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Characterizing the aperiodic behavior of seismic waves using the scale index analysis

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Abstract

The scale index analysis determines the degree of aperiodicity and chaos in nonlinear dynamical systems. The scale index parameters provide quantitative information on the aperiodicity and chaos in a system in the interval between 0 and 1. Aperiodicity and chaotic behavior of the seismic waves can be studied by this wavelet-based method. In this work, the method is applied firstly to the Duffing oscillator for calibration and secondly to the time series of selected seismic waves to determine and classify their aperiodic and chaotic characteristics. The results indicate that the method is efficient in distinguishing aftershocks from independent earthquakes. The scale index parameters computed from the time series of 23 October 2011, 10:41:21 Van-Tabanlı (ML:6.6) earthquake are in the range of 0.67–0.98, indicating relatively strong aperiodicity hence strong chaotic behavior. On the other hand, the parameters computed from the time series of 09 November 2011, 19:23:33 Van-Edremit (ML:5.6) earthquake are in the range of 0.27–0.62, showing relatively weak aperiodicity hence weak chaotic behavior. The scale index analysis is presented as a unique quantitative approach in seismic wave comparison, complementary to the established seismological analysis techniques.

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Abbreviations

ψ u, s(t):

wavelet function

Wf(u,s):

wavelet transform

S(s):

scalogram function

\( {\overline{S}}^{inner}(s) \) :

normalized inner scalogram function

S :

scalogram scale

i scale :

scalogram scale index

J(s):

time interval

c(s):

initial time boundary

d(s):

final time boundary

γ :

Duffing oscillator magnitude

γ c :

bifurcation value of magnitude

δ :

Duffing oscillator slowing rate

M L :

Richter magnitude

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Authors and Affiliations

  1. Department of Physics, College of Sciences, Koç University, Istanbul, Turkey

    Nazmi Yılmaz

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  1. Nazmi Yılmaz
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Correspondence to Nazmi Yılmaz.

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Responsible editor: Longjun Dong

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Yılmaz, N. Characterizing the aperiodic behavior of seismic waves using the scale index analysis. Arab J Geosci 14, 2063 (2021). https://doi.org/10.1007/s12517-021-08408-1

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