Analysis of the Geomagnetic Activity of the Dst Index and Self-Affine Fractals Using Wavelet Transforms

The geomagnetic activity of the Dst index is analysed using wavelet transforms and it is shown that the Dst index possesses properties associated with self-affine fractals. Foe example, the power spectral density obeys a power-law dependence on frequency and therefore Dst can be viewed as a self-affine fractal dynamic process. It is shown that the wavelet covariance exponent, which is based on wavelet variance analysis is identical to the power-law exponent for a time series with s power spectral density which obeys a power-law dependence on frequency. Therefore, the wavelet covariance exponent provides a direct measure of the strength of persistence of the Dst indices. One of the advantages of wavelet analysis is that many inherent problems encountered in Fourier transform methods, such as windowing and detrending, are not necessary.