利用IGRF模型计算全张量地磁梯度

doi:10.11720/wtyht.2020.1416

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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

Received: 02 September 2019 Published: 24 June 2020

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	Yang ZHONG
	Yan-Wu GUAN
	Jia-Qiang SHI
	Feng XIAO

Cite this article:

Yang ZHONG,Yan-Wu GUAN,Jia-Qiang SHI, et al. The calculation method of full tensor geomagnetic gradient based on IGRF model[J]. Geophysical and Geochemical Exploration, 2020, 44(3): 582-590.

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https://www.wutanyuhuatan.com/EN/10.11720/wtyht.2020.1416 OR https://www.wutanyuhuatan.com/EN/Y2020/V44/I3/582

Geographic coordinate system and geocentric coordinate system

Legendre polynomials of order 0~3

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

Order 0-3 adjoint Legendre polynomials

Contour map of the total geomagnetic field

Contour map of geomagnetic field deviation(a) and dip angle(b)

Three-component contour map of the geomagnetic field

Full-tensor geomagnetic gradient contour map

Contour map of the sum of the three tensor components on the main diagonal

Table of point position magnetic field values in the test area

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