1452:
Fratter, Isabelle; Gillet, Nicolas; Hamilton, Brian; Hamoudi, Mohamed; Hulot, Gauthier; Jager, Thomas; Korte, Monika; Kuang, Weijia; Lalanne, Xavier; Langlais, Benoit; Léger, Jean-Michel; Lesur, Vincent; Lowes, Frank J; Macmillan, Susan; Mandea, Mioara; Manoj, Chandrasekharan; Maus, Stefan; Olsen, Nils; Petrov, Valeriy; Ridley, Victoria; Rother, Martin; Sabaka, Terence J; Saturnino, Diana; Schachtschneider, Reyko; Sirol, Olivier; Tangborn, Andrew; Thomson, Alan; Tøffner-Clausen, Lars; Vigneron, Pierre; Wardinski, Ingo; Zvereva, Tatiana (27 May 2015).
25:
144:, which is intended for navigation in the next few years.) It is updated at 5-year intervals, reflecting the most accurate measurements available at that time. The current 13th edition of the IGRF model (IGRF-13) was released in December 2019 and is valid from 1900 until 2025. For the interval from 1945 to 2015, it is "definitive" (a "DGRF"), meaning that future updates are unlikely to improve the model in any significant way.
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1451:
Thébault, Erwan; Finlay, Christopher C; Beggan, Ciarán D; Alken, Patrick; Aubert, Julien; Barrois, Olivier; Bertrand, Francois; Bondar, Tatiana; Boness, Axel; Brocco, Laura; Canet, Elisabeth; Chambodut, Aude; Chulliat, Arnaud; Coïsson, Pierdavide; Civet, François; Du, Aimin; Fournier, Alexandre;
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133:. It was created by fitting parameters of a mathematical model of the magnetic field to measured magnetic field data from surveys, observatories and satellites across the globe. The IGRF has been produced and updated under the direction of the
471:{\displaystyle {\vec {B}}(r,\phi ,\theta ,t)=-\nabla V(r,\phi ,\theta ,t)=-\left({\dfrac {\partial V}{\partial r}},{\dfrac {1}{r}}{\dfrac {\partial V}{\partial \theta }},{\dfrac {1}{r\sin \theta }}{\dfrac {\partial V}{\partial \phi }}\right)}
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749:{\displaystyle V(r,\phi ,\theta ,t)=a\sum _{n=1}^{N}\sum _{m=0}^{n}\left({\frac {a}{r}}\right)^{n+1}\left(g_{n}^{m}(t)\cos m\phi +h_{n}^{m}(t)\sin m\phi \right)P_{n}^{m}\left(\cos \theta \right)}
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1350:{\displaystyle K_{n}={\begin{cases}{\frac {1}{2^{n}}}&{\text{; }}m=0\\{\frac {1}{2^{n}}}{\sqrt {\frac {2(n-m)!}{(n+m)!}}}&{\text{; }}m>0\end{cases}}}
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term usually present in the associated
Legendre functions is omitted in this formulation and is instead accounted for in the Gauss coefficients.
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1180:{\displaystyle P_{n}^{m}(\cos \theta )=K_{n}\sin ^{m}\theta \ {\frac {d^{m+n}}{d(\cos \theta )^{m+n}}}(\cos ^{2}\theta -1)^{n}}
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The IGRF model covers a significant time span, and so is useful for interpreting historical data. (This is unlike the
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The Gauss coefficients are modelled as a piecewise-linear function of time with a 5-year step size.
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is a standard mathematical description of the large-scale structure of the
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24:
1501:"The International Geomagnetic Reference Field: A "Health" Warning"
1454:"International Geomagnetic Reference Field: the 12th generation"
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1503:. IAGA working group V-MOD: Geomagnetic Field Modeling.
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Standard model of the structure of Earth's magnetic field
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Notes concerning correct use and limitations of IGRF
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The magnetic scalar potential model consists of the
49:. Unsourced material may be challenged and removed.
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967:{\displaystyle P_{n}^{m}\left(\cos \theta \right)}
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201:{\displaystyle {\vec {B}}(r,\phi ,\theta ,t)}
779:is radial distance from the Earth's center,
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58:"International Geomagnetic Reference Field"
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109:Learn how and when to remove this message
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152:The IGRF models the geomagnetic field
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251:{\displaystyle V(r,\phi ,\theta ,t)}
47:adding citations to reliable sources
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974:are the Schmidt quasi-normalized
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1522:IGRF Model Description by IAGA
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1499:Lowes, F.J. (January 2010).
923:are Gauss coefficients, and
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1609:Magnetic field of the Earth
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127:Earth's main magnetic field
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1482:10.1186/s40623-015-0228-9
916:{\displaystyle h_{n}^{m}}
884:{\displaystyle g_{n}^{m}}
210:magnetic scalar potential
1461:Earth, Planets and Space
1392:{\displaystyle (-1)^{m}}
1473:2015EP&S...67...79T
859:is the Earth's radius,
832:{\displaystyle \theta }
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1604:Geomagnetism
1554:expanding it
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41:Please help
36:verification
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1593:Categories
1546:geophysics
1433:References
998:and order
978:of degree
69:newspapers
1374:−
1289:−
1162:−
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454:∂
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406:∂
398:∂
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349:−
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313:∇
310:−
295:θ
289:ϕ
274:→
237:θ
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187:θ
181:ϕ
166:→
99:June 2016
1505:Archived
1406:See also
129:and its
1469:Bibcode
1328:;
1242:;
83:scholar
1467:(79).
1417:Magsat
1190:where
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1544:This
1457:(PDF)
90:JSTOR
76:books
1550:stub
1363:The
1335:>
891:and
121:The
62:news
1477:doi
1147:cos
1115:cos
1072:sin
1046:cos
951:cos
733:cos
696:sin
657:cos
429:sin
45:by
1595::
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932:P
909:m
904:n
900:h
877:m
872:n
868:g
847:a
787:N
767:r
743:)
729:(
723:m
718:n
714:P
709:)
702:m
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690:t
687:(
682:m
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654:)
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648:(
643:m
638:n
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629:(
623:1
620:+
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607:r
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599:(
592:n
587:0
584:=
581:m
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566:1
563:=
560:n
552:a
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543:t
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534:,
528:,
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316:V
307:=
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280:(
271:B
246:)
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228:,
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219:V
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178:,
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172:(
163:B
112:)
106:(
101:)
97:(
87:·
80:·
73:·
66:·
39:.
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