On the dynamics of the magnetosphere based on time series analysis of geomagnetic indices

Abstract

A detailed analysis has been made of 13 periods of 20 days of the AE data. The average correlation dimension is found to be 3.4, and the calculated dimension is found to depend on the magnetospheric activity such that more active periods have smaller dimensions. This apparent correlation dimension does not, however, imply that the magnetospheric system behind the AE data is low-dimensional when studied as an autonomous dynamical system. On the contrary, bicoloured noise is shown to share many properties with the AE data. It is shown that the AE data have a characteristic autocorrelation time, if properly defined, of approximately 120 minutes (118 ±9 minutes). The structure function (SF) of the AE data shows that the scaling properties of the AE time series change, within error limits, at about the same time scale. For times shorter than 113 (±9) minutes the AE data have a scaling exponent H=0.5, which is similar to that of coloured noise with spectral exponent α = 2. After the break the scaling exponent decreases to about 0.15. It i s also shown that the scaling properties of the AE data can be directly derived from the autocorrelation function. It is suggested that the break in the power spectrum of the AE data at a period of approximately 300 minutes is due to the characteristic autocorrelation time of approximately 120 minutes, which is about a half of the critical period in the power spectrum. This is related in turn to the change of the scaling properties of the AE data at about the same characteristic time scale. It seems that the low-frequency part of the power spectrum (α = 1) mainly arises from the turbulent driving by the solar wind which has a similar power spectrum, whereas the high-frequency part (α = 2) is more intrinsic to the magnetosphere. Conventionally the SF has been used to study the affinity of time series. One can easily distinguish a smooth, differentiable time series, for which H =1 at small values of λ, from a nondifferentiable fractal curve, for which 0<H<l. It is shown that the SF can be used in time series analysis also in the case when the time series is not affine, but there appears different scaling behaviour for different time scales. It is further shown that, in addition to the scaling properties, this method can also reveal (quasi)periodic features of the analysed data. The advantage of the method is that it conveniently visualises the periods of the analysed time series.