Maps of the Earth's magnetic field have been made for navigational purposes since at least the time of Edmond Halley (q.v.); for details see Main field modeling . This activity has culminated in production of the International Geomagnetic Reference Field (q.v.) using a representation of the main field in spherical harmonic (or geomagnetic or Gauss) coefficients by least‐squares fitting to global data set. The basic mathematical representation and statistical procedure were developed by C.F. Gauss (q.v.); the current approach using computers is described in Barraclough and Malin (1968).
The geomagnetic field B is represented as the gradient of a potential V satisfying Laplace's equation:
the solution of which is written in terms of spherical harmonics as the sum
where 
are the usual spherical coordinates, a is Earth's radius, and 
is an associated Legendre function (see Harmonics, spherical ). The measured component of the magnetic field is determined by differentiating V and setting 
to...
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Bibliography
Backus, G.E., 1988. Bayesian inference in geomagnetism. Geophysical Journal, 92: 125–142.
Barraclough, D.R., and Malin, S.R.C., 1968. 71/1 Inst. Geol. Sci. HMSO, London.
Bloxham, J., and Gubbins, D., 1986. Geomagnetic field analysis—IV. testing the frozen‐flux hypothesis. Geophysical Journal of the Royal Astronomical Society, 84: 139–152.
Bloxham, J., Gubbins, D., and Jackson, A., 1989. Geomagnetic secular variation. Philosophical Transactions of the Royal Society of London, 329: 415–502.
Gubbins, D., 1983. Geomagnetic field analysis I: Stochastic inversion. Geophysical Journal of the Royal Astronomical Society, 73: 641–652.
Shure, L., Parker, R.L., and Backus, G.E., 1982. Harmonic splines for geomagnetic modelling. Physics of the Earth and Planetary Interiors, 28: 215–229.
Whaler, K.A., and Gubbins, D., 1981. Spherical harmonic analysis of the geomagnetic field: An example of a linear inverse problem. Geophysical Journal of the Royal Astronomical Society, 65: 645–693.
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Gubbins, D. (2007). Core‐Based Inversions for the Main Geomagnetic Field. In: Gubbins, D., Herrero-Bervera, E. (eds) Encyclopedia of Geomagnetism and Paleomagnetism. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-4423-6_48
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