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Modelling the core magnetic field of the Earth

The magnetic field generated in the core of the Earth is often represented by spherical harmonics of the magnetic potential. It has been found from looking at the equations of spherical harmonics, and from studying the values of the spherical harmonic coefficients derived from data from Magsat, that this is an unsatisfactory way of representing the core field. Harmonics of high degree are characterized by generally shorter wavelength expressions on the surface of the Earth, but also contain very long wavelength features as well. Thus if it is thought that the higher degree harmonics are produced by magnetizations within the crust of the Earth, these magnetizations have to be capable of producing very long wavelength signals. Since it is impossible to produce very long wavelength signals of sufficient amplitude by using crustal magnetizations of reasonable intensity, the separation of core and crustal sources by using spherical harmonics is not ideal. We suggest that a better way is to use radial off-centre dipoles located within the core of the Earth. These have several advantages. Firstly, they can be thought of as modelling real physical current systems within the core of the Earth. Secondly, it can be shown that off-centred dipoles, if located deep within the core, are more effective at removing long wavelength signals of potential or field than can be achieved by using spherical harmonics. The disadvantage is that it is much more difficult to compute the positions and strengths of the off-centred dipole fields, and much less easy to manipulate their effects (such as upward and downward continuation). But we believe, along with Cox and Alldredge & Hurwitz, that the understanding that we might obtain of the Earth’s magnetic field by using physically reasonable models rather than mathematically convenient models is very important. We discuss some of the radial dipole models that have been proposed for the nondipole portion of the Earth’s field to arrive at a model that agrees with observations of secular variation and excursions.