IGRF

The International Geomagnetic Reference Field (IGRF) is the standard mathematical model of the Earth's main magnetic field and its secular variation. It provides a globally consistent description of the geomagnetic field at the Earth's surface and above, used as a reference by researchers and for navigation.

The IGRF represents the field as the gradient of a scalar potential, expanded in spherical harmonics with time-dependent Gauss coefficients g_n^m and h_n^m. The expansion is typically carried out to degree and order 13. Coefficients are determined by fitting observations from magnetic observatories, ships, aircraft, and satellites. The model characterizes internal-field sources (primarily the core) and secular variation, while external magnetospheric and crustal contributions are treated separately in other models.

The epoch specification provides the field at a reference date, and a predicted secular variation allows calculation for other dates. The IGRF is maintained by the International Association of Geomagnetism and Aeronomy (IAGA) and updated approximately every five years, with new coefficient sets published along with predicted fields for the subsequent five years.

The IGRF underpins many practical and scientific applications, including compass calibration, satellite navigation, geomagnetic surveys, and space weather research. It serves as a foundational reference for understanding the dynamics of the Earth's interior and its magnetic environment.