Investigation of Fractality and Stationarity Behaviour on Earthquake

  • Bikash SadhukhanEmail author
  • Somenath Mukherjee
  • Sugam Agarwal
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 968)


In this paper, an investigation has been made to detect the self-similarity and stationarity nature of magnitude of occurred Earthquake by exploring the fractal pattern and the variation nature of frequency of the essential parameter, Magnitude of occurred earthquake across the different place of the world. The time series of magnitude (19.04.2005 to 07.11.2017), of occurred earthquakes, collected from U.S.G.S. have been analyzed for exposing the nature of scaling (fractality) and stationary behavior using different statistical methodologies. Three conventional methods namely Visibility Graph Analysis (VGA), Wavelet Variance Analysis (WVA) and Higuchi’s Fractal Dimension (HFD) are being used to compute the value of Hurst parameter. It has been perceived that the specified dataset reveals the anti-persistency and Short-Range Dependency (SRD) behavior. Binary based KPSS test and Time Frequency Representation based Smoothed Pseudo Wigner-Ville Distribution (SPWVD) test have been incorporated to explore the nature of stationarity/non-stationarity of that specified profile where the magnitude of earthquake displays the indication of non-stationarity character.


Earthquake Hurst Parameter (H) Visibility Graph Analysis (VGA) Wavelet Variance Analysis (WVA) Higuchi’s Fractal Dimension (HFD) Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test Smoothed Pseudo Wigner-Ville Distribution (SPWVD) 


  1. Albert, R., Barabasi, A.: Statistical mechanics of complex networks. Rev. Mod. Phys. 74(1), 47–97 (2002)MathSciNetCrossRefGoogle Scholar
  2. Dutta, P.K., Mishra, O.P., Naskar, M.K.: A review of operational earthquake forecasting methodologies using linguistic fuzzy rule-based models from imprecise data with weighted regression approach. J. Sustain. Sci. Manage. 8(2), 220–235 (2013)Google Scholar
  3. Enescu, B., Struzik, Z.R., Ito, K.: Wavelet-based multifractal analysis of real and simulated time series of earthquakes. Annuals of Disaster Prevention Research Institute, Kyoto University, pp. 1–14 (2004)Google Scholar
  4. Fong, S., Nannan, Z.: Towards an adaptive forecasting of earthquake time series from decomposable and salient characteristics. In: PATTERNS 2011: The Third International Conferences on Pervasive Patterns and Applications, pp. 53–60. IARIA (2011)Google Scholar
  5. Gomez, C., Mediavilla, A., Hornero, R., Abasolo, D., Fernandez, A.: Use of the Higuchi’s fractal dimension for the analysis of MEG recordings from Alzheimer’s disease patients. Med. Eng. Phys. 31(3), 306–313 (2009)CrossRefGoogle Scholar
  6. Higuchi, T.: Approach to an irregular time series on the basis of the fractal theory. Phys. D Nonlinear Phenom. 31, 277–283 (1988). Scholar
  7. Kanamori, H., Brodsky, E.E.: The physics of earthquakes. Phys. Today 54, 34 (2001)CrossRefGoogle Scholar
  8. Lacasa, L., Luque, B., Luque, J., Nuno, J.: The visibility graph: a new method for estimating the Hurst exponent of fractional Brownian motion. EPL (Europhys. Lett.) 30001, 1–5 (2009)Google Scholar
  9. Michas, G., Sammonds, P., Vallianatos, F.: Dynamic multifractality in earthquake time series: insights from the Corinth rift, Greece. Pure. appl. Geophys. 172(7), 1909–1921 (2015)CrossRefGoogle Scholar
  10. Mukherjee, S., Ray, R., Khondekar, M.H., Samanta, R., Sanyal, G.: Characterisation of wireless network traffic: fractality and stationarity. In: ICRCICN 2017, IEEE, pp. 79–83. IEEE, Kolkata (2017)Google Scholar
  11. Ogata, Y.: A prospect of earthquake prediction research. Stat. Sci. 28(4), 521–541 (2013)MathSciNetCrossRefGoogle Scholar
  12. Panduyos, J.B., Villanueva, F.P., Padua, R.N.: Fitting a fractal distribution on Philippine seismic data: 2011. SDSSU Multidiscip. Res. J. 1(1), 50–58 (2013)Google Scholar
  13. Percival, D.: Estimation of wavelet variance, pp. 619–631 (1995)Google Scholar
  14. Percival, D., Guttorp, P.: Long Memory Process, the Allan Variance and Wavelets, pp. 1–15 (1994)Google Scholar
  15. Percival, D., Mondal, D.: M-estimation of wavelet variance, pp. 623–657. Elsevier (2012)Google Scholar
  16. Preethi, G., Santhi, B.: Study on techniques of earthquake prediction. Int. J. Comput. Appl. 29(4), 0975–8887 (2011)Google Scholar
  17. Priyadarshini, E.: An analysis of the persistence of earthquakes in Indonesia using rescaled range. Indian J. Sci. Technol. 9(21), 1 (2016)CrossRefGoogle Scholar
  18. Ray, R., Khondekar, M.H., Ghosh, K., Bhattacharjee, A.K.: Memory persistency and nonlinearity in daily mean dew point across India. Theor. Appl. Climatol. 124, 119–128 (2015)CrossRefGoogle Scholar
  19. Wang, W.: Stochasticity, Nonlinearity and Forecasting of Streamflow Processes. IOS Press, Amsterdam (2006)Google Scholar
  20. Wairimu, M.J.: Features Affecting Hurst Exponent estimation on time series. Jomo Kenyatta University of Agriculture and Technology, Juja (2013)Google Scholar
  21. Yulmetyev, R., Gafarov, F., Hanggi, P., Nigmatullin, R., Kayumov, S.: Possibility between earthquake and explosion seismogram differentiation by discrete stochastic non-Markov processes and local Hurst exponent analysis. Phys. Rev. E 64(066132), 1–14 (2001)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Bikash Sadhukhan
    • 1
  • Somenath Mukherjee
    • 1
  • Sugam Agarwal
    • 1
  1. 1.Department of Computer Science and EngineeringTechno India College of TechnologyKolkataIndia

Personalised recommendations