Cai Lin, Wan Xiaoyun, Hsu Houtse, Ran Jiangjun, Meng Xiangchao, Luo Zhicai, Zhou Zebing
MOE Key Laboratory of Fundamental Physical Quantities Measurement, Hubei Key Laboratory of Gravitation and Quantum Physics, School of Physics, Huazhong University of Science and Technology, Wuhan, 430074, China.
Institute of Geophysics, Huazhong University of Science and Technology, Wuhan, 430074, China.
Sci Rep. 2021 Feb 11;11(1):3581. doi: 10.1038/s41598-021-81840-1.
Due to the independence of the gradiometer instrument's orientation in space, the second invariant [Formula: see text] of gravity gradients in combination with individual gravity gradients are demonstrated to be valid for gravity field determination. In this contribution, we develop a novel gravity field model named I3GG, which is built mainly based on three novel elements: (1) proposing to utilize the third invariant [Formula: see text] of the gravity field and steady-state ocean circulation explorer (GOCE) gravity gradient tensor, instead of using the [Formula: see text], similar to the previous studies; (2) applying an alternative two-dimensional fast fourier transform (2D FFT) method; (3) showing the advantages of [Formula: see text] over [Formula: see text] in the effect of measurement noise from the theoretical and practical computations. For the purpose of implementing the linearization of the third invariant, this study employs the theory of boundary value problems with sphere approximation at an accuracy level of [Formula: see text]. In order to efficiently solve the boundary value problems, we proposed an alternative method of 2D FFT, which uses the coherent sampling theory to obtain the relationship between the 2D FFT and the third invariant measurements and uses the pseudo-inverse via QR factorization to transform the 2D Fourier coefficients to spherical harmonic ones. Based on the GOCE gravity gradient data of the nominal mission phase, a novel global gravity field model (I3GG) is derived up to maximum degree/order 240, corresponding to a spatial resolution of 83 km at the equator. Moreover, in order to investigate the differences of gravity field determination between [Formula: see text] with [Formula: see text], we applied the same processing strategy on the second invariant measurements of the GOCE mission and we obtained another gravity field model (I2GG) with a maximum degree of 220, which is 20 degrees lower than that of I3GG. The root-mean-square (RMS) values of geoid differences indicates that the effects of measurement noise of I3GG is about 20% lower than that on I2GG when compared to the gravity field model EGM2008 (Earth Gravitational Model 2008) or EIGEN-5C (EIGEN: European Improved Gravity model of the Earth by New techniques). Then the accuracy of I3GG is evaluated independently by comparison the RMS differences between Global Navigation Satellite System (GNSS)/leveling data and the model-derived geoid heights. Meanwhile, the re-calibrated GOCE data released in 2018 is also dealt with and the corresponding result also shows the similar characteristics.
由于重力梯度仪在空间中方向的独立性，重力梯度的第二不变量[公式：见原文]与各个重力梯度相结合，被证明对重力场确定是有效的。在本论文中，我们开发了一种名为I3GG的新型重力场模型，它主要基于三个新元素构建：（1）提议利用重力场的第三不变量[公式：见原文]和稳态海洋环流探测器（GOCE）重力梯度张量，而不是像之前的研究那样使用[公式：见原文]；（2）应用一种替代的二维快速傅里叶变换（2D FFT）方法；（3）从理论和实际计算中表明[公式：见原文]在测量噪声影响方面优于[公式：见原文]。为了实现第三不变量的线性化，本研究采用了球近似下边界值问题的理论，精度为[公式：见原文]。为了有效解决边界值问题，我们提出了一种替代的2D FFT方法，它利用相干采样理论获得2D FFT与第三不变量测量之间的关系，并通过QR分解使用伪逆将二维傅里叶系数转换为球谐系数。基于标称任务阶段的GOCE重力梯度数据，推导了一个新的全球重力场模型（I3GG），最高阶次为240，对应赤道处83公里的空间分辨率。此外，为了研究[公式：见原文]与[公式：见原文]在重力场确定上的差异，我们对GOCE任务的第二不变量测量应用了相同的处理策略，得到了另一个最高阶次为220的重力场模型（I2GG），比I3GG低20阶。大地水准面差异的均方根（RMS）值表明，与重力场模型EGM2008（2008年地球引力模型）或EIGEN - 5C（EIGEN：欧洲通过新技术改进的地球重力模型）相比，I3GG的测量噪声影响比I2GG低约20%。然后通过比较全球导航卫星系统（GNSS）/水准测量数据与模型推导的大地水准面高度之间的RMS差异，独立评估I3GG的精度。同时，还处理了2018年发布的重新校准的GOCE数据，相应结果也显示出类似的特征。
