利用IGRF模型计算全张量地磁梯度

doi:10.11720/wtyht.2020.1416

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摘要

国际地磁参考场(IGRF)是一种描述地球主磁场的国际通用模型。目前利用该模型能够计算任意点位的地磁七要素,但随着航空全张量磁测技术的发展,对地球主磁场的全张量磁梯度数据有着迫切的需求。笔者梳理了IGRF模型的计算原理并进一步推导出球谐展开的全张量磁梯度表达式,实现了任意给定点位地磁场七要素和全张量的计算,并用地磁七要素与美国国家海洋和大气管理局(NOAA)网站计算数据进行对照,结果准确可靠。绘制了某地区地磁场的全张量磁梯度等值线图,结果满足Laplace方程,为航空全张量磁梯度测量中选择学习飞行工区和飞行高度提供了理论依据。

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	钟炀
	管彦武
	石甲强
	肖锋

关键词 ： IGRF, 全张量磁梯度, 球谐分析, 勒让德多项式

Abstract：

The international geomagnetic reference field (IGRF) is a general international model for describing the earth’s main magnetic field. At present,this model can be used to calculate the seven elements of geomagnetic field at any point. However,with the development of aeronautical full tensor magnetic measurement technology,there is an urgent need for full tensor geomagnetic gradient data. In this paper,the calculation principle of the IGRF model is summarized and the expression of the full tensor geomagnetic gradient with spherical harmonic expansion is derived. The calculation of the seven elements of geomagnetic field and the full tensor geomagnetic gradient at any given point is realized. Comparing with the calculated data from the website of the National Oceanic and Atmospheric Administration of the United States (NOAA),the results are accurate and reliable. The contour map of the full tensor geomagnetic field in a region is drawn, and the results were in accordance with the Laplace equation. It provides the theoretical basis for the selection of learning flight working area and flight height in the aeromagnetic survey.

Key words： IGRF FTMG spheric harmonic analysis legendre polynomials

收稿日期: 2019-09-02 出版日期: 2020-06-24

P631

基金资助:国家重点研发计划“航空磁场测量技术系统研制”(2017YFC0602000)

作者简介: 钟炀(1995-),男,吉林长春人,硕士研究生,主要研究方向为地球探测与信息技术。Email: zhongyang18@mails.jlu.edu.cn

引用本文:

钟炀, 管彦武, 石甲强, 肖锋. 利用IGRF模型计算全张量地磁梯度[J]. 物探与化探, 2020, 44(3): 582-590.
Yang ZHONG, Yan-Wu GUAN, Jia-Qiang SHI, Feng XIAO. The calculation method of full tensor geomagnetic gradient based on IGRF model. Geophysical and Geochemical Exploration, 2020, 44(3): 582-590.

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https://www.wutanyuhuatan.com/CN/10.11720/wtyht.2020.1416 或 https://www.wutanyuhuatan.com/CN/Y2020/V44/I3/582

Fig.1 地理坐标系与地心坐标系

Table 1 0~3阶勒让德多项式

n	m	伴随勒让德多项式 P_n_,_m(cosθ)	高斯规格化伴随勒让德多项式 Pⁿ^,^m(cosθ)	施密特拟规格化伴随勒让德多项式 $P n m$ (cosθ)
0	0	1	1	1
1	0	cosθ	cosθ	cosθ
1	1	sinθ	sinθ	sinθ
2	0	$12$ (3cos²θ-1)	$16$ (3cos²θ-1)	$12$ (3cos²θ-1)
2	1	3cosθsinθ	$12$ cosθsinθ	$3$ cosθsinθ
2	2	3sin²θ	$12$ sin²θ	$32$ sin²θ
3	0	$12$ cosθ(5cos²θ-3)	$130$ cosθ(5cos²θ-3)	$12$ cosθ(5cos²θ-3)
3	1	$32$ sinθ(5cos²θ-1)	$130$ sinθ(5cos²θ-1)	$38$ sinθ(5cos²θ-1)
3	2	15cosθsin²θ	$16$ cosθsin²θ	$154$ cosθsin²θ
3	3	15sin³θ	$16$ sin³θ	$58$ sin³θ

Table 2 0~3阶伴随勒让德多项式

Fig.2 总地磁场B等值线

Fig.3 地磁场偏角D(a)及倾角I(b)等值线

Fig.4 地磁场三分量(a)B_x(b)B_y(c)B_z等值线

Fig.5 全张量地磁梯度等值线

Fig.6 主对角线上3个张量分量之和等值线

Table 3 测区内点位磁场值

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