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Spherical Cap Regularization of GOCE normal equation systems

Bernhard Metzler(1) and Roland Pail(1)

(1) Graz University of Technology, Steyrergasse 30, 8010 Graz, Austria


Due to the special configuration of the satellite orbit, the least-squares estimation of a gravity field model represented in spherical harmonic functions based on GOCE measurements is an ill-posed problem. Since the primary reason for the ill-posedness are the missing data on the poles, the spherical cap regularization approach has been introduced. In principle, a stabilizing function which is restricted to the regions where no measurements are available is used to stabilize the system.

Besides the regularization parameter that controls the power of the regularization the choice of an appropriate stabilizing function is essential. The better the stabilizing function fits the measurement data, the stronger the regularization can be applied without producing harmfuls effects. Too strong a regularization can lead to Gibbs phenomenon in the transition zone around 83.5° latitude where the measured data coincides with the stabilizing function.

The extent of the Gibbs phenomenon depends on the one hand on the power of the regularization and on the other hand on the differences between the stabilizing function and the measured data at 83.5° latitude. The larger the differences and the larger the regularization parameter, the larger the oszillations in the transition zone will be. In order to avoid the occurrance of this phenomenon several strategies have been investigated, that allow a smooth transition from the measured data to the introduced function. Consequently, a strong regularization is possible even with a function that does not fit the measurements perfectly.


Workshop poster

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