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Fractal description of the complex beatings: How to describe quantitatively seismic waves?

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  • Nigmatullin, Raoul R.
  • Vorobev, Artem S.
  • Nepeina, Kseniia S.
  • Alexandrov, Pavel N.

Abstract

In this paper, we suggest a new algorithm for description of complex beatings. Under the complex beating we understand a signal, which contains the high-frequency (HF) component that is located between two low-frequency (LF) envelopes having random origin. These beatings are associated with the so-called blow-like signals (BLS) and a typical example of the BLS can be associated with the registered earthquakes signals. For description of these signals, it becomes possible to separate two envelopes from the HF-component located between them and find their amplitude-frequency response (AFR) based on the non-orthogonal amplitude-frequency analysis of the smoothed signals (NAFASS) approach that was suggested earlier by one of the authors (RRN) in paper [1]. It was successfully applied for description of economic data having also multi-frequency structure. In order to separate these envelopes from the HF component one can notice that the most signals of such kind have a fractal (self-similar) structure. It means that under reasonable compression/scaling of these signals they keep approximately their initial structure. This scaling property can be tested on many types of the different signals. In the results of application of the NAFASS approach one can describe quantitatively the desired envelopes and obtain their AFRs. As an example, we considered the randomly taken data that were recorded from EQs station located in Kyrgyzstan. We deliberately chose the different types of the EQs signals in order to demonstrate the flexibility and wide applicability of the proposed algorithm. We expect that this algorithm can find a wide application for description of many BLS that are met frequently in many natural phenomena and engineering applications.

Suggested Citation

  • Nigmatullin, Raoul R. & Vorobev, Artem S. & Nepeina, Kseniia S. & Alexandrov, Pavel N., 2019. "Fractal description of the complex beatings: How to describe quantitatively seismic waves?," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 171-182.
    • Handle: RePEc:eee:chsofr:v:120:y:2019:i:c:p:171-182
    DOI: 10.1016/j.chaos.2019.01.017
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    References listed on IDEAS

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    1. Nigmatullin, Raoul R. & Toboev, Vyacheslav A. & Lino, Paolo & Maione, Guido, 2015. "Reduced fractal model for quantitative analysis of averaged micromotions in mesoscale: Characterization of blow-like signals," Chaos, Solitons & Fractals, Elsevier, vol. 76(C), pages 166-181.
    2. Kantelhardt, Jan W & Koscielny-Bunde, Eva & Rego, Henio H.A & Havlin, Shlomo & Bunde, Armin, 2001. "Detecting long-range correlations with detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 295(3), pages 441-454.
    3. Longjun Dong & Xibing Li & Gongnan Xie, 2014. "Nonlinear Methodologies for Identifying Seismic Event and Nuclear Explosion Using Random Forest, Support Vector Machine, and Naive Bayes Classification," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-8, February.
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