Hexagonal grid mean free-air gravity anomaly data construction and its statistical advantage analysis
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摘要: 传统地理网格在重力场数据处理和解算中被广泛使用,但也带来诸多不便,例如网格面积不等、各向同性差等。针对地球重力场中地理网格的使用所带来的局限性,本文首次提出采用具有分层结构的六边形网格系统对重力测量数据分布区域进行划分,基于开源的H3离散球面网格系统构建我国陆地重力测量数据区域3种分辨率的六边形网格,并利用我国81万余实测重力资料,构建了上述3种分辨率下的六边形网格平均重力异常数值模型,以及平均大小与之对应的地理网格平均重力异常数值模型,最后统计对比了地理网格和六边形网格两种剖分方式下网格平均空间重力异常值的代表误差大小。结果表明: L=3、4、5三种分辨率下的六边形网格与面积近似相等的67.8′、24.5′、9.2′的地理网格相比,(1)网格内包含实测点的网格数量占总网格数量比更高,包含实测点的网格占比分别提高1.54%、1.44%和2.81%。(2)平均网格重力异常代表误差分别减小0.398mGal、0.259mGal和0.188mGal。综上所述,分层六边形网格系统因其近似等积和各项同性特征,在地球重力场数据统计和数据生产中具有应用优势。尽管层次六边形网格系统在地球重力场的球谐合成与分析、地形效应的快速计算、数值积分计算等方面也有良好的应用前景,但不可否认的是,它的使用和推广仍面临许多需要解决的难题,例如六边形网格的非等纬度分布引起的Legendre计算问题,以及如何使用FFT技术在该不规律分布下实现高效计算。Abstract: Objectives: The widespread use of traditional geographic grids in gravity field data processing has brought many inconveniences, such as unequal grid areas and poor isotropic characteristics. In order to solve the above problems in the application of geographic grid in the earth gravity field, we propose for the first time to apply a hierarchical hexagonal grid system to gravity data gridding in the mainland of China. Methods: An open-source Discrete Global Grid System (DGGS) H3 is selected to generate hexagonal grid groups at three resolutions in continental area of China. Then we use more than 810000 in-situ gravity data to construct numerical models of average gravity anomaly on hexagonal grid with different resolutions and geographic grid with corresponding resolutions. Finally, we calculated and compared the commission errors of the grid average free-air gravity anomaly under the geographic grid and hexagonal grid. Results: The results show that:(1) Compared with 67.8 ', 24.5 ' and 9.2 ' geographic grids, the hexagonal grids with L=3, 4 and 5 resolutions have approximately the same area. (2) Hexagonal grids have more effective grids covering measured points than geographic grids. For example, the improvements of the percentages of effective grids in total in hexagonal grids under three resolution levels are 1.54%、1.44% and 2.81% respectively compared to the geographic grids. (3) Hexagonal grids have smaller commission error than geographic grids. For example, under the above three resolution levels, the mean commission errors of the hexagonal grid gravity anomalies are reduced by 0.398mGal、0.259mGal and 0.188mGal respectively, compared to that of the geographic grid gravity anomalies. Conclusions: The layered hexagonal grid system has advantages in the application of earth gravity field data statistics and data production due to its quasi-homogeneous and quasi-isotropic horizontal resolution over the entire sphere. Although the layered hexagonal grid system also has good application prospects in spherical harmonic synthesis and analysis of the earth's gravity field, rapid calculation of terrain effects, numerical integration calculation, etc., it is undeniable that its use and promotion still faces many problems that need to be solved, such as the calculation problems caused by the non-equal latitude distribution of the hexagonal grids, and how to use FFT technology to achieve efficient calculation under this uneven distribution.
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