李新星^1,2,,
李建成^1,,,
刘晓刚³,
范昊鹏²,
靳超⁴
1. 武汉大学测绘学院, 武汉 430079
2. 信息工程大学地理空间信息学院, 郑州 450001
3. 西安测绘研究所, 西安 710054
4. 61365部队, 天津 300000

基金项目: 国家自然科学基金（41404020，41774018，42174001）和军队"双重"建设项目资助


详细信息

作者简介: 李新星, 男, 1988年生, 武汉大学博士研究生, 战略支援部队信息工程大学讲师, 主要从事物理大地测量方向研究.E-mail: minibad@126.com

通讯作者: 李建成, 男, 教授, 研究方向为物理大地测量.E-mail: jcli@whu.edu.cn

中图分类号: P223

收稿日期:2021-04-12
修回日期:2021-05-21
上线日期:2021-11-10

Spherical harmonic synthesis of local hexagonal grid point gravity anomalies with non-full-order Legendre method combined with spherical harmonic rotation transformation

LI XinXing^1,2,,
LI JianCheng^1,,,
LIU XiaoGang³,
FAN HaoPeng²,
JIN Chao⁴
1. School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China
2. Institute of Geospatial Information, Information Engineering University, Zhengzhou 450001, China
3. Xi'an Research Institute of Surveying and Mapping, Xi'an 710054, China
4. 61365 Troops, Tianjin 300000, China


More Information

Corresponding author: LI JianCheng,E-mail:jcli@whu.edu.cn

MSC: P223

--> Received Date: 12 April 2021
Revised Date: 21 May 2021
Available Online: 10 November 2021


摘要
摘要:本文首次提出基于六边形网格剖分的全球重力场结构，并解决了局部六边形网格点模型重力异常快速计算问题.首先，采用全新的方法给出缔合Legendre函数值从稳定振荡区到快速衰减区分界线的理论表达式，并基于该公式提出一种基于跨阶次递推的非全次Legendre方法，实现了高纬度地区点的快速球谐综合.其次，引入球谐旋转（Spherical Harmonic Rotation）理论，实现了2160阶次的球谐系数在坐标系旋转下的变换，结合非全次Legendre方法，解决了中低纬度地区点的快速球谐综合.通过计算南极洲（高纬）低分辨率和加里曼丹岛（低纬）高分辨率六边形网格重力异常表明，非全次Legendre方法以10^-19m·s^-2精度水平与传统全阶次方法计算结果吻合，且计算效率提升1倍多，旋转变换结合非全次Legendre方法的计算精度在10^-16m·s^-2，效率提升近5倍.本文提出的方法不仅提升了球谐综合的计算效率，凡是有高纬度的缔合Legendre函数计算的问题，都可利用该方法提升效率，同时，超高阶次球谐旋转变量变换的实现将在地磁场模型构建、计算机视觉、量子物理等领域发挥重要作用.
关键词: 球谐综合/
重力场模型/
Legendre函数/
球谐旋转变换/
跨阶次递推/
非全次Legendre/
六边形网格

Abstract:This paper proposes a global gravity field structure based on hexagonal grid division for the first time, and solves the problem of calculation efficiency of local hexagonal grid point gravity anomalies. First, a brand new method is used to achieve the theoretical expression of the boundary between the stable oscillation zone and the fast decay zone of the value of associated Legendre functions (ALFs). Then, we use this formula to propose a non-full-order Legendre method based on cross-degree-order recursion, which can be used to calculate gravity anomalies quickly at points of high latitudes. Second, we introduce the theory of spherical harmonic rotation (SHR) and realize the transformation of ultra-high-degree spherical harmonic coefficients by rotating the coordinate system. Combined with the non-full-order Legendre method, gravity anomalies of mid- and low-latitude points can be quickly calculated. The calculation of low-resolution hexagonal grid gravity anomalies on Antarctica (high latitude region) and high-resolution hexagonal grid ones on Kalimantan (low latitude region) shows that the non-full-order Legendre method has a precision level of 10^-19m·s^-2 compared with the traditional full-order method, and the calculation efficiency is more than doubled. The calculation accuracy of the rotation transformation combined with the non-full-order Legendre method is 10^-16m·s^-2, and the efficiency is increased by nearly 5 times. The research in this paper not only improves the efficiency of spherical harmonic synthesis, but also improves the calculation efficiency wherever there needs ALFs calculations at high latitude points. At the same time, the realization of ultra-high-degree spherical harmonic rotation transformation will play an important role in the theoretical research of geomagnetic field modeling, computer vision, quantum physics and other fields.
Key words:Spherical harmonic synthesis/
Earth gravitational model/
Legendre function/
Spherical harmonic rotation transformation/
Cross-degree-order recursion/
Non-full-order Legendre/
Hexagonal grid



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