Regional gravity field refinement for (quasi-) geoid determination based on spherical radial basis functions in Colorado
Regional gravity field refinement for (quasi-) geoid determination based on spherical radial basis functions in Colorado
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DOI：
10.1007/s00190-020-01431-2
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发表时间：
2020-10
影响因子：
4.4
通讯作者：
Qing Liu;M. Schmidt;L. Sánchez;M. Willberg
中科院分区：
文献类型：
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作者：
Qing Liu;M. Schmidt;L. Sánchez;M. Willberg
本研究提出了一个解决方案的“1厘米大地水准面实验”（科罗拉多实验）使用球面径向基函数（SRBFs）。作为来自世界各地的14个参与机构中唯一使用SRBFs的团体，我们在本文中突出了SRBFs的方法。对影响SRBFs在重力场模拟中性能的4个最重要因素的设置进行了详细的说明，即（1）带宽的选择，（2）SRBFs的位置，（3）SRBFs的类型以及（4）为减小边缘效应而进行的数据区扩展。覆盖相同光谱范围的两种类型的基函数分别用于地面和机载测量。对地面数据采用非平滑香农函数，避免了光谱信息的损失。利用具有平滑特性的三次多项式（CuP）函数作为低通滤波器对机载数据进行滤波，滤除高频噪声。虽然理论上证明了将不同观测值的不同SRBFs结合起来的想法是可能的，但在这项研究中，它首次应用于真实的数据。当结合地面数据的Shannon函数和机载数据的CuP函数时，我们的高度异常结果的RMS误差沿着GSV 17基准w.r.t验证数据（这是“科罗拉多实验”中其他贡献的平均结果）下降了5%，与通过使用Shannon函数获得的结果相比，这两个数据集。这种改进表明了针对不同观测类型使用不同SRBF的有效性和益处。将全球重力模型、地形模型、地面重力数据和航空重力数据相结合，讨论了各数据集对最终解的贡献。通过在GGM和地形模型中加入地面数据，高程异常结果相对于验证数据的均方根误差从4 cm降到1.8 cm，加入航空数据后，均方根误差进一步降到1 cm。与所有贡献的平均结果的比较表明，我们的高度异常和大地水准面高度解在GSVS17基准分别有一个RMS误差为1.0厘米和1.3厘米，我们的高度异常结果给出了一个RMS值为1.6厘米，在整个研究区，这都是最小的参与者。
This study presents a solution of the ‘1 cm Geoid Experiment’ (Colorado Experiment) using spherical radial basis functions (SRBFs). As the only group using SRBFs among the fourteen participated institutions from all over the world, we highlight the methodology of SRBFs in this paper. Detailed explanations are given regarding the settings of the four most important factors that influence the performance of SRBFs in gravity field modeling, namely (1) the choosing bandwidth, (2) the locations of the SRBFs, (3) the type of the SRBFs as well as (4) the extensions of the data zone for reducing the edge effect. Two types of basis functions covering the same spectral range are used for the terrestrial and the airborne measurements, respectively. The non-smoothing Shannon function is applied to the terrestrial data to avoid the loss of spectral information. The cubic polynomial (CuP) function which has smoothing features is applied to the airborne data as a low-pass filter for filtering the high-frequency noise. Although the idea of combining different SRBFs for different observations was proven in theory to be possible, it is applied to real data for the first time, in this study. The RMS error of our height anomaly result along the GSVS17 benchmarks w.r.t the validation data (which is the mean results of the other contributions in the ‘Colorado Experiment’) drops by 5% when combining the Shannon function for the terrestrial data and the CuP function for the airborne data, compared to those obtained by using the Shannon function for both the two data sets. This improvement indicates the validity and benefits of using different SRBFs for different observation types. Global gravity model (GGM), topographic model, the terrestrial gravity data, as well as the airborne gravity data are combined, and the contribution of each data set to the final solution is discussed. By adding the terrestrial data to the GGM and the topographic model, the RMS error of the height anomaly result w.r.t the validation data drops from 4 to 1.8 cm, and it is further reduced to 1 cm by including the airborne data. Comparisons with the mean results of all the contributions show that our height anomaly and geoid height solutions at the GSVS17 benchmarks have an RMS error of 1.0 cm and 1.3 cm, respectively; and our height anomaly results give an RMS value of 1.6 cm in the whole study area, which are all the smallest among the participants.