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Multiscale multifractal detrended fluctuation analysis of earthquake magnitude series of Southern California

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  • Fan, Xingxing
  • Lin, Min

Abstract

The multifractal characteristics of magnitude time series of earthquakes that occurred in Southern California from 1990 to 2010 are studied in this work. A method for the scale division of the magnitude of these earthquakes based on empirical mode decomposition (EMD) and multifractal analysis is proposed. This method gains a new insight into measuring multifractal properties of the magnitude time series at multiple scales, and it reveals further information about the dynamic seismic behavior. By using EMD, a time series can be decomposed into mode time series that represent different time–frequency components. We find that time–frequency components show long-range correlation with different Hurst exponents by using R∕S analysis. Based on the different fractal structures of components, we consider three different scale series: Micro-, Mid- and Macro-scale subsequences, which are superposed and reconstructed by the components. The multifractal properties of the three scale subsequences are analyzed by using multifractal detrended fluctuation analysis (MF-DFA). The results show that the three different scale subsequences have various shapes of multifractal spectra and corresponding distinct properties. The Micro-scale subsequence singularity spectrum shows left-skewed, indicating a relative dominance of the lower Hurst exponent; the Mid-scale subsequence has a right-skewed singularity spectrum; the Macro-scale subsequence exhibits the most significant persistence and shows the strongest multifractality.

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  • Fan, Xingxing & Lin, Min, 2017. "Multiscale multifractal detrended fluctuation analysis of earthquake magnitude series of Southern California," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 479(C), pages 225-235.
    • Handle: RePEc:eee:phsmap:v:479:y:2017:i:c:p:225-235
    DOI: 10.1016/j.physa.2017.03.003
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    References listed on IDEAS

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    3. Ke Ma & Long Guo & Wangheng Liu, 2018. "Investigation of the Spatial Clustering Properties of Seismic Time Series: A Comparative Study from Shallow to Intermediate-Depth Earthquakes," Complexity, Hindawi, vol. 2018, pages 1-10, November.

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