为了研究卫星重力梯度技术对中高频地球重力场反演精度的影响，本文基于时空域混合法，利用Kaula正则化反演了250阶GOCE地球重力场。模拟结果表明：第一，时空域混合法是精确和快速求解高阶地球重力场的有效方法；第二，Kaula正则化是降低正规阵病态性的重要方法；第三，基于改进的预处理共轭梯度迭代法可快速求解大型线性方程组，计算速度较直接最小二乘法至少提高1000倍；第四，基于卫星轨道误差1 cm和卫星重力梯度误差3×10-12 /s2，在250阶处反演累计大地水准面和重力异常的精度分别为9.295 cm和0.204 mGal。第五，论证了基于国际GRACE和GOCE卫星计划反演高精度和高空间分辨率地球重力场的互补性。
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.
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