Possibility of robust detrended fluctuation analysis as a method for identifying fractal properties of geomagnetic time series

Abstract

Geomagnetic data has been demonstrated to exhibit fractal properties, which are analysed using various fractal methods. These methods allow the characterization of geomagnetic activity during certain periods using the Hurst exponent. In this study, the geomagnetic activity during the quiet period of the month of December 2011 is analysed using the r-DFA method, of which viability to identify fractal properties of geomagnetic data has not been tested yet, and also using its established predecessor; the detrended fluctuation analysis (DFA). The results show that the r-DFA method is indeed viable to be used upon geomagnetic time series, with comparable if not better performance compared to its predecessor.

Identification of Fractal Properties in Geomagnetic Data of Southeast Asian Region during Various Solar Activity Levels

“…Aside from the scaling properties of the data, another attribute that can be observed from the periodograms is the spectral peaks. From Table 2, this study found that the year 2009, 2013, and 2015 showed the same number of peaks at the same hour marks; 6 h, 8 h, 12 h, and 24 h. As for the study of Rabiu et al [22], all the years studied-1996, 2000, and 2002-also showed the same number of peaks at the same hour marks (albeit different from our findings of peaks) of 8 h, 12 h, and 24 h, with an exception for the peak at the 6 h mark which was only present in the KOU station H-component data for the year 2000. While the identification of the point at which the scaling properties change is purely a qualitative process [52,53] and the use of power spectrum analysis as a method is not optimized to indicate precisely the scaling properties of a data [54], the fact remains that all the periodograms showed a change in scaling rule, a multifractal scaling [55,56].…”

“…On the other hand, the newer method of r-DFA has been prominently utilized in analyzing hydrological data [16][17][18] and to a lesser extent, other types of data such as meteorological data [19], medical data [20], and solar activity data [21]. As for geomagnetic data, to date, it has been subjected to the method of r-DFA [22], but not to an extensive degree. Hence, this study utilized the method to analyze geomagnetic data.…”