Optimization fitting of the eccentric dipole models to the observed geomagnetic field

Abstract

Abstract We have obtained formulas to calculate the field components of an eccentric dipole (ED) with an arbitrarily directed moment from specified coordinates of the dipole center and from its moment vector. With these formulas, the model dipole position was fitted to the observed geomagnetic field, and the approximation accuracy was estimated according to the standard deviation from IGRF along the X, Y, and Z components; the fitting procedure was checked in several tests. We computed the ED parameters (position and moment orientation) and harmonic coefficients of the ED field for 50 years using surface IGRF components, discovered some changes, and compared them with those according to the Schmidt eccentric dipole model. It was found that the nondipolar contributions to the geomagnetic field increase as the dipole field decays with time, and the dipole center drifts northand eastward away from the Earth’s gravity center. The main contribution of the dipole part in the Gaussian spherical harmonic expansion of the geomagnetic field turned out to come from the terms with n of 1 to 5 rather than from two first terms, and the contribution of higher harmonics increases with time. Therefore, the Schmidt ED approximation based on the first eight Gauss coefficients (n≤ 2) must have only relative significance indicating changes of the parameters. On the other hand, world magnetic anomalies (WMA) show up already in two first Gauss terms rather than since the third term as it has been commonly assumed.