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,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中国大陆陆地重力测量数据区域3种分辨率的六边形网格,并利用中国81万余条实测重力资料,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,剖分层级L=3、4、5的六边形网格与面积近似相等的67.8′、24.5′、9.2′的四边形地理网格相比,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%；平均网格重力异常代表误差分别减小0.398 mGal、0.259 mGal和0.188 mGal。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,以及如何使用快速傅里叶变换技术在该不规律分布下实现高效计算。
Abstract:ObjectivesThe 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.
MethodsFirst, an open-source discrete global grid system H3 is selected to generate hexagonal grid groups at three resolutions in the mainland of China. Then we use more than 810 000 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.
ResultsThe results show that compared with 67.8′, 24.5′ and 9.2′ geographic grids, the hexagonal grids with grid partitioning levels L=3, 4, and 5 have approximately the same area. 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. 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 0.398 mGal, 0.259 mGal and 0.188 mGal, respectively, compared to that of the geographic grid gravity anomalies.
ConclusionsThe 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 fast fourier transformation technology to achieve efficient calculation under this uneven distribution.
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http://ch.whu.edu.cn/cn/article/doi/10.13203/j.whugis20220569
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图 3 中国部分区域六边形网格层次剖分结构示意图
Figure 3. Schematic Diagram of the Hierarchical Structure of Hexagonal Grid in Parts of China
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图 4 网格内实测点数量统计情况
Figure 4. Distribution of Number of Grids Containing Measurement Points
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图 6 网格平均重力异常的代表误差大小及分布
Figure 6. Magnitude and Distribution of Commission Errors of Grid-Averaged Gravity Anomalies
表 1 六边形网格的参数统计表
Table 1 Statistics of Hexagonal Grid Parameters
L NL 平均面积/km2 平均边长/km 0 122 4 250 546.847 700 0 1 107.712 591 000 1 842 607 220.978 242 9 418.676 005 500 2 5 882 86 745.854 034 7 158.244 655 800 3 41 162 12 392.264 862 1 59.810 857 940 4 288 122 1 770.323 551 7 22.606 379 400 5 2 016 842 252.903 364 5 8.544 408 276 6 14 117 882 36.129 052 1 3.229 482 772 
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表 2 中国区域内两种网格剖分情况对比
Table 2 Comparison of Meshing of Two Shapes in China
六边形网格 四边形地理网格 L 网格数 分辨率/(′) 网格数 3 820 67.8 842 4 5 748 24.5 5 722 5 40 150 9.2 40 603
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表 3 包含测量点的网格数量统计
Table 3 Statistics of Number of Grids Containing Measurement Points
六边形网格 四边形地理网格 L 网格数 有点网格数 有效网格占比/% 分辨率/(′) 网格数 有点网格数 有效网格占比/% 3 820 819 99.88 67.8 842 828 98.34 4 5 748 5 566 96.83 24.5 5 722 5 458 95.39 5 40 150 28 414 70.77 9.2 40 603 27 594 67.96
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表 4 网格平均重力异常的代表误差均值统计情况
Table 4 Statistics of Commission Errors of Grid-Averaged Gravity Anomalies
六边形网格 四边形地理网格 L 网格数 代表误差/mGal 分辨率/(′) 统计网格数 代表误差/mGal 3 811 31.129 67.8 750 31.527 4 4 709 21.195 24.5 4 749 21.454 5 21 190 13.243 9.2 20 502 13.431
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