Advertisement

A Comparison of Data Weighting Methods for the Combination of Satellite and Local Gravity Data

Conference paper
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 127)

Abstract

The combination of heterogeneous gravity data is among the most involved problems in gravity field modeling. With newly available gravity data from dedicated satellites, such as CHAMP, GRACE and GOCE, additional low-frequency information about the gravity field will be available. Local or regional data collected closer to the Earth’s surface allows the resolution of the medium to high frequency components of the gravity field. Although for applications, such as geoid determination, most of the power is contained in the lower frequencies, a geoid at the cm-level, which is required by oceanography and geodesy alike, will require a much wider spectrum than the one that can be resolved by satellite methods. To enhance and widen the gravity field spectrum, a data combination process is essential.

The comparison of data weighting methods for the spectral combination of satellite and local gravity data is the topic of the paper. The quality of each method is evaluated with respect to the requirements, inherent assumptions and errors. Based on the detailed characterization of the methods, the quasi-deterministic method seems to be the most promising for the combination of satellite and local gravity data.

Keywords

Combination methods Gravity field modeling Satellite gravity missions Filters 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Blahut RE (1987) Principles and practice of information theory. Addison-Wesley, Reading, Mass.Google Scholar
  2. Blais JAR (1987) Information theory and optimal estimation. Manuscr Geod 12: 238–244.Google Scholar
  3. Evans JD, Featherstone WE (2000) Improved convergence rates for the truncation error in gravimetric geoid determination. J Geod 74 (2): 239–0248CrossRefGoogle Scholar
  4. Haagmans R (2000) A synthetic Earth for use in Geodesy. J Geod 74: 503–511.CrossRefGoogle Scholar
  5. Haagmans R, Prijatna K, Omang O (2002) An alternative concept for validation of GOCE gradiometry results based on regional gravity. To be published in the Proc of the 3rd Meet Int Gravity Geoid Com. Thessaloniki, Greece.Google Scholar
  6. Heck B (1979) Zur lokalen Geoidbestimmung aus terrestrischen Messungen vertikaler Schweregradienten. DGK, series C, no. 259.Google Scholar
  7. Heck B, Grüninger W (1987) Modification of Stokes’ integral formula by combination of two classical approaches. Proc IAG Symp, XIX IUGG General Assembly, pp 319–337.Google Scholar
  8. Heiskanen WA, Moritz H (1967) Physical geodesy. Freeman and Co., San Francisco.Google Scholar
  9. Jekeli C (1981) Alternative methods to smooth the Earth’s gravity field. Department of Geodetic Science. Rep 327. Ohio State University. Columbus.Google Scholar
  10. Kern M, Schwarz KP, Sneeuw N (2002) A study on the combination of satellite, airborne and terrestrial gravity data. To be published by the J Geod.Google Scholar
  11. Kern M (2003) An analysis of the combination and downward continuation of satellite, airborne and terrestrial gravity data. Department of Geomatics Engineering. Rep 20172. The University of Calgary.Google Scholar
  12. Kullback S, Leibler RA (1951) On information and sufficiency. Ann Math Stats. 22: 79–86.CrossRefGoogle Scholar
  13. Kusche J (2002) Inverse Probleme bei der Gravitationsfeldbestimmung mittels SST- und SGG- Satellitenmissionen. DGK, series C, no. 548.Google Scholar
  14. Lemoine FG, Kenyon SC, Factor JK, Trimmer RG, Pavlis NK, Chinn DS, Cox CM, Klosko SM, Luthcke SB, Torrence MH, Wang YM, Williamson RG, Pavlis EC, Rapp RH, Olson TR (1998) The Development of the joint NASA GSFC and the National Imagery and Mapping Agency (NIMA) Geopotential Model EGM96. Rep. NASA TP-1998–206861.Google Scholar
  15. Lehmann R (1996) Information measures for global geopotential models. J Geod 70: 342–348.Google Scholar
  16. Moritz H (1975) Integral formulas and collocation. Department of Geodetic Science. Rep 234. The Ohio State University. Columbus.Google Scholar
  17. Oppenheim AV, Schafer RW (1999) Discrete-time signal processing. Prentice Hall signal processing series. Second edition.Google Scholar
  18. Rapp RH, Rummel R (1975) Methods for the computation of detailed geoids and their accuracy. Department of Geodetic Science and Surveying. Rep 233. Ohio State University. Columbus.Google Scholar
  19. Schwarz KP (1984) Data types and their spectral properties. Proc Int Summer School on local gravity field approximation. Ed. KP Schwarz. Bejing. China. pp 1–66.Google Scholar
  20. Shannon CE (1948) A mathematical theory of communication. Bell Syst Techn J 27 (379–426): 623–656.Google Scholar
  21. Sjöberg LE (1979) Integral formulas for heterogeneous data in physical geodesy. Bull Géod 53: 297–315.CrossRefGoogle Scholar
  22. Sjöberg LE (1981) Least squares combination of satellite and terrestrial data in physical geodesy. Ann Geophys 37: 25–30.Google Scholar
  23. Tscherning CC, Rapp RH (1974) Closed covariance expressions for gravity anomalies, geoid undulations, and deflections of the vertical implied by anomaly degree variance models. Department of Geodetic Science. Rep 208. Ohio State University, Columbus.Google Scholar
  24. Vanícek P, Featherstone WE (1998) Performance of three types of Stokes’s kernel in the combined solution for the geoid. J Geod 72: 684–697.CrossRefGoogle Scholar
  25. Wang YM (1993) On the optimal combination of potential coefficient model with terrestrial gravity data for 1’1+ 1 computations. Manuscr Geod 18: 406–416.Google Scholar
  26. Wenzel HG (1981) Zur Geoidbestimmung durch Kombination von Schwereanomalien und einem Kugelfunktionsmodell mit Hilfe von Integralformeln. Z Verm. 3: 102–111.Google Scholar
  27. Wenzel HG (1982) Geoid computation by least-squares spectral combination using integral kernels. Proc. IAG General Meet. Tokyo. pp 438–453.Google Scholar
  28. Wichiencharoen C (1984) A comparison of gravimetric undulations computed by the modified Molodenskij truncation method and the method of least squares spectral combination by optimal integral kernels. Bull Géod 58: 494–509.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • M. Kern
    • 1
  1. 1.Department of Geomatics EngineeringThe University of CalgaryCalgaryCanada

Personalised recommendations