The Hurst exponents of the geomagnetic horizontal component during quiet and active periods

Abstract

The focus in this paper is mainly to characterize the fractal properties denoted by the Hurst exponent of geomagnetic field during quiet and active periods of geomagnetism activity. Analysis is made on the time series of the geomagnetic horizontal component data, H, which were acquired by the Magnetic Data Acquisition System (MAGDAS) developed by the Space Environment Research Center (SERC) of Kyushu University in Japan. The data set covers the quiet and active periods in August 2005 at the equatorial stations of Cebu and Davao in the Philippines. This month had very intense geomagnetic storm with the Dstmin, Kp and Ap indices for the quietest and active days of the month are −20 nT, 2, 6 and −216 nT, 9, 110 respectively. For both stations, the data sampling interval is 1 second for each time periods or one day giving a sample size of 86,400. Using the fast Fourier transform, the power law of the data time series was obtained in the shorter time periods of 10 minutes to 6 hours. This observed power spectrum law exhibit scaling with corresponding Hurst exponents of 0.3–0.5 for quiet periods and 0.5–0.7 for active periods for both stations. For comparison, other fractal techniques were performed which are rescaled range analysis (RS) and detrended fluctuation analysis (DFA) on the data set, and the same ranges of the Hurst exponents were obtained. The work also includes simulation of the similar sized data sets by generating the fractional Brownian motions (FBM) with the Hurst exponents of 0.3–0.7. Our results show that the H component at these equatorial stations is a fractal in nature and become more persistent during active periods of geomagnetism activity. Thus, the Hurst exponent could be used to characterize the geomagnetic time series during quiet and active periods.