Latitudinal variation of stochastic properties of the geomagnetic field

Abstract

Abstract. We explore the stochastic fractal qualities of the geomagnetic field from 210 mm ground-based magnetometers during quiet and active magnetospheric conditions. We search through 10 yr of these data to find events that qualify as quiet intervals, defined by Kp ≤ 1 for 1440 consecutive minutes. Similarly, active intervals require Kp ≥ 4 for 1440 consecutive minutes. The total for quiet intervals is ∼ 4.3 × 10 6 and 2 × 10 8 min for active data points. With this large number of data we characterize changes in the nonlinear statistics of the geomagnetic field via measurements of a fractal scaling. A clear difference in statistical behavior during quiet and active intervals is implied through analysis of the scaling exponents; active intervals generally have larger values of scaling exponents. This suggests that although 210 mm data appear monofractal on shorter timescales, the scaling changes, with overall variability are more likely described as a multifractional Brownian motion. We also find that low latitudes have scaling exponents that are consistently larger than for high latitudes.

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

“…It is known that the HFD of geomagnetical variations can be described as a normally distributed random value [8]. Annual averaged values and standard deviations of HFD for H,D,Z-components in 2011, as parameters of normal distribution, were calculated.…”

“…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.…”

“…The majority of studies noted the effect of reducing the fractal dimension of geomagnetic variations or fluctuations in geomagnetic indices during geomagnetic disturbances at high [11] and low latitudes [5,7]. 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.…”

Efficient calculation of fractal properties via the Higuchi method

“…signals that have only a single type of scaling. Many other theoretical data types exist that have been used to analyze signals that lack local scaling regularity, but rather have a regularity which varies in time or space [24,42]. There is also a recent effort to generalize the Higuchi method to distinguish monofractal from multifractal dynamics based on relatively short time series [6].…”

Comment on "Ultra low frequency (ULF) electromagnetic anomalies associated with large earthquakes in Java Island, Indonesia by using wavelet transform and detrended fluctuation analysis" by Febriani et al. (2014)

“…1 we note many decreases of α in correspondence with increases in the spectral density ratio. This inverse correspondence may be explained by taking into account that the spectral density ratio, the DFA α exponent, and the fractal dimension D of the ULF geomagnetic field are sensitive to global trends in geomagnetic activity (see Masci, 2010Masci, , 2011aWanliss et al, 2014). Namely, when the geomagnetic activity decreases, the reduction of the geomagnetic field horizontal component is usually larger than the reduction of the vertical component.…”