International Geomagnetic Reference Field

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The International Geomagnetic Reference Field (IGRF) is a standard mathematical description of the Earth's main magnetic field and its secular variation. It is the product of a collaborative effort between magnetic field modellers and the institutes involved in collecting and disseminating magnetic field data from satellites and from observatories and surveys around the world.

Spherical Harmonics[edit]

Mathematically, the IGRF model consists of the Gauss coefficients which define a spherical harmonic expansion of the magnetic scalar potential.

  V(r,\phi,\theta) = a \sum_{\ell=1}^L\sum_{m=0}^\ell
  \left(\frac{a}{r}\right)^{\ell+1} \left(g_\ell^m\cos m\phi + h_\ell^m\sin m\phi\right) P_\ell^m\left(\cos\theta\right)

where r is radial distance from the Earth's center, L is the maximum degree of the expansion, \phi is East longitude, \theta is colatitude (the polar angle), a is the Earth's radius, g_\ell^m and h_\ell^m are Gauss coefficients, and P_\ell^m\left(\cos\theta\right) are the Schmidt normalized associated Legendre functions of degree l and order m.

IGRF models are standardized for a particular year, reflecting the most accurate measurements available at that time, and indicating a small-scale, slow time variation of the Earth's overall magnetic field.

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