Fractal properties of SYM‐H during quiet and active times

Abstract

Detrended fluctuation analysis was applied to the magnetic storm index SYM‐H for the epoch 1981–2002. The objective was to determine the characteristic fractal statistical differences, if any, between a quiet and active magnetosphere. The entire data set comprises over 11 million points that include numerous intervals that can be classified as quiet or active. For quiet intervals we required Kp ≤ 1 for 10,000 consecutive minutes. Similarly, to qualify as an active interval required Kp ≥ 4 for 10,000 consecutive minutes. All active intervals included magnetic storms. Detrended fluctuation analysis was applied to each of these intervals to obtain local scaling exponents. A clear difference in statistical behavior during quiet and active intervals is implied through analysis of the scaling exponents for the quiet and active intervals; active intervals generally have larger values of scaling exponents. This implies that although SYM‐H appears monofractal on shorter timescales, it is more properly described as a multifractional Brownian motion. An overall trend toward higher scaling exponents was also discovered for increasing magnetospheric activity, possibly implying an increase in organization with magnetospheric activity. The overall distribution of the scaling exponents for active intervals was Gaussian. For quiet intervals, however, it was bi‐Gaussian, perhaps indicative of different internal (magnetospheric) and external (solar wind) nonlinear forcings.

Intermittency and multifractional Brownian character of geomagnetic time series

“…It is known that the Earth's magnetospheric dynamics is characterized by persistent dynamic correlations (e.g., Dobias and Wanliss, 2009) and near-criticality dynamics (e.g., Consolini, 2002;Wanliss and Uritsky, 2010), which are correlated features in self-organized critical systems in stationary conditions also away from the critical point (Woodard et al, 2007). Furthermore, the persistent character of the magnetospheric dynamics has been shown to undergo dynamical changes during magnetic storms and substorms (e.g., Wanliss, 2005;Balasis et al, 2006;Wanliss and Dobias, 2007). These points suggest that the more complex observed relation between the multifractional nature and the intermittent character of the geomagnetic fluctuations (see, e.g., Figs.…”

“…It has been found that the fractal character of several geomagnetic time series, for example those relative to the geomagnetic indices AE, Dst and SYM-H, changes during magnetic storms and substorms (Uritsky and Pudovkin, 1998;Wanliss, 2005;Balasis et al, 2006;Wanliss and Dobias, 2007;Dobias and Wanliss, 2009). In particular, it has been noticed that the self-similarity properties of these time series change when an intense magnetospheric/geomagnetic activity event approaches.…”

Wavelet-based multiscale analysis of geomagnetic disturbance

“…We also compare the temporal history of these storms as measured by magnetograms and the SYM-H time series. Let us recall that the SYM-H index, measured in nT, is a ground-based magnetic index developed to describe geomagnetic disturbance fields at middle-and low-latitudes with a high-time resolution (Wanliss, 2005a;Wanliss and Showalter, 2006). It is the oneminute high-resolution version of Dst, derived using data from magnetic observatories close enough to the magnetic equator, so as not to be influenced by auroral current systems.…”

“…Some previous works have demonstrated the statistical self-affinity properties observed in the geomagnetic times series (Chang, 1999;Sitnov et al, 2001;Uritsky et al, 2001Uritsky et al, , 2006Kovacs et al, 2001;Lui, 2002;Wanliss, 2005a;Balasis et al, 2006;Wanliss and Dobias, 2007).…”

“…Extending research into the fractal spectral properties of the SYM-H index, studied by Wanliss (2005a), and of the Dst index, developed by Balasis et al (2006), we examine the geomagnetic disturbances recorded at three geomagnetic observatories. The purpose of this study is to apply wavelet analysis to reveal the fractal properties and LRD characteristics of geomagnetic disturbances, directly reflected by geomagnetic field recordings.…”