Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Albert, R., Barabasi, A.: Statistical mechanics of complex networks. Rev. Mod. Phys. 74(1), 47–97 (2002)
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)
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)
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)
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)
Higuchi, T.: Approach to an irregular time series on the basis of the fractal theory. Phys. D Nonlinear Phenom. 31, 277–283 (1988). https://doi.org/10.1016/0167-2789(88)90081-4
Kanamori, H., Brodsky, E.E.: The physics of earthquakes. Phys. Today 54, 34 (2001)
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)
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)
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)
Ogata, Y.: A prospect of earthquake prediction research. Stat. Sci. 28(4), 521–541 (2013)
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)
Percival, D.: Estimation of wavelet variance, pp. 619–631 (1995)
Percival, D., Guttorp, P.: Long Memory Process, the Allan Variance and Wavelets, pp. 1–15 (1994)
Percival, D., Mondal, D.: M-estimation of wavelet variance, pp. 623–657. Elsevier (2012)
Preethi, G., Santhi, B.: Study on techniques of earthquake prediction. Int. J. Comput. Appl. 29(4), 0975–8887 (2011)
Priyadarshini, E.: An analysis of the persistence of earthquakes in Indonesia using rescaled range. Indian J. Sci. Technol. 9(21), 1 (2016)
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)
Wang, W.: Stochasticity, Nonlinearity and Forecasting of Streamflow Processes. IOS Press, Amsterdam (2006)
Wairimu, M.J.: Features Affecting Hurst Exponent estimation on time series. Jomo Kenyatta University of Agriculture and Technology, Juja (2013)
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)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Sadhukhan, B., Mukherjee, S., Agarwal, S. (2019). Investigation of Fractality and Stationarity Behaviour on Earthquake. In: Thampi, S., Marques, O., Krishnan, S., Li, KC., Ciuonzo, D., Kolekar, M. (eds) Advances in Signal Processing and Intelligent Recognition Systems. SIRS 2018. Communications in Computer and Information Science, vol 968. Springer, Singapore. https://doi.org/10.1007/978-981-13-5758-9_32
Download citation
DOI: https://doi.org/10.1007/978-981-13-5758-9_32
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-13-5757-2
Online ISBN: 978-981-13-5758-9
eBook Packages: Computer ScienceComputer Science (R0)