Gauss Series

The Gauss series is a widely used expression for the scalar magnetic potential of the Earth’s magnetic field . Recorded in geocentric spherical coordinates $r$ ${\ displaystyle r}$ $r$ , $\theta$ ${\ displaystyle \ theta}$ $\ theta$ , $\lambda$ ${\ displaystyle \ lambda}$ $\ lambda$ , it is used as an international standard for a normal geomagnetic field ^[1] :

V(r,\theta ,\lambda ,t)=\sum _{n=1}^{N}\left({\frac {R}{r}}\right)^{n+1}\sum _{m=0}^{n}\left(g_{n}^{m}(t)\cos m\lambda +h_{n}^{m}(t)\sin m\lambda \right)P_{n}^{m}(\cos \theta )

{\ displaystyle V (r, \ theta, \ lambda, t) = \ sum _ {n = 1} ^ {N} \ left ({\ frac {R} {r}} \ right) ^ {n + 1} \ sum _ {m = 0} ^ {n} \ left (g_ {n} ^ {m} (t) \ cos m \ lambda + h_ {n} ^ {m} (t) \ sin m \ lambda \ right ) P_ {n} ^ {m} (\ cos \ theta)}

V (r, \ theta, \ lambda, t) = \ sum ^ N_ {n = 1} \ left (\ frac {R} {r} \ right) ^ {n + 1} \ sum ^ n_ {m = 0 } \ left (g ^ m_n (t) \ cos m \ lambda + h ^ m_n (t) \ sin m \ lambda \ right) P ^ m_n (\ cos \ theta)

Where:

$r$ ${\ displaystyle r}$ $r$ - distance from the center of the earth,
$\theta$ ${\ displaystyle \ theta}$ $\ theta$ - complement geographic latitude , that is, the polar angle,
$\lambda$ ${\ displaystyle \ lambda}$ $\ lambda$ - longitude
$R$ ${\ displaystyle R}$ $R$ - standard radius of the Earth (6371.2 km),
$g_{n}^{m}(t)$ ${\ displaystyle g_ {n} ^ {m} (t)}$ $g ^ m_n (t)$ and $h_{n}^{m}(t)$ ${\ displaystyle h_ {n} ^ {m} (t)}$ $h ^ m_n (t)$ - Gaussian coefficients, depending on time t ^[2] ,
$P_{n}^{m}$ ${\ displaystyle P_ {n} ^ {m}}$ $P_ {n} ^ {m}$ - Schmidt - normalized adjoint Legendre functions of degree n , of order m .

Literature

IAGA Division V, Working group 8. International Geomagnetic Reference Field - Epoch 2005 Revision Of The IGRF for 2005-2010. (International Geomagnetic Field Standard - IGRF Review of the 2005 Era for 2005—2010)
Volokhov S. A. et al. Spatial harmonic analysis of the magnetic field of technical objects by the method of integral transformations of magnetic signatures / S. A. Volokhov, A. V. Kildishev, P. N. Dobrodeev, L. F. Ivleva // Vestnik KhGPU, graduation 84, series НРСТ (New solutions in modern technologies). - Kharkov: KHGPU, 2000, C41-44.

Links

http://www.ngdc.noaa.gov/IAGA/vmod/
http://www.ngdc.noaa.gov/IAGA/vmod/igrf10koeff.xls (inaccessible link)

Notes

↑ IAGA V-MOD Geomagnetic Field Modeling: International Geomagnetic Reference Field IGRF-11
↑ Links to the coefficient table of the international standard for the era of 2005-2010 (IGRF-10) and the program for calculating the elements of the geomagnetic field are on the International Geomagnetic Reference Field page.

[1] IAGA V-MOD Geomagnetic Field Modeling: International Geomagnetic Reference Field IGRF-11

[2] Links to the coefficient table of the international standard for the era of 2005-2010 (IGRF-10) and the program for calculating the elements of the geomagnetic field are on the International Geomagnetic Reference Field page.

Gauss Series

Literature

Links

Notes

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