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Gravity field analysis from preprocessed and calibrated GOCE observations ? The Delft Approach

Prof. Dr. Roland Klees(1), Dr Pavel Ditmar(1) , and Ir Sander Van Eck van der Sluijs(1)

(1) Delft University of Technology, P.O. Box 5058, 2600GB Delft, Netherlands


The current status of the Delft approach to the gravity field analysis of GOCE level 1b data is presented.

The goal of the research is to develop algorithms and software to obtain the optimal estimation of the Earth’s gravit field from GOCE SGG and SST data. The philosophy behind the Delft approach can be summarized as follows: (a) no reduction, interpolation, re-sampling etc. of data at the pre-processing stage in order to preserve the stochastic properties of data noise and the information content in the data; (b) proper data weighting even in the presence of frequency-dependent noise and data gaps; (c) selection of a high maximum degree (300) to be solved for in order to recover all information contained in the data; (d) quality description in terms of the auto-covariance matrix of the estimated gravity field parameters in order to allow a proper interpretation and combination of the results with other gravity data.

The primary observations are the 4 components of the Eoetvoes tensor in the LORF and time-averaged satellite accelerations. The latter are to be derived from the precise kinematic GOCE orbit by a three-point differentiation scheme. The primary unknowns are the spherical harmonic coefficients of the residual gravitational potential complete to degree 300. A regularized least-squares solution is computed using a preconditioned conjugate gradient algorithm without the explicit computation of the design matrix and the normal matrix. Efficient block-diagonal pre-conditioners for gravity gradients and satellite accelerations reduce the number of iterations. Fast spherical harmonic synthesis and co-synthesis algorithms are used to apply the design matrix and its transpose to a vector. Data are accurately weighted according to their stochastic properties by a low-level preconditioned conjugate gradient method with ARMA filtering. First-order Tikhonov regularization is combined with the generalized cross-validation method to estimate the regularization parameter from the data. Column-by-column assembly of the normal matrix, based on the fast spherical harmonic synthesis and co-synthesis algorithms, is used to compute the auto-covariance matrix of the potential coefficients.

The results of extensive numerical computations are presented using a simulated 6-months GOCE data set consisting of gravity gradients and precise orbit information. Stand-alone and combined inversions of gravity gradients and precise orbit data will be presented for various sampling rates, colored noise scenarios including non-stationary noise, and data gaps of variable duration.


Full paper

Keywords: ESA European Space Agency - Agence spatiale europeenne, observation de la terre, earth observation, satellite remote sensing, teledetection, geophysique, altimetrie, radar, chimique atmospherique, geophysics, altimetry, radar, atmospheric chemistry