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

Abstract

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 J ²-term, the spherical approximation models are improved so that the accuracies of the boundary conditions can be theoretically raised to O(J ²₂ · T), which is approximately equivalent to O(T ²). 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 J ²-term have accuracies of 10⁻⁸ and the order can reach up to 280.