Geomagnetic Reference Field

Earth's magnetic field can be approximated by a series expansion of orthogonal spherical harmonics. This expansion is an infinite series in terms of coefficients g_n^m and h_n^m where m varies from 0 to n and n varies from 1 to infinity. Typically, the series is truncated at n = 10 or more recently n = 12 (i.e. 12 terms). In the spherical coordinate system, the expansion of Earth's magnetic field in terms of the magnetic potential, V in spherical harmonics can be written as:

where R_E is the mean radius of the Earth (6371.2 km) and P_n^m (cos θ) are the Schmidt quasi-normalized associated Legendre functions where θ is the colatitude (90-latitude) and φ is the longitude. Schmidt (1934) introduced the following normalization constant for the associated Legendre function P_n^m(x):

The associated Legendre function becomes:

The 'Gauss' normalized coefficients g_n^m and h_n^m are determined experimentally by combining earth-based and satellite measurements of Earth's magnetic field every 5 years. The most recent set of coefficients has been released for 2015 by the V-MOD Working Group of the International Association for Geomagnetism and Aeronomy (IAGA) and is known as the International Geomagnetic Reference Field (IGRF).

Geomagnetic field intensity for epoch 2005

Geomagnetic field direction (inclination or angle from vertical) for epoch 2005.

References

Cain, J. C., S. J. Hendricks, R. A. Langel, and W. V. Hudson, A proposed model for the international geomagnetic reference field-1965, J. Geomag. Geoelectr., 19, 335-355, 1967.

Campbell, W., Introduction to geomagnetic fields, Cambridge University Press, Cambridge, 1997.

Chapman, S. and J. Bartels, Geomagnetism, 2 vols., pp 1049, Oxford University Press, London, 1940.

Langel, R. A., Main Field, Chapter Four in Geomagnetism, ed. J. A. Jacobs, Academic Press, London, 1987.

Maus, S. et al., The 10th generation International Geomagnetic Reference Field, Geophys J. Int., 161, 561-565, 2005.

Peddie, N. W., International Geomagnetic Reference Field: The Third Generation, J. Geomag. Geoelectr., 34, pp. 309-326, 1985.

Schmidt, A., Der magnetische mittlepunkt de erde und seine Bedeutung, Gerlands Beitr. Geophys., 41, 346-358, 1934.