利用改进的Hotine积分确定地球外部重力场

doi:10.11947/j.AGCS.2023.20210442

测绘学报 ›› 2023, Vol. 52 ›› Issue (3): 397-404.doi: 10.11947/j.AGCS.2023.20210442

利用改进的Hotine积分确定地球外部重力场

冯进凯¹, 吴晓平¹, 王庆宾¹, 赵东明¹, 黄子炎^1,2

1. 信息工程大学地理空间信息学院, 河南郑州 450001;
2. 信息工程大学研究生院, 河南郑州 450001

收稿日期:2021-08-17 修回日期:2022-10-21 发布日期:2023-04-07
通讯作者: 黄子炎 E-mail:huangziyan1995@126.com
作者简介:冯进凯(1992-),男,博士生,讲师,研究方向为物理大地测量。E-mail:fengjinkai1992@163.com
基金资助:
国家自然科学基金(42174001;42174007;42174008)

Using the improved Hotine integral to determine earth gravity field

FENG Jinkai¹, WU Xiaoping¹, WANG Qingbin¹, ZHAO Dongming¹, HUANG Ziyan^1,2

1. Institute of Geospatial Information, Information Engineering University, Zhengzhou 450001, China;
2. Graduate Institute, Information Engineering University, Zhengzhou 450001, China

Received:2021-08-17 Revised:2022-10-21 Published:2023-04-07
Supported by:
The National Natural Science Foundation of China (Nos. 42174001;42174007;42174008)

摘要/Abstract

摘要： 为解决Hotine积分计算低空扰动引力径向分量时的奇异性问题,本文从Hotine积分公式入手,分析了产生奇异性的原因及其影响;并在此基础上根据分区原理推导出Hotine积分的无奇异公式,本文算法将内区视为扰动重力值相等的微小平面,直接进行数学积分以消除奇异性,最后从理论上阐述了本文算法的优势。数值试验结果表明,相较于传统方法,改进后的Hotine积分在整个积分区域内连续,地表附近扰动引力径向分量的计算结果奇异性消除,而且高度越低,精度越好。此外,经过改化,Hotine积分核函数变为边界面上扰动重力差分形式,这减弱了远区地面数据对计算结果的影响,改进后的Hotine积分对地面数据的需求量相比于传统算法降低了近20倍,而且高度越低,对积分半径的要求越低。本文算法适用于低空外部重力场计算,而且效能较高。

关键词: 扰动重力, Hotine积分, 奇异性, 积分半径

Abstract: To solve the singularity problem of Hotine integral in calculating the radial component of disturbing gravity at a low altitude, this paper analyzes the causes and effects of singularity in traditional Hotine integral, on which the nonsingular formula of Hotine integral is derived according to the partition principle. The basic idea of the new method is to divide the integral region into inner region and far region, and the inner region is regarded as a micro plane with equal disturbing gravity value, in which we integrate the integral kernel function directly to eliminate singularity, then the advantages of the new method are expounded theoretically. The numerical results show that compared with the traditional Hotine integral, the improved one is continuous in the whole integral region, and the singularity of radial disturbing gravity is eliminated near the surface, besides the accuracy increases with the altitude decreases. What's more, the input data turns to the disturbing gravity difference on the ground, which reduces the influence of remote ground disturbing gravity in the calculation results. Numerical results show the demand for ground disturbing gravity data of the improved Hotine integral is nearly 20 times lower than that of the traditional algorithm, and the lower the height, the lower the demand for the integral radius.In conclusion, the algorithm proposed in this paper is suitable for the calculation of low altitude earth gravity field with high efficiency.

Key words: disturbing gravity, Hotine integral, singularity, integral radius

中图分类号:

P223

冯进凯, 吴晓平, 王庆宾, 赵东明, 黄子炎. 利用改进的Hotine积分确定地球外部重力场[J]. 测绘学报, 2023, 52(3): 397-404.

FENG Jinkai, WU Xiaoping, WANG Qingbin, ZHAO Dongming, HUANG Ziyan. Using the improved Hotine integral to determine earth gravity field[J]. Acta Geodaetica et Cartographica Sinica, 2023, 52(3): 397-404.

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利用改进的Hotine积分确定地球外部重力场

Using the improved Hotine integral to determine earth gravity field

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