Earth Science Informatics

, Volume 8, Issue 1, pp 255–265 | Cite as

A software package for computing a regional gravimetric geoid model by the KTH method

Software Article


Nowadays, the geodetic community has aimed to determine 1-cm accuracy gravimetric geoid model, which satisfies the demands of most engineering applications. However, the gravimetric geoid determination is a difficult mission which needs an exclusive attention to obtain reliable results for this purpose. Today, Least-Squares Modification of Stokes (LSMS) formula which is so-called the KTH method (Swedish Royal Institute of Technology) has been performed in the regional geoid studies. Based upon the earlier investigations, the KTH method provides more reasonable results than the Remove Compute Restore technique, especially in roughly terrain with sparse terrestrial gravity data. Nevertheless, a compact and practical software package is now not available for users and researchers in geosciences. Thus, in this paper, a scientific software called “LSMSSOFT” is developed and presented by adding a new algorithm which speeds up the evaluation of Stokes’ integral. Afterwards, the LSMSSOFT is applied to a case study for the construction of a geoid model over the Auvergne test area in France. Consequently, the algorithm treated in the software and its results imply that the LSMSSOFT is an alternative software package for modelling the gravimetric geoid by the KTH method.


Evaluation of Stokes’ integral Gravimetric geoid Modification of Stokes’ formula Software package Terrestrial gravity data 


  1. Abbak RA, Erol B, Ustun A (2012a) Comparison of the KTH and remove-compute-restore techniques to geoid modelling in a mountainous area. Comput Geosci 48:31–40CrossRefGoogle Scholar
  2. Abbak RA, Sjoberg LE, Ellmann A, Ustun A (2012b) A precise gravimetric geoid model in mountainous areas with scarce gravity data – a case study in Central Turkey. Studia Geophysica et Geodaetica 56:909–927CrossRefGoogle Scholar
  3. Ågren J, Sjöberg EL, Kiamehr R (2009) The new gravimetric quasigeoid model KTH08 over Sweden. J Appl Geodesy 3:143–153CrossRefGoogle Scholar
  4. Bjerhammar A (1973) Theory of errors and generalized matrix inverses. Elsevier, AmsterdamGoogle Scholar
  5. Duquenne H (2007) A data set to test geoid computation methods. Harita Dergisi. Special Issue. pp 61–65Google Scholar
  6. Ecker E, Mittermayer E (1969) Gravity corrections for the influence of the atmosphere. Boll Geofis Teor Appl 11:70–80Google Scholar
  7. Ellmann A (2004) The geoid for the baltic countries determined by the least squares modification of Stokes formula. PhD thesis. Royal Institute of Technology (KTH). Division of Geodesy, StockholmGoogle Scholar
  8. Ellmann A (2005a) Computation of three stochastic modifications Stokes formula for regional geoid determination. Comput Geosci 31(/6):742–755CrossRefGoogle Scholar
  9. Ellmann A (2005b) Two deterministic and three stochastic modifications of Stokes’ formula: a case study for the Baltic countries. J Geodesy 79:11–23CrossRefGoogle Scholar
  10. Ellmann A, Sjöberg LE (2004) Ellipsoidal correction for the modified Stokes formula. Boll Geod Sci Aff 63:3Google Scholar
  11. Huang J, Vaníček P, Novak P (2000) An alternative algorithm to FFT for the numerical evaluation of Stokes’s integral. Studia Geophysica et Geodaetica 44:374–380CrossRefGoogle Scholar
  12. Janak J, Vaníček P (2005) Mean free-air gravity anomalies in the mountains. Studia Geophysica et Geodaetica 49:31–42CrossRefGoogle Scholar
  13. 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. PhD thesis, royal institute of technology (KTH). Department of transport and economics, StockholmGoogle Scholar
  14. Kiamehr R, Sjöberg EL (2010) KTH-GEOLAB scientific software for precise geoid determination based on the least-squares modification of Stokes’ formula. Royal institute of technology (KTH), Division of geodesy, Stockholm. Technical manualGoogle Scholar
  15. Kotsakis C, Sideris MG (1999) On the adjustment of combined GPS/levelling/geoid networks 73(8):412–421Google Scholar
  16. Mayer-Guerr T, Kurtenbach E, Eicker A (2010) ITG-Grace2010 gravity field model.
  17. Meissl P (1971) A study of covariance functions from discrete mean value. Technical report, Dept. Geod. Sci. Ohio State University, ColumbusGoogle Scholar
  18. Molodensky MS, Eremeev VF, Yurkina MI (1962) Methods for study of the external gravity field and figure of the Earth. Israel program for scientific translationGoogle Scholar
  19. Pavlis NK, Holmes SA, Kenyon SC, Factor JK (2012) The development and evaluation of the earth gravitational model 2008 (EGM2008). J Geophys Res Solid Earth 117:38CrossRefGoogle Scholar
  20. Press WH, Teukolsky SA, Vetterling WT, Flannery BP (2007) Numerical recipes: the art of scientific computing. Cambridge University Press, New YorkGoogle Scholar
  21. Sjöberg LE (1981) Least squares combination of satellite and terrestrial data in physical geodesy. Ann Geophys 37(1):25–30Google Scholar
  22. Sjöberg LE (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 UppsalaGoogle Scholar
  23. Sjöberg LE (1991) Refined least squares modification of Stokes formula. Manuscripta Geodaetica 16:367–375Google Scholar
  24. Sjöberg LE (1999) The iag approach to the atmospheric geoid correction in Stokes’ formula and a new strategy. J Geodesy 73:362–366CrossRefGoogle Scholar
  25. Sjöberg LE (2003a) A general model of modifying Stokes formula and its least squares solution. J Geodesy 77:790–804Google Scholar
  26. Sjöberg LE (2003b) A solution to the downward continuation effect on the geoid determination by Stokes formula. J Geodesy 77:94–100CrossRefGoogle Scholar
  27. Sjöberg LE (2007) The topographic bias by analytical continuation in physical geodesy. J Geodesy 87:345–350CrossRefGoogle Scholar
  28. Sjöberg LE, Hunegnaw A (2000) Some modifications of Stokes’ formula that account for truncation and potential coefficient errors. J Geodesy 74:232–238CrossRefGoogle Scholar
  29. Ulotu PE (2009) Geoid model of tanzania from sparse and varying gravity data density by the KTH method. PhD thesis, royal institute of technology (KTH), Division of Transport and Economics, StockholmGoogle Scholar
  30. Ustun A, Abbak RA (2010) On global and regional spectral evaluation of global geopotential models. J Geophys Eng 7(4):369–379CrossRefGoogle Scholar
  31. Vaníček P, Kleusberg A (1987) The Canadian geoid – stokes approach. Manuscripta Geodatica 12:86–98Google Scholar
  32. Vincent S, Marsch J (1974) Gravimetric global geoid. In: on the use of artifical satellites for geodesy and geodynamicsGoogle Scholar
  33. Wong L, Gore R (1969) Accuracy of geoid heights from the modified Stokes kernels. J Royal Astron Soc 18:81–91CrossRefGoogle Scholar
  34. Yildiz H, Forsberg R, Ågren J, Tscherning CC, Sjöberg LE (2012) Comparison of remove-compute-restore and least squares modification of Stokes’ formula techniques to quasi-geoid determination over the auvergne test area. J Geodetic Sci 2(1):53–64CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of Geomatics EngineeringSelcuk UniversityKonyaTurkey

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