CHAOS IN GEOMAGNETIC REVERSAL RECORDS - A COMPARISON BETWEEN EARTHS MAGNETIC-FIELD DATA AND MODEL DISK DYNAMO DATA

The Earth's geomagnetic field reverses its polarity at irregular time intervals. However, it is not clear whether a reversal is a determinis tic (low-dimensional) or a random (high-dimensional) process; the dura tion-frequency distribution of the polarity time intervals resembles t hose generated by random processes, but many models suggest that a geo magnetic field reversal can be the outcome of a deterministic dynamics , that of the convection in the Earth's outer core. The latter, in tur n, is only a part of an extremely complex system, made up of both terr estrial and extraterrestrial subsystems nonlinearly interacting with e ach other over a wide range of time scales. We studied the geomagnetic field reversal patterns by means of several techniques of nonlinear d ynamics and compared the results obtained on actual geomagnetic revers al data with synthetic reversal sequences generated by the Rikitake an d Chillingworth-Holmes models of the Earth's magnetic field. We analyz ed 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 structure s similar to those associated with the Lorenz attractor. We measured t he correlation dimension Dc of the synthetic and geomagnetic data by m eans 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 th ose of randomized reversal sequences and suggest that the Earth's geom agnetic field reversal dynamics is not random. However, the limited si ze of the magnetic reversal data set (282 points) and the poor converg ence of the correlation integrals make a quantitative assessment of lo w-dimensional chaos impossible. Our analysis sets a lower limit to the correlation dimension of the geomagnetic reversal dynamics: D-C > 3.