A Phase-Transition Model for Geomagnetic Polarity Reversals.

Abstract

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.

A Coupled Map Lattice model for geomagnetic polarity reversals that exhibits realistic scaling

“…He concluded, however, that the apparent scaling does not warrant selfsimilarity and demonstrated that the non-stationary Poisson model (McFadden and Merrill, 1984;Lutz and Watson, 1988) provides an adequate description for the distribution of interval lengths. Seki and Ito (1993) obtained a similar result to Gaffin (1989), but interpreted the power law distribution as an evidence of the dynamical phase-transition state of geodynamo.…”

“…The model in Seki and Ito (1993) has a similar to Sornette's model feedback mechanism and exhibits critical behavior like the power-law distribution of the polarity reversal intervals. The behavior of model, however, differed from that of geomagnetic data in the power exponent being −0.5, while the power exponent obtained from geomagnetic data was −1.5.…”

“…We take the view that a model is good if the total distribution can be explained by the single model without assuming the existence of different states. Seki and Ito (1993) stressed some peculiar properties of a stable distribution with a form of power-law like…”

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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.

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Multifractality and punctuated equilibrium in the Earth's magnetic field polarity reversals

“…Recently, Seki & Ito [ 1993] proposed that the scaling property of the polarity reversal data could be evidence of a near critical configuration tbr the geodynamo. Using a simple model (a Q2R dissipative model), they clearly noted that the model selforganizes to a critical configuration independently of the initial conditions, showing a power law distribution of the polarity intervals, when energy dissipation, accompanying polarity reversals, is taken into account.…”