Study Of Determining The GOCE Satellite Gravity Field Based On Torus Approach

The determination of Earth gravity field model with high accuracy and high resolution is one of the main scientific themes of modern geodesy,and has important significance to geodesy,solid geophysics and oceanography.A large number of satellite gradiometry observations are obtained by electrostatic gravity gradiometer which is equipped on the GOCE satellite launched on March 17,2009.It greatly improves the accuracy of median-to-short wavelengths of the gravity field and promotes the centimeter-level geoid research which is the important geodesy goal in the 21st century.Probably the most commonly used techniques for solving GOCE satellite gravity filed are:the direct approach,the time-wise approach,the space-wise approach,the tensor invariant approach and the Torus approach.The Torus approach has not been used in GOCE measured data processing.The computational efficiency of Torus is greatly improved by using the 2D-FFT and the block-diagonal least-squares adjustment,so it can be used to recover gravity field fast based on the massive amount of GOCE satellite observations.The principle of Torus method is deeply studied in this paper,and the main contents and conclusions are as follows:1.The theory of earth gravity field determination with GOCE satellite gradiometry data is described,including transformation between the time systems,relationship between the coordinate systems and satellite gradiometry observations,the measurement principle of GOCE satellite gravity gradiometry,the situation of GOCE tasks and current methods of gravity field determination with GOCE observations.2.The principle and key technologies of Torus method are studied deeply.Practical formulas for spherical harmonic synthesis and analysis on Torus using the 2D-FFT are derived.The arrangement of potential coefficients and the application of block-diagonal least-squares adjustment is used.The regularization method solving for ill-condition of the normal equation is discussed,including the principle of Kaula regularization and Tikhonov regularization,and the L curve method to determine the regularization parameters.3.The method to reduce the gradiometry observations from the real orbits to nominal orbits is studied.The expression of first and second order derivatives with respect to height and inclination of the gravitational gradient observations in Taylor series expansion is derived.The results shows the reduction error based on reference model could up to 0.767 mE.The reduction error and the influence of reference model can be reduced by the iterative strategy based on remove-restore approach.Meanwhile,the griding error also can be reduced.4.The method to determinate the nominal orbit is deeply studied.The methods to interpolate quaternions,satellite position and velocity are studied.The cubic spline interpolation performs better than the other methods and the error of satellite position and velocity interpolation are mm and um/s,respectively.5.Kriging,Shepard,Continuous curvature tension spline method and nearest neighbor method are used for gridding of gradiometry observations,and Kriging method performs best and the error is within 1 mE.6.The Torus method for earth gravity field determination is proved feasible with simulated data.The influence of the grid error and the reference model can be weakened by the iteration.The gravity model complete to degree and order 200 is computed using simulated satellite gravity gradient with 5 nE/Hz1/2 white noise.The accuracy of the Torus method is slightly lower than the direct method,while the computational efficiency is greatly improved by using the 2D-FFT and the block-diagonal least-squares adjustment.7.The processing strategy of components with low precision and colored noise at low frequency in satellite gradiometry observations is studied.In order to reduce the influence of low-precision components in coordinate system transformation,the simulation values are used to replace the low-precision components Vxy and Vyz.The effects of different filtering methods to deal with the colored noise in GOCE satellite gravitational gradient observations are compared and analyzed.The method combination Butterworth with remove-restore is proposed and verified by the GOCE satellite measured data.8.The effect of grid resolution and reference model is analyzed.The optimal grid resolution is 24'×24' for determination satellite gravity field model up to degree and order 200 using 71-day data.EGM2008 is chosen as the reference model,and its influence focuses on the coefficients below degree and order 60.9.The GOCE satellite gravity model named GOCE_TorusO complete to 200 d/o are recovered using 71-day GOCE satellite gradiometry observations.It is assessed with the GPS/leveling data in China and USA.GOCE_TorusO and the first generation model released by ESA have a similar accuracy.GOCE_TorusO is better than EGM2008 in China due to the contribution of GOCE gravity gradiometry data.10.The satellite gravity field models complete to 200 d/o and 220 d/o are recovered using satellite gradiometry observations from 11,2009 to 8,2011.The validation of Torus models reveales a similar accuracy with the direct model GOSG01C and the models at the same period released by ESA.The accuracy of GOCE_Torus1 is improved by 5.8 cm than EGM2008 corrected for the omission errors using the EGM2008 coefficients between the spherical harmonic degrees from 200 up to 2190.The geoid degree error and cumulative error of GOCE_Torus2 compared with EIGEN-6C4 are 1.51 cm and 8.21 cm,respectively.