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.
Barraclough D R, Harwood J M, Leaton B R, et al. A definitive model of the geomagnetic field and its secular variation for 1965—I.Derivation of model and comparison with the IGRF[J]. Geophysical Journal International, 1978,55(1):111-121.
doi: 10.1111/j.1365-246X.1978.tb04750.x
An Z C, Xu Y F. Spherical harmonic analysis and international geomagnetic reference[J]. Seismological and Geomagnetic Observation and Research, 1982,3(5):22-26.
An Z C, Xu Y F. The spherical harmonic model of the global geomagnetic field is tested with data from China[J]. Seismological and Geomagnetic Observation and Research, 1983,4(5):1-13.
An Z C, Wang Y H, Xu Y F, et al. Calculation and evaluation of IGRF[J]. Computing Techniques for Giophysical and Geochenical Exploration, 1988,10(2):93-99.
An Z C. Method of calculating the annual mean values of observatory by using IGRF[J]. Seismological and Geomagnetic Observation and Research, 1987,8(5) : 15-18.
An Z C. Geomagnetic field over China and adjacent at epoch 1995.0derived from the seventh generation IGRF[J]. Progress in Geophysics, 1997,12(3):22-26.
Lin Y F, Zeng X P, Guo Q H. Analysis of secular variations of non-dipole geomagnetic field in east asia[J]. Chinese Journal of Geophysics, 1985,28(5):482-496.
[11]
Matteo N A, Morton Y T. Ionosphere geomagnetic field: Comparison of IGRF model prediction and satellite measurements 1991—2010[J]. Radio Science, 2011,46(4):1-10.
[12]
Xu W Y. Revision of the high-degree Gauss coefficients in the IGRF 1945—1955 models by using natural orthogonal component analysis[J]. Earth,Planets and Space, 2002,54(7):753-761.
doi: 10.1186/BF03351728
[13]
Maus S, Fairhead D, Hemant K, et al. A near-surface geomagnetic field model to spherical harmonic degree 720[C]// AGU Fall Meeting Abstracts, 2006.
Zhang S Q, Yang D M, Li Q, et al. The consistence analysis of IGRF model value and annual mean value of some geomagnetic observatories in China[J]. Seismological and Geomagnetic Observation and Research, 2008,29(2):42-49.
[15]
Molina F, de Santis A. Considerations and proposal for a best utilization of IGRF over areas including a geomagnetic observatory[J]. Physics of the Earth and Planetary Interiors, 1987,48(3-4):379-385.
doi: 10.1016/0031-9201(87)90162-2
[16]
任国泰. 关于东亚大陆磁场的研究[J]. 地球物理学报, 1981(4):404-414.
[16]
Ren G T. A comparison between regional model and global model of the geomagnetic field[J]. Geophysical and Geochemical Exploration, 1981,?(4):404-414.
An Z C. A comparison between regional model and global model of the geomagnetic field[J]. Geophysical and Geochemical Exploration, 1991,15(4):248-254.
[18]
Smart D F, Shea M A, Flückiger E O. Magnetospheric models and trajectory computations[J]. Space Science Reviews, 2000,93(2):305-333.
doi: 10.1023/A:1026556831199
[19]
Smart D F, Shea M A. The limitations of using vertical cutoff rigidities determined from the IGRF magnetic field models for computing aircraft radiation dose[J]. Advances in Space Research, 2003,32(1):95-102.
doi: 10.1016/S0273-1177(03)90375-9
[20]
Davis J. Mathematical modeling of earth’s magnetic field[R]. Technical Note,Virginia Tech, Blacksburg, 2004.
Chai S J, Chen S D, Zhang S. Calculation and software realization of international geomagnetic reference field[J]. Journal of Jilin University:Information Science Edition , 2015,33(3):280-285.
Yang M Y, Guan X Y, Li W S. Calculation of IGRF international geomagnetic reference field model[J]. Electronic Measurement Technology, 2017,40(6):97-100.
[24]
Campbell W H. Introduction to geomagnetic fields[M]. Cambridge: Cambridge University Press, 2003: 19-33.
[25]
Balmino G, Barriot J, Koop R, et al. Simulation of gravity gradients: a comparison study[J]. Bulletin Geodesique, 1991,65(4):218-229.
doi: 10.1007/BF00807265
[26]
Abramowitz M, Stegun I A, Romer R H. Handbook of mathematical functions with formulas,graphs,and mathematical tables[M]. Gaithersburg:National Bureau of Standards Department of Commerce, 1988: 331-341.
[27]
Blakely R J. Potential theory in gravity and magnetic applications[M]. London: Cambridge University Press, 1996: 100-127.