Stochastic Modeling of GOCE Gravitational Tensor Invariants
The aim of the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) Mission is to provide global and regional models of the Earth’s time-averaged gravity field and of the geoid with high spatial resolution and accuracy. The approach based on t
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Stochastic Modeling of GOCE Gravitational Tensor Invariants Jianqing Cai and Nico Sneeuw
Abstract The aim of the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) Mission is to provide global and regional models of the Earth’s time-averaged gravity field and of the geoid with high spatial resolution and accuracy. The approach based on the rotational invariants of the gravitational tensor constitutes an independent alternative to conventional analysis methods. Due to the colored noise characteristic of individual gradiometer observations, the stochastic model assembly of the rotational invariants is a highly challenging task on its own. In principle, the invariants’ variance-covariance (VC) information can be deduced from the gravitational gradients (GG) by error propagation. But the huge number of gradiometer data and the corresponding size of the VC matrix prohibit this approach. The time series of these invariants, however, display similar stochastic characteristics as the gravitational gradients. They can thus be decorrelated by means of numerical filters. A moving-average (MA) filter of order 50 has been estimated and a filter cascade (high-pass and MA filters) has been developed. This filter cascade has been implemented in the decorrelation of the GOCE tensor invariant observation model.
15.1 Introduction Typically, gradiometer data analysis is performed at the level of individual gravity gradients (GG). This approach embraces a variety of methods commonly classified into space-wise or time-wise methods. Alternatively, gradiometer data analysis can be performed using rotational invariants, which are, in general, non-linear combinations of all GGs. The resulting observation equations are independent from the orientation
J. Cai (B) · N. Sneeuw Institute of Geodesy, Universität Stuttgart, Geschwister-Scholl-Straße 24D, 70174 Stuttgart, Germany e-mail: [email protected]
F. Flechtner et al. (eds.), Observation of the System Earth from Space - CHAMP, GRACE, GOCE and Future Missions, Advanced Technologies in Earth Sciences, DOI: 10.1007/978-3-642-32135-1_15, © Springer-Verlag Berlin Heidelberg 2014
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of the gravitational tensor,1 cf. (Baur et al. 2008; Pedersen and Rasmussen 1990 and Rummel 1986). Due to the colored noise behavior of gradiometer measurements the stochastic modeling of invariants is of elementary importance. Previous studies on the application of invariants to GOCE data analysis, however, did not take into account stochastic modeling. One possibility to deduce the stochastic model is applying (non-linear) error propagation to the observed GGs. Because of the huge number of gradiometer data, their VC matrix cannot be stored due to memory limitations. For example, the size of this matrix is 1.76 PB just for one month real GOCE SGG observations. According to our actual studies, e.g., (Baur et al. 2010; Cai et al. 2010), it is not possible to simply deduce the invariants’ VC information from the originating gravitational gradients by error propagat
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