- Open Access
Application of GOCE data for regional gravity field modeling
Earth, Planets and Space volume 61, pages835–843(2009)
In principle, every component of a disturbing gravity gradient tensor measured in a satellite orbit can be used to obtain gravity anomalies on the Earth’s surface. Consequently, these can be used in combination with ground or marine data for further gravity field modeling or for verification of satellite data. Theoretical relations can be derived both in spectral and spatial forms. In this paper, we focus on the derivation of a spatial integral form in the geocentric spherical coordinates that seems to be the most convenient one for regional gravity field modeling. All of the second partial derivatives of the generalized Stokes’s kernel are derived, and six surface Fredholm integral equations are formulated and discretized. The inverse problems formulated for particular components clearly reveal different behaviors in terms of numerical stability of the solution. Simulated GOCE data disturbed with Gaussian noise are used to study the performance of two regularization methods: truncated singular value decomposition and ridge regression. The optimal ridge regression method shows slightly better results in terms of the root mean squared deviation of the differences from the exact solution.
Andrilli, S. and D. Hecker, Elementary Linear Algebra, 644 pp., Elsevier, Amsterdam, 2003.
Aster, R. C., B. Borchers, and C. H. Thurber, Parameter Estimation and Inverse Problems, 301 pp., Elsevier, Amsterdam, 2005.
Bronshtein, I. N., K. A. Semendyayev, G. Musiol, and H. Muehlig, Handbook of Mathematics, 1153 pp., Springer, Berlin, 2004.
Drinkwater, M. R., R. Haagmans, D. Muzi, A. Popescu, R. Floberghagen, M. Kern, and M. Fehringer, The GOCE gravity mission: ESA’s first core earth explorer, in Proceedings of the 3rd International GOCE User Workshop, ESA SP-627, 1–8, 2007.
European Space Agency, GOCE L1B Products User Handbook, ESA Technical Note GOCE-GSEG-EOPG-TN-06-0137, 90 s., 2006.
Heiskanen, W. and H. Moritz, Physical Geodesy, Freeman, San Francisco, 1967.
Hoerl, A. E. and R. W. Kennard, Ridge regression: biased estimation for nonorthogonal problems, Technometrics, 12, 55–67, 1970.
Kern, M. and R. Haagmans, Determination of gravity gradients from terrestrial gravity data for calibration and validation of gradiometric GOCE data, in Gravity, Geoid and Space Missions, edited by Jekeli, Bastos, and Fernandes, 95–100, Springer, Berlin, 2005.
Lemoine, F. G., S. C. Kenyon, J. K. Factor, R. G. Trimmer, N. K. Pavlis, D. S. Chinn, C. M. Cox, S. M. Klosko, S. B. Luthcke, M. H. Torrence, Y. M. Wang, R. G. Williamson, E. C. Pavlis, R. H. Rapp, and T. R. Olson, The development of the joint NASA GSFC and NIMA Geopotential Model EGM96, NASA Technical Paper NASA/TP-1998-206861, Goddard Space Flight Center, Greenbelt, USA, 1998.
Martinec, Z., Green’s function solution to spherical gradiometric boundary-value problems, J. Geod., 77, 41–49, 2003.
Novák, P. and E. W. Grafarend, The effect of topographical and atmospheric masses on spaceborne gravimetric and gradiometric data, Stud. Geophys. Geodaet., 50, 549–582, 2006.
Pizzetti, P., Sopra il calcolo teorico delle deviazioni del geoide dall’ ellissoide, Atti R. Accad. Sci. Torino, 46, 331, 1911.
Reed, G. B., Application of kinematical geodesy for determining the short wave length components of the gravity field by satellite gradiometry, Technical Report No. 201, Department of Geodetic Science, The Ohio State University, Columbus, Ohio, 1973.
van Gelderen, M. and R. Rummel, The solution of the general geodetic boundary value problem by least squares, J. Geod., 75, 1–11, 2001.
van Gelderen, M. and R. Rummel, Corrections to “The solution of the general geodetic boundary value problem by least squares”, J. Geod., 76, 121–122, 2002.
Xu, P. L., Determination of surface gravity anomanlies using gradiometric observables, Geophys. J. Int., 110, 321–332, 1992.
Xu, P. L., Truncated SVD methods for discrete linear ill-posed problems, Geophys. J. Int., 135, 505–514, 1998.
Xu, P. L. and R. Rummel, Generalized ridge regression with applications in determination of potential fields, Manuscr. Geod., 20, 8–20, 1994.
About this article
Cite this article
Janák, J., Fukuda, Y. & Xu, P. Application of GOCE data for regional gravity field modeling. Earth Planet Sp 61, 835–843 (2009). https://doi.org/10.1186/BF03353194
- Pizzetti integral formula
- inverse problem