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The gravitational gradient tensor’s invariants and the related boundary conditions

Science China Earth Sciences 2010年第5期53卷 781-790页

作者： YU JinHai1,2,3 & ZHAO DongMing4 1 College of Earth Science, Graduate University of Chinese Academy of Sciences, Beijing 100049, China 2 Institute of Geodesy and Geophysics, Chinese Academy of Sciences, Wuhan 430077, China 3 State Key Laboratory of Astronautic Dynamics, Xi’an 710043, China 4 Zhengzhou Institute of Surveying and Mapping, Zhengzhou 450052, China College of Earth Science Graduate University of Chinese Academy of Sciences Beijing China Institute of Geodesy and Geophysics Chinese Academy of Sciences Wuhan China State Key Laboratory of Astronautic Dynamics Xi’an China Zhengzhou Institute of Surveying and Mapping Zhengzhou China

Here we report new approaches of recovering the Earth gravitational field from GOCE (Gravity field and steady-state Ocean Circulation Explorer) gradiometric data with the help of the gradient tensor’s invariants. Our results only depend on GOCE satellite’s position and gradiometry, in other words, they are completely independent of the satellite attitude. First, starting from the invariants, linearization models are established, which can be referred as the general boundary conditions on the satellite’s orbit. Then, the spherical approximation expressions for the models are derived, and the corresponding solving methods for them are discussed. Furthermore, considering effects of J2-term, the spherical approximation models are improved so that the accuracies of the boundary conditions can be theoretically raised to O ( J 2/2 T), which is approximately equivalent to O(T2). Finally, some arithmetic examples are constructed from EGM96 model based on the derived theories, and the computational results illustrate that the spherical models have accuracies of 10-7 and the order recovering the gravitational field can reach up to 200, and the models with regard to effect of J2-term have accuracies of 10-8 and the order can reach up to 280.

关键词： the Earth’s gravitational field gravitational gravidiometry tensor’s invariant

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