New definitions of an eccentric dipole for the geomagnetic field

Abstract

Optimum eccentric dipoles are calculated from the geomagnetic field models using several different minimum conditions in the least-squares method. In this calculation the three components of the dipole moment vector as well as its location are determined. The higher harmonics above the quadrupole, which have been neglected in the conventional definition, are also taken into account. The dipoles thus defined are named ‘the LSM-dipoles’ in this paper. By definition, these LSM-dipoles are not necessarily parallel to the conventional eccentric dipole whose vector dipole moment is the same as that of the centered dipole. This circumstance is not inconsistent with the fact that the vector dipole moment of a given distribution of magnetic field is independent of the choice of the origin of the coordinate system. Derivations based on four different minimum conditions are presented; for example, the total magnetic energy integrated over the whole space outside the Earth's core is minimized. The four LSM-dipoles determined are located 4–23° south of and 4–12° north of the ordinary eccentric dipole position, and migrate with speeds a little larger than for the latter. Differences are also found between the radial distances from the Earth's center of these dipoles and that of the ordinary eccentric dipole, but these differences are small relative to the differences in the longitudinal and latitudinal directions. However, these dipoles (including the conventional eccentric dipole) follow traces that are qualitatively similar to each other in spite of the differences in their location and drift rate. This suggests that although the position of an LSM-dipole is dependent on the (centered) quadrupole and higher terms, the time variation in its position is mainly controlled by the quadrupole.