Chaos in Geomagnetic Reversal Records: Comparison Between Earth’s Magnetic Field Data and Model Disk Dynamo Data

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The Earth's geomagnetic field reverses its polarity at irregular time intervals. However, it is not clear whether a reversal is a deterministic (low-dimensional) or a random (high-dimensional) process; the duration-frequency distribution of the polarity time intervals resembles those generated by random processes, but many models suggest that a geomagnetic field reversal can be the outcome of a deterministic dynamics, that of the convection in the Earth's outer core. The latter, in turn, is only a part of an extremely complex system, made up of both terrestrial and extraterrestrial subsystems nonlinearly interacting with each other over a wide range of time scales. We studied the geomagnetic field reversal patterns by means of several techniques of nonlinear dynamics and compared the results obtained on actual geomagnetic reversal data with synthetic reversal sequences generated by the Rikitake and Chillingworth-Holmes models of the Earth's magnetic field. We analyzed both the geomagnetic and the synthetic reversal scales by nonlinear forecasting and found that we cannot predict the geomagnetic reversal sequence with nonlinear forecasting. Predictability of the synthetic data varies widely depending on the model parameters. Phase portraits of data obtained from the magnetic field models show fractal structures similar to those associated with the Lorenz attractor. We measured the correlation dimension DC of the synthetic and geomagnetic data by means of the Grassberger-Procaccia method and found that DC always has a value of about one for the synthetic data. The correlation integrals for the geomagnetic reversal sequence behave very differently from those of randomized reversal sequences and suggest that the Earth's geomagnetic field reversal dynamics is not random. However, the limited size of the magnetic reversal data set (282 points) and the poor convergence of the correlation integrals make a quantitative assessment of low-dimensional chaos impossible. Our analysis sets a lower limit to the correlation dimension of the geomagnetic reversal dynamics: DC > 3.