AN ENHANCED SPACE-WISE SIMULATION FOR GOCE DATA REDUCTION Federica Migliaccio (1) , Mirko Reguzzoni (1) , Fernando Sansò (1) and Carl Christian Tscherning (2) (1) DIIAR - Sezione Rilevamento - Politecnico di Milano - P.za Leonardo da Vinci, 11 - 20133 Milano - Italy (2) Department of Geophysics - University of Copenhagen - Juliane Maries Vej, 30 - 2100 Copenhagen, Denmark ABSTRACT Polar gaps effects, gridding effects and noise propagation from GOCE T rr data into harmonic coefficients estimates, by the so-called space-wise approach, have been extensively studied. To this aim two techniques are possible, namely the fast spherical collocation and the numerical integration. Recently the conclusion has been drawn that the two methods are almost equivalent, though collocation reveals to be more robust against aliasing and polar gaps [9]. Now several generalizations need to be implemented and integrated in order to come to a final architecture of the software. The integration of non-radial components and the effects of small rotations are presented in a parallel paper [10]. In this work we aim at integrating the information coming from T rr , T r and T data, in order to better understand the improvement in the low frequency band. To obtain this result, we simulated a realistic data grid on a spherical boundary, implementing a realistic (and close to optimal) grid step and including realistic polar gaps effects. 1 THE RATIONAL FOR A JOINT USE OF T zz AND T Originally this paper was intended to study in numerical terms the joint effects of a number of features of the GOCE mission [4] which are difficult to be analytically studied according to the so-called space-wise approach [8] [11]. Such factors can be: the presence of polar gaps [1] [7], the misalignment of measurement axes with respect to an orbital frame [10] and, specially, the shape of the noise spectrum [3]. At the same time we wanted to improve our simulations by including other functionals of the anomalous potential T, measured during the mission; the first idea was to treat simultaneously T zz , T z and T. The first quantity comes from the gradiometer, while the second could be derived from a combination of GPS-orbit and accelerometers, like the third which can be achieved by the so-called energy integral approach [5] [14]. Since the parameters of noise statistics have been changed quite recently, due to ESA’s decision of dismissing the FEEP (Field Emission Electric Propulsion) system, we decided first of all to test what was the effect of the new error spectrum on the space-wise approach. We simulated a noisy data set of second radial derivatives, i.e. Y 0 = T rr + ν , in order to check the convergence of the space-wise iterative scheme [10]; contrary to the previous behaviour, the iterations show that the “small” perturbative operator has in fact a norm very close to 1 so that convergence is strongly questioned. The reason why this happens can be understood from the iterative formula, which in this case writes 0 ) ˆ ( ˆ Y S T L S T c Φ Φ + = (1) where: L(T ) = T rr , Φ = Wiener filter, Φ c = complementary Wiener filter = I –Φ , S = solver = AG , G = gridder, A = harmonic analyser. Note that the iteration in the second member basically tends to reconstitute the low-frequency part of the signal, which is lost by Wiener-filtering. ____________________________________________ Proc. Second International GOCE User Workshop “GOCE, The Geoid and Oceanography”, ESA-ESRIN, Frascati, Italy, 8-10 March 2004 (ESA SP-569, June 2004)