Abstract
There exist several limitations in the calculation of the earth's gravity field based on the measurement data at the centroids of geographic grid cells. To address these issues, we propose using the hexagonal geodesic discrete global grid system in the spherical harmonic (SH) analysis and synthesis of the earth's gravity field. We show that using interpolation of the associated Legendre functions (ALFs) and transformation of the SH coefficients (SHCs) with rotation improves the efficiency of SH synthesis with non-equal latitudinal quasi-hexagonal grid points. Our analysis also indicates that the global SH analysis (GSHA) with the quasi-hexagonal grids significantly reduces the number of necessary observations while ensuring the accuracy of the recovered SHCs. The results in this paper also confirm that both methods based on ALFs interpolation and SH rotation can quickly compute the synthetic gravity anomalies with the accuracy level of 10–11 mGal. It is also seen that in GSHA, using the ISEA4H grid saves ~ 37% necessary observations compared with the classic geographic grid without any appreciable loss of accuracy. Moreover, it could reduce the aliasing of power from the higher to lower degrees in GSHA considerably, which is one of the important factors affecting the consistency of the earth's gravitational model with the real gravity field.
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Acknowledgements
We thank Dr. Liang Wei, Dr Liu Xiaogang, and Professor Ben Jin for their precious suggestions for preparing and revising the manuscript. The authors would also like to express their gratitude to EditSprings (https://www.editsprings.com/) for the expert linguistic services provided.
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Key Technologies Research and Development Program (Grant No. 2018YFB0505304), National Natural Science Foundation of China (Grant Nos. 41404020, 41671409).
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XL and JL designed the research; XL and XT performed the research; XL and SL analyzed the data; and XL and HF wrote the paper.
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Li, X., Li, J., Tong, X. et al. The employment of quasi-hexagonal grids in spherical harmonic analysis and synthesis for the earth's gravity field. J Geod 96, 89 (2022). https://doi.org/10.1007/s00190-022-01653-6
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DOI: https://doi.org/10.1007/s00190-022-01653-6