Stochastic Modeling of GOCE Gravitational Tensor Invariants

  • Jianqing Cai
  • Nico Sneeuw
Part of the Advanced Technologies in Earth Sciences book series (ATES)


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.


Power Spectral Density Gravity Gradient Colored Noise Gravity Field Model Stochastic Characteristic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



We gratefully acknowledge the financial support of the BMBF (Bundesministerium für Bildung und Forschung) and the DFG (Deutsche ForschungsGemeinschaft). Within the GEOTECHNOLOGIEN programme. Furthermore, we kindly acknowledge helpful support in the estimation of the filter by W.-D. Schuh and I. Krasbutter.


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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Institute of GeodesyUniversität StuttgartStuttgartGermany

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