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Regional improvement of global geopotential models using GPS/Leveling data

  • Mahdi Mosayebzadeh
  • Alireza A. Ardalan
  • Roohollah Karimi
Article
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Abstract

Global geopotential models are widely used in the remove-compute-restore technique for local gravity field modeling. In this paper, a method for regional improvement of global geopotential models using GPS/Leveling data is presented. The part of the spherical harmonic expansion degrees that can be subject to the regional improvement is determined depending on the spatial resolution of the GPS/Leveling data and the size of the study region. In this method, a global geopotential model is required as the original model. Using the GPS/Leveling data corrected for the systematic errors, the geoid surface is obtained at the GPS/Leveling points. By expanding the gravity potential of the geoid surface into the spherical harmonics, a mathematical model is made to estimate the spherical harmonic coefficients of the regionally improved geopotential model. To stabilize the mathematical model, pseudo data of the gravitational potential type produced by the original model on the entire Earth’s surface are added to the GPS/Leveling data. The relative weight of the two types of the data, i.e., the GPS/Leveling data and the pseudo data, is selected based on fitting the original model to the GPS/Leveling data. As numerical tests, the regionally improved geopotential model of the USA from degree 8 to 779 and the regionally improved geopotential model of Iran from degree 12 to 339 are developed. To develop both regionally improved geopotential models, the EGM2008 model up to degree 2160 is selected as the original model. The assessments at the GPS/Leveling checkpoints show that the regionally improved geopotential model of the USA has a 23% improvement and the regionally improved geopotential model of Iran has an 8% improvement with respect to the original model. The numerical tests confirm the efficiency of the proposed method for the regional improvement of global geopotential models using the GPS/Leveling data.

Keywords

regionally improved geopotential model global geopotential model GPS/Leveling data geoid leakage effect 

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References

  1. Albertella A., Migliaccio F. and Sansò F., 1991. The aliasing effect in coefficients estimation. In: Rapp R. and Sansò F. (Eds), Determination of the Geoid: Present and Future. International Association of Geodesy Symposia, 106. Springer-Verlag, Berlin, Germany, 10–15.CrossRefGoogle Scholar
  2. Burša M., Kouba J., Raděj K., True S.A., Vatrt V. and Vojtíšková M., 1998. Mean Earth’s equipotential surface from Topex/Poseidon altimetry. Stud. Geophys. Geod., 42, 459–466.CrossRefGoogle Scholar
  3. Erol B., 2012. Spectral evaluation of Earth geopotential models and an experiment on its regional improvement for geoid modelling. J. Earth Syst. Sci., 121, 823–835.CrossRefGoogle Scholar
  4. Featherstone W.E., 2002. Expected contributions of dedicated satellite gravity field missions to regional geoid determination with some examples from Australia. J. Geospat. Eng., 4, 1–18.Google Scholar
  5. Forsberg R., 1985. Gravity field terrain effect computations by FFT. Bull. Geod., 59, 342–360.CrossRefGoogle Scholar
  6. Forsberg R. and Sideris M., 1993. Geoid computations by the multi-band spherical FFT approach. Manuscr. Geod., 18, 82–90.Google Scholar
  7. Förste C., Bruinsma S.L., Abrikosov O., Lemoine J.M., Marty J.C., Flechtner F., Balmino G., Barthelmes F. and Biancale R., 2014. EIGEN-6C4: The latest combined global gravity field model including GOCE data up to degree and order 2190 of GFZ Potsdam and GRGS Toulouse. GFZ Data Services (http://doi.org/10.5880/icgem.2015.1).Google Scholar
  8. Garcia R.V., 2002. Local Geoid Determination from GRACE Mission. Report 460. Department of Civil and Environmental Engineering and Geodetic Sciences, The Ohio State University, Columbus, OH.Google Scholar
  9. Goossens S., 2010. Applying spectral leakage corrections to gravity field determination from satellite tracking data. Geophys. J. Int., 181, 1459–1472.Google Scholar
  10. Groten E., 2004. Fundamental parameters and current (2004) best estimates of the parameters of common relevance to astronomy, geodesy, and geodynamics. J. Geodesy, 77, 724–731.CrossRefGoogle Scholar
  11. Haagmans R., Min E., Gelderen M., Eynatten M., 1993. Fast evaluation of convolution integrals on the sphere using 1D FFT and a comparison with existing methods for Stokes’ integral. Manuscr. Geod., 18, 227–241.Google Scholar
  12. Han S.C., Jekeli C. and Shum C. K., 2002. Aliasing and polar gap effects on geopotential coefficient estimation: space-wise simulation study of GOCE and GRACE. In: Ádám J. and Schwarz K.P. (Eds), Vistas for Geodesy in the New Millennium. International Association of Geodesy Symposia, 125. Springer-Verlag, Berlin, Germany, 181–186.Google Scholar
  13. Heiskanen W.A. and Moritz H., 1967. Physical Geodesy. W.F. Freeman, San Francisco, CA.Google Scholar
  14. Hsu H. and Lu Y., 1995. The regional geopotential model in China. Boll. Geod. Sci. Affini, 54, 161–175.Google Scholar
  15. Jekeli C., 1996. Spherical harmonic analysis, aliasing, and filtering. J. Geodesy, 70, 214–223.CrossRefGoogle Scholar
  16. Kearsley A. and Forsberg, R., 1990. Tailored geopotential models- Applications and shortcomings. Manuscr. Geod., 15, 151–158.Google Scholar
  17. Koch K. R. and Kusche J., 2002. Regularization of geo-potential determination from satellite data by variance components. J. Geodesy, 76, 259–268.Google Scholar
  18. Kotsakis C. and Sideris M.G., 1999. On the adjustment of combined GPS/levelling/geoid networks. J. Geodesy, 73, 412–421.CrossRefGoogle Scholar
  19. Li X., 2018. Modeling the North American vertical datum of 1988 errors in the conterminous United States. J. Geod. Sci., 8, DOI: 10.1515/jogs-2018-0001.Google Scholar
  20. Lu Y., Hsu H.T. and Jiang F.Z., 2000. The regional geopotential model to degree and order 720 in China. In: Schwarz K.P. (Ed.), Geodesy Beyond 2000. International Association of Geodesy Symposia, 121. Springer-Verlag, Berlin, Germany, 143–148.CrossRefGoogle Scholar
  21. Martinec Z., 1996. Stability investigations of a discrete downward continuation problem for geoid determination in the Canadian Rocky Mountains. J. Geodesy, 70, 805–828.CrossRefGoogle Scholar
  22. Mikhail E.M. and Ackermann F.E., 1982. Observations and Least Squares. University Press of America, Lanham, MD.Google Scholar
  23. Pavlis N.K., 1988. Modeling and Estimation of a Low Degree Geopotential Model from Terrestrial Gravity Data. Report 386. Department of Civil and Environmental Engineering and Geodetic Sciences, The Ohio State University, Columbus, OH.Google Scholar
  24. Pavlis N.K., Holmes S.A., Kenyon, S.C. and Factor J.K., 2012. The development and evaluation of the Earth Gravitational Model 2008 (EGM2008). J. Geophys. Res.-Solid Earth, 117, B04406, DOI: 10.1029/2011JB008916.Google Scholar
  25. Petit G. and Luzum B., 2010.Google Scholar
  26. Petit G. and Luzum B. 2010. IERS Conventions. IERS Technical Note No. 36. Verlag des Bundesamts fur Kartographie und Geodasie, Frankfurt am Main, Germany.Google Scholar
  27. Saadat A., Safari A. and Needell D., 2018. IRG2016: RBF-based regional geoid model of Iran. Stud. Geophys. Geod., 62, 380–407. DOI: 10.1007/s11200-016-0679-x.CrossRefGoogle Scholar
  28. Sánchez L., Čunderlík R., Dayoub N., Mikula K., Minarechová Z., Šíma Z., Vatrt V. and Vojtíšková M., 2016. A conventional value for the geoid reference potential W0. J. Geodesy, 90, 815–835.CrossRefGoogle Scholar
  29. Sansò F., 1990. On the aliasing problem in the spherical harmonic analysis. J. Geodesy, 64, 313–330.CrossRefGoogle Scholar
  30. Schwarz K.P., Sideris M.G., Forsberg R., 1990. Use of FFT methods in physical geodesy. Geophys. J. Int., 100, 485–514.CrossRefGoogle Scholar
  31. Sideris M.G., 1994a. Geoid determination by FFT techniques. In: Sansò F. (Ed.), International Geoid School for the Determination and Use of the Geoid. Lecture Notes. International Geoid Service, DIIAR-Politechnico di Milano, Milano, ItalyGoogle Scholar
  32. Sideris M.G., 1994b. Regional geoid determination. In: Vaníček P. and Christou N.T. (Eds), The Geoid and Its Geophysical Interpretation. CRC Press, Boca Raton, FL, 77–94.Google Scholar
  33. Sjöberg L.E., 2005. A discussion on the approximations made in the practical implementation of the remove-compute-restore technique in regional geoid modeling. J. Geodesy, 78, 645–653.CrossRefGoogle Scholar
  34. Sjöberg L.E., 2007. The topographic bias by analytical continuation in physical geodesy. J. Geodesy, 81, 345–350.CrossRefGoogle Scholar
  35. Sjöberg L.E., 2009. On the topographic bias in geoid determination by the external gravity field. J. Geodesy, 83, 967–972.CrossRefGoogle Scholar
  36. Sjöberg L.E. and Bagherbandi M., 2011. A numerical study of the analytical downward continuation error in geoid computation by EGM08. J. Geod. Sci., 1, 2–8.Google Scholar
  37. Soycan M., 2014. Improving EGM2008 by GPS and leveling data at local scale. Boletim de Ciências Geodésicas, 20, 3–18.CrossRefGoogle Scholar
  38. Spetzler J. and Trampert J., 2003. Implementing spectral leakage corrections in global surface wave tomography. Geophys. J. Int., 155, 532–538.CrossRefGoogle Scholar
  39. van Hees G.S., 1990. Stokes formula using fast Fourier technique. Manuscr. Geod., 15, 235–239.Google Scholar
  40. Teunissen P.J.G. and Amiri-Simkooei A.R., 2008. Least-squares variance component estimation. J. Geodesy, 82, 65–82.CrossRefGoogle Scholar
  41. Trampert J. and Snieder R., 1996. Model estimations biased by truncated expansions: possible artifacts in seismic tomography. Science, 271, 1257–1260.CrossRefGoogle Scholar
  42. Tziavos I.N., 1996. Comparisons of spectral techniques for geoid computations over large regions. J. Geodesy, 70, 357–37.Google Scholar
  43. Vaníček P., Sun W., Ong P., Martinec Z., Najafi M., Vajda P. and Ter Horst B., 1996. Downward continuation of Helmert’s gravity. J. Geodesy, 71, 21–34.CrossRefGoogle Scholar
  44. Weber G. and Zomorrodian H., 1988. Regional geopotential model improvement for the Iranian geoid determination. J. Geodesy, 62, 125–141.Google Scholar

Copyright information

© Institute of Geophysics of the ASCR, v.v.i 2019

Authors and Affiliations

  • Mahdi Mosayebzadeh
    • 1
  • Alireza A. Ardalan
    • 1
  • Roohollah Karimi
    • 2
  1. 1.School of Surveying and Geospatial Engineering, College of EngineeringUniversity of TehranTehranIran
  2. 2.Department of Geodesy and Surveying EngineeringTafresh UniversityTafreshIran

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