1. 4.Results (1)Potential coefficients comparisons Fig.3 FIR filtering(Passband:0.005~0.1HZ) Fig.4 Comparison with ESA’s models (filter passband:0.015~0.1HZ) Fig.5 Relative Difference(Passband:0.015~0.1HZ) Fig.6 Relative Difference(Passband:0.015~0.1HZ+DL) (2)Geoid height comparison (Passband:0.005~0.1HZ) Fig.7.Geoid height comparison with EGM08 (3)Gravity anomaly comparison (Passband:0.005~0.1HZ) Fig1. Flow chart The recovery of Earth gravity field from GOCE data based on the invariants of the gravity gradients Wan Xiaoyun 1,2 ， Yu Jinhai 1,2 1,College of Earth Science, Graduate University of Chinese Academy of Sciences, Beijing, 100049, China; 2,Laboratory of Computational Geodynamics, Chinese Academy of Sciences, Beijing, 100049,China. wxy191954@126.com,yujinhai@gucas.ac.cn wxy191954@126.comyujinhai@gucas.ac.cn ABSTRACT: The gravity field can be recovered from a special boundary condition derived from invariants of the gravity gradients under spherical approximation, instead of solving a large number of linear systems of equations. Based on the new approach, we reconstructed the gravity field by analyzing the GOCE data. The low frequency error caused by property of satellite’s gradiometer has been removed by forward – backward filtering, meanwhile white noise in MBW has been diminished by Durbin – Levinson algorithm. The final result from the remove - restore method shows that our approach is effective. 2.Theory Based on the works of Baur [1] and Yu [2], consider the invariants of the gravity gradients, ① Particularly,A=0, which means the gravitational potential is harmonic. So the emphases of our work focus on B and C. We may calculate B and C using actual data as well as B0 and C0 using gravity field model (U), e.g., EGM08, EGM96,etc. Then we can get and. Do linearization processing for T (neglecting terms of O(T2)),where T = V – U, we obtain, 1. Introduction There are many methods to do gravity field recovery using GOCE data, whereas most of them are based on the least square method. However in this approach a large number of linear systems of equations need to be solved, as the unknown parameters will exceed 40000 if we want to recover 200 degrees. In this paper, we will introduce a method based on theory of gravity gradients invariants which can recover the gravity field using harmonic analysis. And then further simplify them with spherical approximation processing, some boundary conditions on orbit surface may be established as follows, ② and ③ Given T is harmonic, we can calculate gravity potential by integration method based on orthogonality of sphere harmonic function. 3.Filtering method We adopt remove-restore method to filter low frequency error. It’s that at first we simulate gravity data using a normal gravity model such as EGM08, and then let observation data subtract the simulated values and get residual values which are then filtered with method of forward- backward filtering in order to solve phase drift problem. Correspondingly, the final values are the sum of simulated values and residual values. Fig.1 and Fig.2 show related information. The filter we adopt is 1000 orders’ FIR filter. Although low frequency error has been filtered, the white noise in MBW has never been processed, so finally we adopt Durbin- Levinson (DL) algorithm to do this job. Fig2. PSD of residual values after FIR filtering(Passband:0.005~0.1HZ) (Raw data is from 1.11.2009 to 10.11.2009) Fig.8.Gravity anomaly comparison with EGM08 5.Conclusion We draw the conclusion that the method based on invariants is indeed an effective and simple way to recover gravity field in high accuracy, and refinement should be made on the filtering strategy to avoid loss of useful information. 6.References [1]. Baur O, Sneeuw S, Grafarend E W. Methodology and use of tensor invariants for satellite gravity gradiometry. J Geodesy, 2008, 82: 279— 293 [2]. Yu J H, Zhao D M. The gravitational gradient tensor’s invariants and the related boundary conditions. Sci China Earth Sci, 2010, 53: 781–790,doi: 10.1007/s11430-010-0014-2 order m No Calculate simulated data Gravity Model Read EGM08 end Recovery Output the new model Yes Read raw data Beginning Filtering Calculate gravity potential coefficients Remove order m degree n Longitude Latitude