Hexagonal grid mean free-air gravity anomaly data construction and its statistical advantage analysis

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.