References

NPG

Nonlinear Processes in Geophysics

NPG

Nonlin. Processes Geophys.

1607-7946

Copernicus Publications

Göttingen, Germany

10.5194/npg-19-657-2012

Multifractal analysis of solar flare indices and their horizontal visibility graphs

Z. G.

¹ ² Anh

² ³ Eastes

³ Wang

D.-L.

Hunan Key Laboratory for Computation & Simulation in Science & Engineering, Xiangtan University, Hunan 411105, China

School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Q4001, Australia

Florida Space Institute, University of Central Florida, Orlando, Florida 32816-2370, USA

29 11 2012

19 6 657 665

2012

This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/3.0/

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The full text article is available as a PDF file from https://npg.copernicus.org/articles/19/657/2012/npg-19-657-2012.pdf

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.

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