WAVES AND STATIONARY PATTERNS IN THE CORE AND THE

INTERPRETATION OF TRANSITION FIELDS IN GEOMAGNETIC

POLARITY REVERSALS

RAYMOND HIDE Department of Physics and Earth Sciences, Oxford University

In the 1950s palaeomagnetic workers introduced the so-called "geocentric axi- al dipole" (GAD) hypothesis, that when averaged over a few thousand years the geomagnetic field at the Earth's surface is symmetric about the rotation axis and close in form to that of a hypothetical dipole placed at the centre of the Earth (see e.g. Jacobs 1987-91). With the aid of the hypothesis they were able from the study of fossilized magnetic field directions in both igneous and sedimentary rocks to adduce important evidence for long-term polar motion and continental drift. The hypothesis can be trusted to a rough first approximation, but its theoretical basis is by no means as secure as seems to be widely believed. According to Hide (1967), owning to gyroscopic (Coriolis) effects, core motions would be particular- ly sensitive to boundary conditions imposed at the core-mantle interface, such as horizontal temperature gradients and undulations in the shape of that interface asso- ciated with slow but time-dependent convection in the overlying mantle. These are characterized by much longer time-scales-millions of years-than those associated with the westward drift of the geomagnetic field and other direct manifestations of core motions. In particular, temporal and spatial characteristics of the geomagnetic field, including the highly variable frequency of polarity reversals and detailed behaviour of transition fields, would be expected to include features that correlate strongly with geological processes.

It followed from these arguments that when dealing with the interpretation of observations of transition fields, serious consideration should be given to the possibility that the observations largely reflect intrinsic behaviour of core motions under the influence of boundary conditions imposed by the mantle. Some workers have indeed recognized this possibility (e.g. Laj et at. 1988) in the interpretation of their results, but a different view is preferred by those who take as a starting point the hypothesis that the electrical conductivity of the D r~ layer at the bottom of the mantle can take very high values (Knitfle and Jeanloz 1986), even comparable with that of the metallic core, over the Pacific hemisphere, and attribute the observed properties of transition fields to electromagnetic screening in the D u layer. The latter view has been defended by Runcom (1993) as follows: "It is less easy to accept (the) idea (that) the core produces fields of different characteristics in different longitudes for times of the order of mantle convection", arguing "that the fundamental starting point in the discussion of core-mantle interactions is the

Surveys in Geophysics 17: 213-214, 1996. 1996 [(luwer Aeadprnir Puhli~her~ Printed in the Netherlandx

214 RAYMOND HIDE

explanation of irregular changes in the length of the day (on decadal time scales) by the interchange of angular momentum between the core and the mantle. The relative rotation of the core relative to the mantle, seen clearly in the westward drift of the non-axial parts of the field in historical times, seems incompatible with the idea that the dynamo produces fields with characteristics (that) remain stationary with respect to the mantle for times long when computed to the lifetime of secular variation foci".

It is instructive to apply this argument to another fluid system, namely Earth's atmosphere, which (like the core) exchange angular momentum with the solid Earth, as evinced by pronounced irregular changes in the iength of the day on sub- decadal time scales. The argument leads to the false conclusion that longitudinal variations of atmospheric variables such as surface pressure, temperature, and wind velocity would average out to zero on time scales much longer than those characteristic of transient disturbances in the atmosphere. Maps of the mean state of the atmosphere (see e.g. Peixoto and Oort 1992) most certainly do not possess this property; indeed they show strong correlations with geographical features! It does not of course follow immediately that because the argument gives an incorrect prediction for the atmosphere it must necessarily fail when applied to the core, but it is clear that implicit in the argument are assumptions that would need to be justified. The main assumption in my view is the implicit neglect of the possibility proposed long ago (Hide 1966) that the core can support large-scale wave motions with phase speeds comparable with the speed of material motion in the core. In such a system, stationary or quasi-stationary disturbances locked to "geographical" features are readily produced, and there is now ample evidence that this general view of core accords with observations.

Magnetohydrodynamic flow in the core is influenced by electromagnetic as well a by thermal and mechanical boundary conditions imposed by the overlying mantle. It follows therefore that if certain regions (e.g. the Pacific hemisphere) of the D" layer at the bottom of the mantle consist of material of high electrical conductivity, then the magnetic field seen near the surface of the Earth would be affected not only by the screening effect of the conducting regions but also by their direct influence on the field produced in the core. The existence of such material does not appear to be consistent with determinations of the "magnetic" radius of the core from geomagnetic secular variation data. The method (Hide 1978) assumes that to a first approximation mantle conductivity can be neglected, and it gives for the magnetic radius of the core a value within two percent of the seismologically determined values (see e.g. Hide and Malin 1981; Voorhies and Benton 1982). This near-agreement between these independent determinations of the mean radius of the core provides a constraint on models of the distribution of electrical conductivity in the mantle which might usefully be applied in future work on the interpretation of polarity reversals and transition fields.