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Various Spherical Harmonic Analysis and Spherical Harmonic Synthesis Algorithms and Their Software Design
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Xiaoyu TANG1, Wenjin CHEN1, *, Xiao GONG2, Xiaolong TAN1
Journal of Geodesy and Geodynamics | 2025, 45(11) : 1121 - 1126, 1184
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Journal of Geodesy and Geodynamics | 2025, 45(11): 1121-1126, 1184
Various Spherical Harmonic Analysis and Spherical Harmonic Synthesis Algorithms and Their Software Design
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Xiaoyu TANG1, Wenjin CHEN1, *, Xiao GONG2, Xiaolong TAN1
Affiliations
  • 1 School of Civil and Surveying and Mapping Engineering, Jiangxi University of Science and Technology, 86 Hongqi Road, Ganzhou 341000, China
  • 2 Jiangxi Science and Technology Infrastructure Platform Center, 1416 Jinggangshan Road, Nanchang 330003, China

    • TANG Xiaoyu, postgraduate, majors in geodesy and surveying engineering, E-mail:

About Author:

TANG Xiaoyu, postgraduate, majors in geodesy and surveying engineering, E-mail:

Published: 2025-11-15 doi: 10.14075/j.jgg.2024.11.540
Outline
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We derive five spherical harmonic analysis algorithms in detail and develop a user-friendly and easy-to-operate practical software using the scientific computing language MATLAB. To validate the performance of five algorithms, we conduct a numerical analysis of the computational efficiency and accuracy of fast Fourier transform(FFT), least squares(LS), weighted least squares(WLS), approximate quadrature(AQ), and first Neumann method(FNM) algorithms at harmonic degrees of 180, 360, 720, 1 800 and 2 160, using the global topographic data DTM2006.0 as a case study. The results show that the AQ algorithm performs best in terms of computational efficiency, while the LS algorithm achieves the highest precision. The residuals of all five algorithms approximately follow a normal distribution, indicating that none of five algorithms exhibit systematic biases.

spherical harmonic analysis  /  spherical harmonic synthesis  /  Earth's gravity field  /  MATLAB  /  software design
唐晓雨, 陈文进, 龚枭, 谭小龙. 多种球谐分析与球谐综合算法研究及其软件设计. 大地测量与地球动力学, 2025 , 45 (11) : 1121 -1126, 1184 . DOI: 10.14075/j.jgg.2024.11.540
Xiaoyu TANG, Wenjin CHEN, Xiao GONG, Xiaolong TAN. Various Spherical Harmonic Analysis and Spherical Harmonic Synthesis Algorithms and Their Software Design[J]. Journal of Geodesy and Geodynamics, 2025 , 45 (11) : 1121 -1126, 1184 . DOI: 10.14075/j.jgg.2024.11.540
Funding
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  • National Natural Science Foundation of China(42264001)
  • Key Research and Development Program of Jiangxi Province(20243BBG71036)
  • Foundation for Doctors of Jiangxi University of Science and Technology(205200100588)
  • Open Fund of Jiangxi Key Laboratory of Safe and Efficient Mining of Rare Metal Resources(2024XJKCCSZ05)
Appendix
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Year 2025 volume 45 Issue 11
26
9
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Article Info
doi: 10.14075/j.jgg.2024.11.540
  • Receive Date：2024-11-27
  • Online Date：2026-10-29
  • Published：2025-11-15
Article Data
Affiliations
History
  • Received：2024-11-27
Funding
National Natural Science Foundation of China(42264001)
Key Research and Development Program of Jiangxi Province(20243BBG71036)
Foundation for Doctors of Jiangxi University of Science and Technology(205200100588)
Open Fund of Jiangxi Key Laboratory of Safe and Efficient Mining of Rare Metal Resources(2024XJKCCSZ05)
Affiliations
    1 School of Civil and Surveying and Mapping Engineering, Jiangxi University of Science and Technology, 86 Hongqi Road, Ganzhou 341000, China
    2 Jiangxi Science and Technology Infrastructure Platform Center, 1416 Jinggangshan Road, Nanchang 330003, China
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表12种不同金属材料的力学参数
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多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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