It is generally considered that the polarity reversal intervals have an exponential distribution. We have examined the distribution using all reversal data back to about 165 m.y. ago, and found that this distribution follows a power-law rather than an exponential. Power laws are common in critical phenomena, and therefore we propose that the geodynamo is marginally stable and that the geomagnetic polarity reversal is a kind of critical phenomenon.We present a simple model in which turbulent eddies in the outer core are assumed to behave as magnetic spins. By numerical simulation, we found that intervals of polarity reversals in the model follow a power-law at a critical state. When the energy dissipation accompanying polarity reversals is taken into account, the model self-organizes to the critical state.
Seki and Ito (1993) showed that the geomagnetic polarity reversals had a power-law distribution and presented a simple model in which the geodynamo was assumed to be a system of magnetic spins in a critical phase-transition state. We present an improved, more realistic model, and obtain a power exponent in agreement with the observed value, which is about −1.5. The revised model is a Coupled Map Lattice (CML). A CML is a dynamical system with discrete time and space, but continuous state. In the present model, elementary dynamo evolves autonomously according to the Lorenz map obtained from Rikitake dynamo dynamics. We examine the behavior of the system and the distribution of polarity reversal intervals for various values of parameters. We find some sets of the parameters which yield a power exponent close to −1.5.
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