Abstract
Abstract. The multifractal properties of the daily solar X-ray brightness, Xl and Xs, during the period from 1 January 1986 to 31 December 2007 which includes two solar cycles are examined using the universal multifractal approach and multifractal detrended fluctuation analysis. Then we convert these time series into networks using the horizontal visibility graph technique. Multifractal analysis of the resulting networks is performed using an algorithm proposed by us. The results from the multifractal analysis show that multifractality exists in both raw daily time series of X-ray brightness and their horizontal visibility graphs. It is also found that the empirical K(q) curves of raw time series can be fitted by the universal multifractal model. The numerical results on the raw data show that the Solar Cycle 23 is weaker than the Solar Cycle 22 in multifractality. The values of h(2) from multifractal detrended fluctuation analysis for these time series indicate that they are stationary and persistent, and the correlations in the time series of Solar Cycle 23 are stronger than those for Solar Cycle 22. Furthermore, the multifractal scaling for the networks of the time series can reflect some properties which cannot be picked up by using the same analysis on the original time series. This suggests a potentially useful method to explore geophysical data.
Highlights
An important aim of solar-terrestrial physics is to understand the causes of geomagnetic activity in general and geomagnetic storms in particular
We examine the multifractal properties of the daily solar X-ray brightness, Xl (i.e., 1–8 A X-rays (Watts m−2)) and Xs (i.e., 0.5–4 A X-rays (Watts m−2)), during the period from 1 January 1986 to 31 December 2007, including two solar cycles, using the universal multifractal approach (Schertzer and Lovejoy 1987) and Multifractal detrended fluctuation analysis (MFDFA) (Kantelhardt et al 2002)
This section examines the multifractal properties of the daily solar X-ray brightness, Xl and Xs, during the period from 1 January 1986 to 31 December 2007 and their horizontal visibility graphs
Summary
An important aim of solar-terrestrial physics is to understand the causes of geomagnetic activity in general and geomagnetic storms in particular. Multifractal analysis was initially proposed to treat turbulence data and is a useful way to characterise the spatial heterogeneity of both theoretical and experimental fractal patterns (Grassberger and Procaccia, 1983; Halsy et al, 1986) It has been applied successfully in many different fields including financial modelling (e.g., Anh et al, 2000; Canessa, 2000), biological systems (e.g., Yu et al, 2001, 2003, 2004, 2006; Anh et al, 2001, 2002; Zhou et al, 2005), geophysical systems (e.g., Schertzer and Lovejoy, 1987; Schmitt et al, 1992; Tessier et al, 1993, 1996; Olsson, 1995; Olsson and Niemczynowicz, 1996; Harris et al, 1996; Lovejoy et al, 1996; Deidda, 2000; Lilley et al, 2006; Kantelhardt et al, 2006; Veneziano et al, 2006; Venugopal et al, 2006; Lovejoy and Schertzer, 2006, 2010a, b; Garcia-Marin et al, 2008; Serinaldi, 2010) and high energy physics (e.g., Ratti et al, 1994). As solar observational techniques improve, fine small-scale structures observed on the solar surface become more pronounced. Abramenko (2005) proposed a scaling of structure functions to Published by Copernicus Publications on behalf of the European Geosciences Union & the American Geophysical Union
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