoc. Prof., Civil Engineering Dept., Faculty of engineering, Minia University, Minia, Egypt

10.21608/jesaun.2023.246329.1283

Abstract

Within the context of the remove-restore technique, this research seeks to determine the best combination of gravity field wavelengths for Egypt’s geoid computation. There are various methods for such a wavelength combination. It has been proposed to merge the regional data signals and the global geopotential earth models, potentially using a modified Stokes’ kernel with various methods. Firstly, from our computations, it can be concluded that the conventional remove-restore technique should not be applied for the determination of gravity anomalies and geoid determination. Also, the outcomes demonstrated that the estimated gravity anomalies utilizing the window approach are independent, the finest, and unbiased and have a minimal difference between the maximum and minimum values. The geoid produced from the GPS levelling has fewer differences between it and the geoids computed using the modified Stokes’ kernels as well as the geoid determined using the window technique than in the case of utilizing the unmodified Stokes’ classical kernel. Finally, the window approach gives, however, completely better outcomes compared to the Stokes unmodified kernel method.

Keywords

Main Subjects

Civil Engineering: structural, Geotechnical, reinforced concrete and steel structures, Surveying, Road and traffic engineering, water resources, Irrigation structures, Environmental and sanitary engineering, Hydraulic, Railway, construction Management.

References

1. Abd-Elmotaal HA, Seitz K, Kühtreiber N, Heck B (2019) AFRgeo_v1.0: a geoid model for Africa. KIT Scientific Working Papers 125. https://doi.org/10.5445/IR/1000097013

2. Novák P, Vaniček P, Véronneau M, Holmes SA, Featherstone WE (2001) On the accuracy of modified Stokes's integration in high-frequency gravimetric geoid determination. J. Geod., 74, 644-654.

3. Sjöberg LE, Hunegnaw A (2000) Some modifications of Stokes’ formula that account for truncation and potential coefficient errors. J Geod 74:232–238.

4. Sjöberg LE (2003a) A computational scheme to model the geoid by the modified Stokes formula without gravity reactions. J Geod 77:423–432.

5. Sjöberg LE (2003b) A general model for modifying Stokes formula and its least-squares solution. J Geod 77:459–464.

6. Featherstone WE (1999) A comparison of gravimetric geoid models over western Australia, computed using modified forms of Stokes’ integral. Journal of the Royal Society of Western Australia 82:137–145.

7. Abd-Elmotaal HA, Ku¨htreiber N (2007) Modified Stokes ker- nel versus window technique: Comparison of optimum combination of gravity field wavelengths in geoid computation.

8. Sjöberg LE (2004) A spherical harmonic representation of the ellipsoidal correction to the modified Stokes formula. J Geod 78:180–186.

9. Abd-Elmotaal HA (2007) Reference geopotential models tailored to the Egyptian gravity field. Boll Geod Sci Affini 66(3):129–144.

10. Silva MA, Blitzkow D, Lobianco MCB (2002) A case study of different modified kernel applications in quasi-geoid determination. Proceedings of the 3rd Meeting of the International Gravity and Geoid Commission, Thessaloniki, Greece, August 26-30, pp 138–143.

11. Featherstone WE (2003) Software for computing five existing types of deterministically modified integration kernel for gravimetric geoid determination. Comput Geosci 29:183– 193.

12. Novák P, Vaníček P, V´eronneau M, Holmes S, Featherstone WE (2001) On the accuracy of modified Stokes integration in high-frequency gravimetric geoid determination. J Geod 74:644–654.

13. Abd-Elmotaal HA, Ku¨htreiber N (2008) An attempt towards an optimum combination of gravity field wavelengths in geoid computation. Observing our Changing Earth, J IAGS 133:203–209, DOI 10.1007/978-3-540-85426-5 24.

14. Pail R, Bruinsma S, Migliaccio F, Förste C, Goiginger H, Schuh W, Höck E, Reguzzoni M, Brockmann J, Abrikosov O, Veicherts M, Fecher T, Mayrhofer R, Krasbutter I, Sansó F, Tscherning C (2011) First GOCE gravity field models derived by three different approaches. J Geod 85(11):819–843, DOI 10.1007/s00190-011-0467-x.

15. Abd-Elmotaal HA, Makhloof A (2013) Gross-errors detection in the shipborne gravity data set for Africa. Presented at Geodetic Week, Essen, Germany, October 8-10, 2013 2013.

16. Abd-Elmotaal HA and Makhloof A (2013) Comparison of Recent Geopotential Models for the Recovery of the Gravity Field in Egypt. Geodetic week conference 8-11 Oktober 2013.

17. Abd-Elmotaal HA, Abd-Elbaky M, Ashry M (2013) 30 meters digital height model for. VIII Hotine-Marussi Symposium, Rome, Italy, June 17–22, 2013.

18. Abd-Elmotaal HA, Kühtreiber N (2003) Geoid determination using adapted reference field, seismic Moho depths, and variable density contrast. J Geod 77(1-2):77–85.

19. Abd-Elmotaal HA, Ashry M (2013) The 3′′ digital height model for Egypt - egh13. 8th International Conference of Applied Geophysics, Cairo, Egypt, February 25-26, 2013.

20. Forsberg R (1993) Modelling the fine structure of the geoid: methods, data requirements, and some results. Surv Geo- phys 14:403–418.

21. Sansó F (1997) Lecture notes: Int school for the determination and use of the geoid. Int Geoid Service, DIIAR-Politecnico diMilano, Milan.

22. Rapp R, Rummel R (1975) Methods for the computation of detailed geoids and their accuracy. Ohio State University, Department of Geodetic Science and Surveying, Rep 233.

23. Vincent S, Marsh J (1974) Gravimetric global geoid. In: Veis G (ed) Proc Int Symp on the use of artificial satellites for geodesy and geodynamics, Athens.

24. Heiskanen WA, Moritz H (1967) Physical Geodesy. Freeman, San Francisco.

25. Molodenesky MS, Eremeev VF, Yurkina MI (1962) Meth- odes for the study of the external gravitational field and figure of the Earth. Israel Program for Scientific Translations, Jerusalem.

26. Meissl P (1971) Preparation for the numerical evaluation of second order Molodensky-type formulas. Ohio State University, Department of Geodetic Science and Surveying, Rep 163.

27. Wong L, Gore R (1969) Accuracy of geoid heights from modified Stokes kernels. Geophys J R Astr Soc 18(1):81–91.

28. Vaníček P, Featherstone WE (1998) Performance of three types of Stokes’ kernel in the combined solution for the geoid. J Geod 72:684–697.

29. Featherstone WE, Evans JD, Olliver JG (1998) A Meissl- modified Vaníček and Kleusberg kernel to reduce the truncation error in geoid computations. J Geod 72:154–160.

30. Grombein T, Seitz K (2010) Die stokes-funktion und modifizierte kernfunktionen. Vernetzt und ausgeglichen: Festschrift zur Verabschiedung von Prof Dr-Ing habil Dr- Ing Eh Günter Schmitt p 89.

31. Colombo O (1981) Numerical methods for harmonic analysis on the sphere. Ohio State University, Department of Geodetic Science and Surveying, Rep 310.

32. Heck B, Seitz K (1991) Harmonische Analyse. Technical Report, Geodetic Institute, University of Karlsruhe.

33. Abd-Elmotaal HA (2004) An efficient technique for harmonic analysis on a spheroid (ellipsoid and sphere). VGI 3(4):126–135.

34. Heck B, Gru¨ninger W (1987) Modification of Stokes’s integral formula by combining two classical approaches. Proceedings of the XIX General Assembly of the IUGG, Vancouver, Canada 2:309–337.

35. Featherstone W, Kirby J, Hirt C, Filmer M, Claessens S, Brown N, Hu G, Johnston G (2011) The AUSGeoid09 model of the Australian height datum. J Geod 85(3):133– 150.

36. Claessens SJ, Hirt C, Amos M, Featherstone W, Kirby J (2011) The NZGEOID09 model of New Zealand. Surv Rev 43(319):2–15.

37. Hanafy M (1987) Gravity field data reduction using height, density, and Moho information. Ph.D. Dissertation, Institute of Theoretical Geodesy, Graz University of Technology.

38. Sünkel H (1985) An isostatic earth model. Ohio State University, Department of Geodetic Science and Surveying, Rep 367.

39. Rummel R, Rapp R, Sünkel H, Tscherning C (1988) Comparison of global topographic/isostatic models to the Earth’s observed gravity field. Ohio State University, Department of Geodetic Science and Surveying, Rep 388.

40. Abd-Elmotaal HA (2008) Gravimetric geoid for Egypt using high-degree tailored reference geopotential model. NRIAG Journal of Geophysics, Special Issue pp 507–531.

41. Abd-Elmotaal HA (2014) Egyptian geoid using ultra high-degree tailored geopotential model. In: Proceedings of the XXV FIG Congress, Kuala Lumpur, Malaysia, June 16-21, 2014, URL http://www.fig.net/pub/fig2014/papers/ts02a/TS02.

42. Förste C, Bruinsma S, Flechtner F, Marty J, Lemoine J, Dahle C, Abrikosov O, Neumayer H, Biancale R, Barthelmes F, Balmino G (2012) A new release of eigen-6c. American Geophysical Union, Fall Meeting, San Francisco, USA, December 3-7, 2012.