On modeling magnetic fields on a sphere with dipoles and quadrupoles

Abstract

This paper assists in the understanding of the global geomagnetic field as it is manifested in models slightly more complex than the centered dipole, with special emphasis on the quadrupole, which among the harmonic components is the chief determinant of the nondipole field configuration. To this end it examines the geometric properties of the three kinds of quadrupoles, as well as their interconvertibility, and the ways in which they can be combined or re solved into constituent parts. Improved methods are developed for establishing the quadrupole parameters (especially the cardinal axes) from spherical harmonic coefficients and for using the various extant analyses to examine the secular change of the quadrupole. Earlier reports of the quadrupole's westward drift are confirmed, its rotation being found to be about 15 minutes per year, but the center of clockwise rotation is markedly displaced from the geographic pole and is situated in the region of the Aleutian Islands. A graphic display clarifies the disparities among different models, promotes the study of relative benefits of refinements in spherical harmonic analysis, and points the way toward a definitive assessment of the quadrupole and especially of its secular change. The way in which one part of the quadrupole combines with the centered dipole to pro duce the eccentric dipole is also examined (with some possible bear ing on radial-dipole models). Support is presented for the hypothesis that the geomagnetic quadrupole tends to hold rather closely to the aspect of a "normal" quadrupole-one with identical configurations for its positive and negative regions. Some properties of octupoles are discussed qualitatively.