On the construction of the models of Earth's gravity field from GOCE data

: pp. 74 - 81
Received: January 28, 2014
Accepted: March 24, 2014
Department of Geodesy, Institute of Geodesy, Lviv Polytechnic National University
Lviv Polytechnic National University; Carpathian branch of S. I. Subbotin name Institute of geophysics of NAS of Ukraine
Lviv Polytechnic National University

As well-known, one of the oldest geodetic problems has today a new development. There is the method of satellite gradientometry allowing essentially improvement of the Earth's gravity field. So, the development of geodesy together with the expansion of various types of measurements is characterized by traditional increase of their level of accuracy and solving the basic problems of geodesy – definition of shape and gravity field of the Earth on the new level. Since basic researches of Laplace, Legendre and Gauss in the theory of Newtonian potential, the classical Legendre-Laplace-Gauss-Maxwell representation of the Earth gravitational potential as a series of solid spherical functions has taken an interdisciplinary significance for the static and time-dependent fields of the Earth and planets. Note that this parameterization of the gravitational potential is not considered to be a standard only, but also as one of the best for modern scientific and applied problems of celestial mechanics, satellite geodesy, and global geodynamics. From 2000 to 2009 years were launched satellites CHAMP, GRACE and GOCE, which are classified as satellites LEO (Low Earth Orbit), the height of the orbit is lower than 500 km. The data from these satellites are LEO significantly clarified and expanded our knowledge of the Earth gravity field. The last achievements of the satellite geodesy is the project of European Space Agency – the GOCE satellite mission (Gravity of field and steady – state of Ocean Circulation Explorer) which is using the satellite gradientometry method. The choice of algorithm, which allows the determination of harmonic coefficients geopotential from gravity gradient tensor components, which is measured as part of the modern approach satellite mission GOCE gradientometry, became significant task for improving long and mean components of the gravitational field via data processing. As a result, in this paper two version of the corresponding harmonic coefficients Cnm, Snm (gravity field models GOCE-LP01s and GOCE-LP02s up to degree/order 250) were derived based on the second Neumann method including the construction of the corresponding Gauss grid.

  1. Heiskanen W.A., Moritz H. (1967) Physical Geodesy. W.H. Freeman, San Francisco, 364 p.
  2. Hofmann–Wellenhof B., H. Moritz, Physical Geodesy. Springer, Wien New York, 2005, 403 p.
  3. Kalman R.E. A new approach to linear filtering and prediction problems. Journal of Basic Engineering, 1960, Vol. 82 (1): 35–45.
  4. Marchenko A.N. (1998) Parameterization of the Earth’s Gravity Field: Point and Line Singularities. Published by Lviv Astronomical and Geodetic Society. Lviv, Ukraine, 1998, 210 p.
  5. Marchenko A.N. and Schwintzer P. (2003) Estimation of the Earth’s tensor of inertia from recent global gravity field solutions. Journal of Geodesy, Vol. 76. – P. 495–509.
  6. Moritz H. (1977) Introduction to Interpolation and Approximation. Proceedings of the 2nd International School “Approximation Methods in Geodesy”. Ramsau, Austria, August 23 – September 2, 1977. – Wichmann: Karsruhe, 1978. – P. 1–45.
  7. Moritz H. (1979) Report of Special Study Group 539, Fundamental Geodetic Constants, Paper presented at the XVII General Assembly of the IUGG, Int. Assoc. of Geodesy, Canberra, 1979.
  8. Moritz H. (1989) Advanced Physical Geodesy. 2nd edition, H. Wichmann, Karlsruhe.
  9. Moritz H. and B. Hofmann-Wellenhof (1993) Geometry, Relativity, Geodesy. Wichmann, Karlsruhe.
  10. Moritz H., Muller I.I. (1987) Earth’s Rotation. Theory and estimations, New York, Ungar.
  11. Overhauser A.W. (1968) Analytic definition of curves and surfaces by parabolic blending. Tech. Report, No. SL68- 40, Scientific research staff publication. Ford Motor Company, Detroit, 1968.
  12. Pavlis N.K., Holmes S.A., Kenyon S.C., Factor J.K. (2008) An Earth Gravitational Model to Degree 2160:EGM2008.
  13. Geophysical Research Abstracts, Vol. 10, EGU2008–A–01891, 2008, EGU General Assembly 2008.
  14. Seeber G. (2003) Satellite Geodesy 2nd completely revised and extended edition. Walter de Gruyter, Berlin New York, 2003. – 589 p.
  15. Sideris M. G. (2005) Geoid determination by FFT techniques // International School for the Determination and Use of the Geoid. – Budapest University of Technology and Economics, 2005. – 64 p.
  16. Sneeuw N. (1994) Global spherical harmonic analysis by least-squares and numerical quadrature methods in historical perspective. Physical Geodesy. Springer, Wien New York, 1994. – 713 p.
  17. Wessel P., Smith W.H.F. (2004) The Generic Mapping Tools (GMT, Version 4). Technical Reference and Cookbook, Honolulu, HI and Silver Spring, MD, January 2004. – 123 p.