The International Geomagnetic Reference Field (IGRF) is a series of mathematical models of the main geomagnetic field and its secular variation. Each model consists of a set of spherical harmonic (or Gauss) coefficients, g and h in a series expansion of the geomagnetic potential V=a∑n=1N∑m=0n(a/r)n+1[gnmcosmφ+hnmsinmφ]Pnm(cosθ), where a is the mean radius of the Earth (6371.2 km); r the radial distance from the center of the Earth; Φ the east longitude measured from Greenwich; θ the geocentric colatitude; and Pnm(cosθ) the associated Legendre function of degree n and order m, normalized according to the convention of Schmidt [see, e.g., Langel (1987)]. In principle, N should be ∞ but the Working Group is of the opinion that in practice the available data for most epochs do not justify N greater than 10. This value is chosen to maintain consistency between models at different epochs. The coefficients are in units of nanotesla (nT).
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R. A. Langel (1992) studied this question.