Why does the Earth's magnetic field flip over the course of history? What attempts have been made to model this phenomenon mathematically?

Paleomagnetologist Michael Fuller is an emeritus professor from University of California, Santa Barbara and now a senior researcher at the University of Hawaii's School of Earth Science and Technology in its Institute of Geophysics and Planetology. His research has concentrated on polar shifts from the magnetic records trapped in Hawaiian lavas and on corings from the sea bed. Here is his explanation.

We know from magnetic records locked in rocks that the Earth's magnetic field has reversed many times in the past. We don't really know why but we have some theories that are being borne out in mathematical models.

We also know that the magnetic field of the sun reverses as well-- every 11 years, whereas the Earth's reverses irregularly. The last geomagnetic reversal for Earth was about 780,000 years ago. The historic reversal rate for Earth seems to be once every few hundred thousand years, but it has varied widely; on at least two occasions, the field has maintained one polarity for tens of millions of years.

Motion in the Earth's liquid core generates the planet's magnetic field
Image: National Geophysical Data Center
GEODYNAMO. Motion in the Earth's liquid core generates the planet's magnetic field.

Thus, the only two magnetic fields for which we have any significant historical record--those of the Earth and the sun--are bistable. They spend most of the time in a stable state with the magnetic field aligned roughly with the spin axis. The form of the stable geomagnetic field is like that of a bar magnet at the center of the Earth. It is what is called a dipole field--with a north and south pole. But occasionally this dipole field switches polarity--north and south reverse--and this process seems to take a few thousand years.

The Earth's field, like the sun's, is produced by dynamo action, which involves two processes. The first is the creation of new magnetic fields from the ambient geomagnetic field. This "field regeneration" takes place because magnetic field lines are trapped in good electrical conductors, such as the molten iron of the Earth's outer core. As Michael Faraday demonstrated, movement of a field line is impeded by an electrical current flowing to oppose that change. Because the molten iron in the core is a good electrical conductor, the field is trapped in the fluid--the frozen field effect. The field is carried along with the fluid as it moves in response to the forces imposed upon it. As the core moves, the field lines are stretched and twisted, and a new magnetic field is created.

Dipole diagram. The magnetic field resembles one that would be produced by a giant bar magnet in the
core of the Earth
Image: National Geophysical Data Center
DIPOLE MAGNET. The magnetic field resembles one that would be produced by a giant bar magnet in the core of the Earth.
The second process is the diffusion of the magnetic fields. In the same way that a drop of colored dye in a swimming pool will soon diffuse throughout the pool, a concentration of magnetic field lines diffuses throughout the planet's outer core. Yet this diffusion must take place against the frozen field effect.

The balance between these two processes determines the evolution of the magnetic field--namely, whether the field decays away or is regenerated. On the large scale of stars and planets, the field lines are caught up in the fluid motion and distorted. They then generate a new magnetic field before they diffuse away.

The geomagnetic field varies continuously. The decay time for the main dipole part of the geomagnetic field, whose constancy and simple geometry permits navigation by magnetic compasses, is probably in the neighborhood of 15,000 years. The largest part of this variation involves smaller features in the non-dipole field, which have smaller time constants and more complicated geometries. The variation must presumably arise from small changes in either of the two processes which give the dynamo action, or both.

So the rare field reversals are most likely caused by larger changes in the flow in the outer core, or in the way in which the field lines are wound into the flow by diffusion. What causes such major changes is not known. Indeed, it may be that such fluctuations are simply extreme examples of the continuum of fluctuations in the dynamo processes--an El Nino in the weather of the outer core.

Several years ago, Gary A. Glatzmier of Los Alamos National Laboratory and Paul H. Roberts of the University of California, Los Angeles achieved a remarkable breakthrough in the mathematical modeling of the geomagnetic field. They solved the equations of electromagnetism and magnetohydrodynamics for the outer core and thereby obtained a computer simulation of the geomagnetic field.

The simulation yielded relatively long periods, when the field was roughly aligned with the rotation axis, that were separated by a rapid flipping of the poles. During this simulated reversal, the non-dipole field became dominant. Attempts are now underway to determine the morphology of the transitional fields during reversals. And it is hoped that these results will inspire still more realistic models and a better understanding of the working of the geodynamo.

Updated on April 13, 1998

Gary A. Glatzmaier of the Institute of Geophysics & Planetary Physics at Los Alamos National Laboratory explains the computer modeling of field reversals.

The first dynamically-consistent, three-dimensional computer simulation of the geodynamo (the mechanism in the Earth's fluid outer core that generates and maintains the geomagnetic field) was accomplished and published by Paul H. Roberts of the University of California at Los Angeles and myself in 1995. We programmed supercomputers to solve the large set of nonlinear equations that describe the physics of the fluid motions and magnetic field generation in the Earth's core.

magnetic pole reversal simulation
Image: Gary A. Glatzmaier, Paul H. Roberts
COMPUTER SIMULATION shows a magnetic pole reversal taking place over a period of about 1,000 years. Magnetic field lines are blue where the field is directed inward and yellow where it is directed outward.

The simulated geomagnetic field, which now spans the equivalent of over 300,000 years, has an intensity, a dipole-dominated structure and a westward drift at the surface that are all similar to the Earth's real field. Our model predicted that the solid inner core, being magnetically coupled to the eastward fluid flow above it, should rotate slightly faster than the surface of the Earth. This prediction was recently supported by studies of seismic waves passing through the core.

In addition, the computer model has produced three spontaneous reversals of the geomagnetic field during the 300,000-year simulation. So now, for the first time, we have three-dimensional, time-dependent simulated information about how magnetic reversals can occur. The process is not simple, even in our computer model. Fluid motions try to reverse the field on a few thousand-year timescale, but the solid, inner core tries to prevent reversals because the field cannot change (diffuse) within the inner core nearly as quickly as in the fluid, outer core.

Only on rare occasions do the thermodynamics, the fluid motions and the magnetic field all evolve in a compatible manner that allows for the original field to diffuse completely out of the inner core so the new dipole polarity can diffuse in and establish a reversed magnetic field. The stochastic (random) nature of the process probably explains why the time between reversals on the Earth varies so much.

Answer originally posted on April 6,1998.

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