引力场关于经度和纬度方向的梯度在两极附近会产生奇异性现象,这将会给诸如重力场和静态洋流探索(GOCE,Gravity field and stesdy-state Oceam Circulation Explorer)数据处理等引力场的研究工作带来诸多不便和困难。这里首先分析了该奇异性产生的原因,即目前采用的球坐标系自身在两极处是奇异的;然后利用Legendre函数的性质推导了一组不含任何奇异性的计算引力场梯度的计算公式;最后与常用的迭代方法进行了实例计算比较,结果表明所导出的公式不仅计算精度大大提高,而且计算用时也不会增加。
Here we report new approaches of recovering the Earth gravitational field from GOCE (Gravity field and steady-state Ocean Circulation Explorer) gradiometric data with the help of the gradient tensor’s invariants. Our results only depend on GOCE satellite’s position and gradiometry, in other words, they are completely independent of the satellite attitude. First, starting from the invariants, linearization models are established, which can be referred as the general boundary conditions on the satellite’s orbit. Then, the spherical approximation expressions for the models are derived, and the corresponding solving methods for them are discussed. Furthermore, considering effects of J2-term, the spherical approximation models are improved so that the accuracies of the boundary conditions can be theoretically raised to O ( J 2/2 T), which is approximately equivalent to O(T2). Finally, some arithmetic examples are constructed from EGM96 model based on the derived theories, and the computational results illustrate that the spherical models have accuracies of 10-7 and the order recovering the gravitational field can reach up to 200, and the models with regard to effect of J2-term have accuracies of 10-8 and the order can reach up to 280.
YU JinHai1,2,3 & ZHAO DongMing4 1 College of Earth Science, Graduate University of Chinese Academy of Sciences, Beijing 100049, China
