Satellite missions CHAMP and GRACE dedicated to global mapping of the Earth’s gravity field yield accurate satellite-to-satellite tracking (SST) data used for recovery of global geopotential models usually in a form of a finite set of Stokes’s coefficients. The US-German Gravity Recovery And Climate Experiment (GRACE) yields SST data in both the high-low and low-low mode. Observed satellite positions and changes in the intersatellite range can be inverted through the Newtonian equation of motion into values of the unknown geopotential. The geopotential is usually approximated in observation equations by a truncated harmonic series with unknown coefficients. An alternative approach based on integral inversion of the SST data of type GRACE into discrete values of the geopotential at a geocentric sphere is discussed in this article. In this approach, observation equations have a form of Green’s surface integrals with scalar-valued integral kernels. Despite their higher complexity, the kernel functions exhibit features typical for other integral kernels used in geodesy for inversion of gravity field data. The two approaches are discussed and compared based on their relative advantages and intended applications. The combination of heterogeneous gravity data through integral equations is also outlined in the article.
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Stegun I.A., 1972. Legendre Functions. In: M. Abramowitz and C.A. Stegun (Eds.), Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables. 10th Printing. National Bureau of Standards, U.S. Government Printing Office, Washington D.C., 332–354.
Arfken G., 1985. Mathematical Methods for Physicists. 3rd Edition. Academic Press, Orlando.
Belikov M.V. and Taybatorov K.A., 1992. An efficient algorithm for computing the Earth’s gravitational potential and its derivatives at satellite altitudes. Manuscripta Geodetica, 17, 104–116.
Blaha G., 1992. Refinement of the satellite-to-satellite line-of-sight acceleration model in a residual gravity field. Manuscripta Geodaetica, 17, 321–333.
Garcia R.V., 2002. Local Geoid Determination From GRACE Data. Report No. 460, Department of Civil and Environmental Engineering and Geodetic Science, The Ohio State University, Columbus, Ohio.
Heiskanen W.A. and Moritz H., 1967. Physical Geodesy. Freeman and Co., San Francisco.
Holota P., 2000. Direct methods in physical geodesy. In: K.P. Schwarz (Ed.), Geodesy Beyond 2000. The challenges of the 1st decade. IAG Symposia 121. Springer, Berlin, Heidelberg, New York, 163–170.
Keller W. and Hess D., 1998. Gradiometrie mit GRACE. Zeitschrift für Vermessungswesen, 124, 137–144.
Keller W. and Sharifi M.A., 2005. Satellite gradiometry using a satellite pair. J. Geodesy, 78, 544–557.
Kellogg O.D., 1929. Foundations of Potential Theory. Springer, Berlin.
Kern M., Schwarz K.P. and Sneeuw N., 2003. A study on the combination of satellite, airborne, and terrestrial gravity data. J. Geodesy, 77, 217–225.
Martinec Z., 2003. Green’s function solution to spherical gradiometric boundary-value problem. J. Geodesy, 77, 41–49.
McCarthy D.D. and Petit G., 2004. IERS Conventions (2003). IERS Technical Note 32. Verlag des Bundesamtes für Kartographie und Geodäsie, Frankfurt am Main.
Montenbruck O. and Gill E., 2001. Satellite Orbits. Model, Methods, Applications. Springer-Verlag, Berlin, Heidelberg.
Moritz H., 1989. Advanced Physical Geodesy. 2nd Edidtion, Wichmann, Karlsruhe.
Novák P. and Grafarend E.W., 2005. Ellipsoidal representation of the topographical potential and its vertical gradient. J. Geodesy, 78, 691–706.
Novák P. and Grafarend E.W., 2006. The effect of topographical and atmospheric masses on spaceborne gravimetric and gradiometric data. Stud. Geophys. Geod., 50, 549–582.
Rummel R., 1980. Geoid Heights, Geoid Height Differences, and Mean Gravity Anomalies from Low-Low Satellite-To-Satellite Tracking-an Error Analysis. Report No. 409, Department of Geodetic Science and Surveying, Ohio State University, Columbus, Ohio.
Sjöberg L., 1979. Integral formulas for heterogeneous data in physical geodesy. Bulletin Géodésique, 53, 279–315.
Swarztrauber P.N., 1979. On the spherical approximation of discrete scalar and vector functions on the sphere. SIAM J. Numer. Anal., 6, 934–949.
van Gelderen M. and Rummel R., 2001. The solution of the general geodetic boundary value problem by least squares. J. Geodesy, 75, 1–11.
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Novák, P. Integral inversion of SST data of type GRACE. Stud Geophys Geod 51, 351–367 (2007). https://doi.org/10.1007/s11200-007-0020-9
- satellite-to-satellite tracking
- Green’s integral