Scaling properties of paleomagnetic reversal sequence

Abstract

Abstract. The history of reversals of main geomagnetic field during last 160 My is analyzed as a sequence of events, presented as a point set on the time axis. Different techniques were applied including the method of boxcounting, dispersion counter-scaling, multifractal analysis and examination of attractor behaviour in multidimensional phase space. The existence of a crossover point at time interval 0.5-1.0 My was clearly identified, dividing the whole time range into two subranges with different scaling properties. The long-term subrange is characterized by monofractal dimension 0.88 and by an attractor, whose correlation dimension converges to 1.0, that provides evidence of a deterministic dynamical system in this subrange, similar to most existing dynamo models. In the short-term subrange the fractal dimension estimated by different methods varies from 0.47 to 0.88 and the dimensionality of the attractor is obtained to be about 3.7. These results are discussed in terms of non-linear superposition of processes in the Earth's geospheres.

The geodynamo as a low-dimensional deterministic system at the edge of chaos

“…Some analyses have suggested that low-dimensional deterministic chaos can explain the record from 85 to 25 Ma ago, but that random processes provide a better model before then [7]. Others have suggested there to be a crossover from a Poissonlike process to a deterministic process at a timescale of approximately 0.5-1.0 Ma, and have associated this with a change in attractor dimension [8]. The possibility that the whole epoch containing the Cretaceous superchron is evidence of non-stationary behaviour (whereas stationary processes have otherwise prevailed) has been proposed [9].…”