Natural orthogonal component analysis of International Geomagnetic Reference Field models and its application to historical geomagnetic models

The International Geomagnetic Reference Field (IGRF) models for 1900–2000 are analysed by means of the method of natural orthogonal components (NOC), and are expressed in the form of NOC series. The obtained NOC series approaches the original IGRF models very rapidly, and therefore the magnetic field can be very well approximated by the first few terms of the NOC series. This feature of the NOC series makes it possible to upgrade the truncation level of historical magnetic models by calculating high-degree Gauss coefficients from the existing low-degree ones. Using the main-field models IGRF 1900–2000, we calculated the principal components of the magnetic field. Each of the components has a specific spatial structure and a varying intensity. The structures of the principal components are rather stable for different periods. Consequently, we can safely assume that the magnetic field just before 1900 consists of the same components, but with different intensities. Taking the model for 1885 (truncation level ) as an example and solving a linear equation system, we calculated the high-degree Gauss coefficients (n= 7–10) from the existing low-degree coefficients (n= 1–6). Adding this model to the model series of IGRF 1900–2000, we will obtain an extended model series for 1885–2000 with a common truncation level . Repeating this procedure, we will obtain a model series extended backward to early ages.