International Geomagnetic Reference Model
Encyclopedia
The International Geomagnetic Reference Field (IGRF) is a standard mathematical description of the Earth's main magnetic field. 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.
expansion of the geomagnetic potential
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.
Spherical Harmonics
Mathematically, the IGRF model consists of the Gauss coefficients which define a spherical harmonicSpherical Harmonic
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expansion of the geomagnetic potential
Magnetic potential
The term magnetic potential can be used for either of two quantities in classical electromagnetism: the magnetic vector potential, A, and the magnetic scalar potential, ψ...
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.