Fractal Dimension Analysis of Earth Magnetic Field during 26 August 2018 Geomagnetic Storm

Abstract

We analyse the fractal nature of geomagnetic field northward and eastward horizontal components with 1 min resolution measured by the four stations Belsk, Hel, Sodankylä and Hornsund during the period of 22 August–1 September, when the 26 August 2018 geomagnetic storm appeared. To reveal and to quantitatively describe the fractal scaling of the considered data, three selected methods, structure function scaling, Higuchi, and detrended fluctuation analysis are applied. The obtained results show temporal variation of the fractal dimension of geomagnetic field components, revealing differences between their irregularity (complexity). The values of fractal dimension seem to be sensitive to the physical conditions connected with the interplanetary shock, the coronal mass ejection, the corotating interaction region, and the high-speed stream passage during the storm development. Especially, just after interplanetary shock occurrence, a decrease in the fractal dimension for all stations is observed, not straightforwardly visible in the geomagnetic field components data.

On the Relationship between the Fractal Dimension of Geomagnetic Variations at Altay and the Space Weather Characteristics

“…In general, this result coincided with the results of the papers mentioned in the introduction. It should be noted that, in our calculations, a statistically reliable relationship of HFD with the space weather characteristics was revealed for all components of the geomagnetic field (H, D, Z), while in previous studies [6][7][8][9], a significant decrease in HFD with geomagnetic disturbances was noted only for the horizontal component.…”

“…The experience of using various methods for estimating the fractal dimension time series has shown that the Higuchi method is one of the most robust methods [9,15]. In this method, the mean distance between the elements of the time series X(j), j = 1, .…”

“…The relationship between the fractal dimension of geomagnetic variations and magnetic storms has been studied by many researchers [4][5][6][7][8][9][10]. Moreover, the fractal dimension of fluctuations in geomagnetic indices, such as AE [11], Sym-H [12],and Dst [13], which are the result of the processing of measurements at several magnetic observatories, were studied.…”

“…Wanliss and co-authors [8] showed that the fractal dimension of geomagnetical variation increased with geomagnetical latitude. It was noted in [9] that the temporal variation of geomagnetic field fractal dimensions at medium and high latitudes is different.…”

The Multiscale Principle in Nature (Principium luxuriæ): Linking Multiscale Thermodynamics to Living and Non-Living Complex Systems

“…Often, emergent behaviors may be described by power laws that reflect the distribution of these events across different scales or levels of the system [34][35][36][37]. In physical terms, the power laws that characterize complex systems are closely related to entropy production through the concept of scaling [38][39][40][41][42][43][44]. This is relevant because systems that can be described by power laws lack a characteristic scale, which implies that each component of the system contributes equally to the global evolution of the system, regardless of its scale [45].…”