Accurate and Rapid Determination of GOCE Earth’s Gravitational Field using Time-Space-Wise Approachassociated with Kaula Regularization 

The GOCE Earth’s gravitational field complete up to degree and order 250 is recovered based on the time-space-wise approach associated with Kaula regularization in order to study the influences of satellite gravity gradiometry on the accuracy of the Earth’s medium-high frequency gravitational field recovery. The simulated results show: Firstly, the time-space-wise approach is an effective way to accurately and rapidly determine the Earth’s high-degree gravitational field; Secondly, the Kaula regularization is one of the key processes to reduce ill condition of normal matrix; Thirdly, the large-scale linear system of equations is solved quickly using the improved pre-conditioned conjugate-gradient iterative approach, and the computing speed can be improved at least 1000 times as compared to the direct least-squares approach; Fourthly, at degree 250, cumulative geoid height and gravity anomaly errors are 9.295 cm and 0.204 mGal with orbital error 1 cm and gravity gradient error 3×10-12 /s2, respectively; Finally, the complementarity of high-accuracy and high-resolution Earth’s gravitational field recovery between international GRACE and GOCE missions is demonstrated.

图1 GOCE地球引力位系数迭代精度

图2 GOCE大地水准面和重力异常累积误差

Wei Zheng, Houtse Hsu, Min Zhong, Meijuan Yun. Accurate and rapid determination of GOCE Earth’s gravitational field using time-space-wise approach associated with Kaula regularization. Chinese Journal of Geophysics, 2011, 54(1): 240-249.