No abstract

S U M M A R YThe modern geomagnetic field is usually expressed as a spherical harmonic expansion. Although the palaeomagnetic record is very incomplete in both space and time, sufficient data are available from a span of ages to generate time-averaged spherical harmonic field models with many degrees of freedom. Here three data sets are considered: directional measurements from lavas, inclination measurements from ocean sediments, and intensity measurements from lavas. Individual data are analysed, as well as siteaverages, using the same methods that have been developed for the modern field, to give models for the past 5 Myr. The normal-polarity field model has an axial-dipole intensity similar to that of the modern-day field, whilst the equatorial-dipole component is very much smaller. The field is not axisymmetric, but shows flux concentrations at the core's surface under Canada and Siberia similar to those observed in the field over historical timescales. Tests on synthetic data show that it is unlikely that these similarities result from the overprinting of the palaeomagnetic field due to inadequate cleaning of the samples. The reverse-polarity field model does not show such obvious features, but this may be due to the sparsity of the data.The patterns observed in the normal-polarity field, with persistent features in the northern hemisphere and a smooth southern hemisphere, could be explained if the present pattern of secular variation is typical of the past several million years. This would reveal itself as large variations over time in the direction of the magnetic vector in regions of high secular variation, with relatively little change over quieter regions. However, we have been unable to find any evidence for a geographical pattern of secular variation in the data.

No abstract

Many studies have used the frozen flux hypothesis to estimate core flow from geomagnetic secular variation (SV). Part of the flow remains indeterminate without some additional constraint. A theorem of Voorhies and Backus states that steady flows can be determined uniquely. Frozen flux requires the time scale of SV, τB, to be much shorter than the diffusion time, τD, and the steady motion theorem requires the time scale for change in flow, τV, be much longer than τB. Here we argue we must also have τV ≪ τD because truly steady flow will eventually lead to a steady equilibrium magnetic field and no SV. We illustrate the difficulty by a numerical example with a prescribed steady flow at the top of the core for which frozen flux inversions never yield the correct velocity. Core motions derived using the steady motions theorem may be grossly in error.

No abstract