在介绍Torus方法反演地球重力场模型的基本原理和方法的基础上,基于圆环面上均匀分布的卫星引力梯度模拟观测值解算了200阶次的地球重力场模型,在无误差情况下,Torus方法解算模型的阶误差RMS小于10-16,验证了该方法的严密性。利用61 d GOCE卫星轨道上无误差的模拟引力梯度观测值解算了200阶次的地球重力场模型,分析了格网化误差、极空白对解算精度的影响,迭代3次后,在不考虑低次系数情况下,模型的大地水准面阶误差和累积误差均较小,最大值仅为0.022 mm和0.099 mm。在沿轨卫星引力梯度模拟数据中加入5 mE/Hz1/2的白噪声,基于Torus方法和空域最小二乘法解算了200阶次的地球重力场模型,Torus方法的精度略低于空域最小二乘法的精度,在不考虑低次项的情况下,两种方法解算模型的大地水准面阶误差最大值分别为1.58 cm和1.45 cm,累积误差最大值分别为6.37 cm和5.55 cm。但由于采用了二维快速傅里叶技术和块对角最小二乘法,极大地提高了计算效率。本文数值结果说明Torus方法是一种独立有效的方法,可用于GOCE任务海量卫星引力梯度观测值反演重力场的快速解算。
The principle of Torus method in Earth's gravity field determination from GOCE satellite gradiometry data is discussed. The Earth's gravity field model complete to degree and order 200 is recovered using simulated satellite gradiometry observations on a Torus grid, and the degree error RMS is smaller than 10-16, which shows the effectiveness of Torus approach. The gravity field model is also resolved using the simulated satellite gradiometry observations given on GOCE orbits of 61 days. The influences of interpolation and polar gaps are analyzed. Without considering the low-order coefficients the geoid degree errors and cumulative errors are very small after three iterations. The maximums of them are only 0.022 mm and 0.099 mm. The white noise with PSD 5 mE/Hz1/2 is added to the simulated observations and the gravity field model complete to degree and order 200 is also computed. The model is compared with that model which is derived using space-wise LS method and the same observations. It shows that the precision of Torus is slightly lower. Without considering the low-order coefficients the maximum geoid degree errors of Torus and space-wise LS method are 1.58 cm and 1.45 cm, and the maximum cumulative geoid errors are 6.37 cm and 5.55 cm, respectively. But the computational efficiency of Torus is greatly improved by using the two-dimensional FFT and the block-diagonal least-squares adjustment. The numerical results show that Torus method is independent and valid. Meanwhile fast resolution of gravity field based on massive amount of GOCE satellite gradiometry observations is feasible.
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