International Geomagnetic Reference Field - Spherical Harmonics

Spherical Harmonics

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=-\ell}^\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 is radial distance from the Earth's center, is the maximum degree of the expansion, is East longitude, is colatitude (the polar angle), is the Earth's radius, and are Gauss coefficients, and are the Schmidt normalized associated Legendre functions of degree and order .

An online calculator is available from NOAA which allows easy evaluation of the most recent (11th generation) IGRF model at any location and time between 1900 and 2015. 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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