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.
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References
Blahut RE (1987) Principles and practice of information theory. Addison-Wesley, Reading, Mass.
Blais JAR (1987) Information theory and optimal estimation. Manuscr Geod 12: 238–244.
Evans JD, Featherstone WE (2000) Improved convergence rates for the truncation error in gravimetric geoid determination. J Geod 74 (2): 239–0248
Haagmans R (2000) A synthetic Earth for use in Geodesy. J Geod 74: 503–511.
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.
Heck B (1979) Zur lokalen Geoidbestimmung aus terrestrischen Messungen vertikaler Schweregradienten. DGK, series C, no. 259.
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.
Heiskanen WA, Moritz H (1967) Physical geodesy. Freeman and Co., San Francisco.
Jekeli C (1981) Alternative methods to smooth the Earth’s gravity field. Department of Geodetic Science. Rep 327. Ohio State University. Columbus.
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.
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.
Kullback S, Leibler RA (1951) On information and sufficiency. Ann Math Stats. 22: 79–86.
Kusche J (2002) Inverse Probleme bei der Gravitationsfeldbestimmung mittels SST- und SGG- Satellitenmissionen. DGK, series C, no. 548.
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.
Lehmann R (1996) Information measures for global geopotential models. J Geod 70: 342–348.
Moritz H (1975) Integral formulas and collocation. Department of Geodetic Science. Rep 234. The Ohio State University. Columbus.
Oppenheim AV, Schafer RW (1999) Discrete-time signal processing. Prentice Hall signal processing series. Second edition.
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.
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.
Shannon CE (1948) A mathematical theory of communication. Bell Syst Techn J 27 (379–426): 623–656.
Sjöberg LE (1979) Integral formulas for heterogeneous data in physical geodesy. Bull Géod 53: 297–315.
Sjöberg LE (1981) Least squares combination of satellite and terrestrial data in physical geodesy. Ann Geophys 37: 25–30.
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.
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.
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.
Wenzel HG (1981) Zur Geoidbestimmung durch Kombination von Schwereanomalien und einem Kugelfunktionsmodell mit Hilfe von Integralformeln. Z Verm. 3: 102–111.
Wenzel HG (1982) Geoid computation by least-squares spectral combination using integral kernels. Proc. IAG General Meet. Tokyo. pp 438–453.
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.
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Kern, M. (2004). A Comparison of Data Weighting Methods for the Combination of Satellite and Local Gravity Data. In: Sansò, F. (eds) V Hotine-Marussi Symposium on Mathematical Geodesy. International Association of Geodesy Symposia, vol 127. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-10735-5_19
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DOI: https://doi.org/10.1007/978-3-662-10735-5_19
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