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 2 2 ( ), O J 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. the Earth's gravitational field, gravitational gravidiometry, tensor's invariant Citation: Yu J H, Zhao D M. The gravitational gradient tensor's invariants and the related boundary conditions.

The gravity field model IGGT_R1 based on the second invariant of the GOCE gravitational gradient tensor

“…Thus the inaccuracies in the transformation matrix cannot be avoided. Specif-ically, investigations by Pail and Plank (2002), Pail et al (2005) and Yu and Zhao (2010) found that arcsec attitude errors can lead the data processing accuracy to barely reach a relative magnitude of 10 −6 − 10 −7 .…”

“…They parameterized the invariants and performed numerical simulations, but the parameterization in the spherical polar coordinate is complicated. Boundary value problems with a sphere approximation including a J 2 term are shown by (Yu and Zhao, 2010;Yu and Wan, 2013). Specifically, the gravity field models are built using spherical harmonic analysis according to the boundary value conditions.…”

Frequency Analysis and Filtering Processing of Gravity Gradient Data from GOCE

“…Yu et al [16] proposed another way to recover gravity field models by constructing two boundary value conditions using invariants of gravity gradients. The gravity potential model can be recovered by spherical E-mail: wxy191954@126.com harmonic analysis and avoid solving large numbers of normal equations.…”