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Application of Fractal Theory Methods for Seismogram Analysis

  • Nikolay A. Makhutov
  • Rasim S. Akhmetkhanov
  • Dmitry O. Reznikov
Chapter
Part of the Innovation and Discovery in Russian Science and Engineering book series (IDRSE)

Abstract

A variety of quantitative and qualitative methods and approaches are being used in risk assessment. One of these approaches is based on the application of the toolkit of nonlinear dynamics, theory of fractals, and multifractals.

The theory of fractals and multifractals is now widely used to describe properties of self-similarity and complex scaling properties of various processes. These studies showed that not all these processes can be characterized by a single value of the fractal dimension. Only one value of the Hausdorff dimension or scaling index is needed for quantitative description of fractals. This value describes the persistence of the geometry or statistical characteristics when the scale is being changed.

The studies on application of fractal analysis for assessing data sets of different nature have shown good results. The possibility to receive data that characterize the dynamic processes in terms of their scale properties gives us a hope that these methods combined with the other ones will allow us to explore the seismic processes more comprehensively and to estimate quantitatively the probability of seismic events within a short-term forecast.

Keywords

Fractals Seismograms Risk assessment Emergency situations Natural hazards 

References

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    Pavlov, A. N., & Anishchenko, V. S. (2007). Multifractal. Analysis of complex signals. Advances in Physical Sciences, 177(8), 859–876 (in Russian).Google Scholar
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    Dikonov, V. P. (2002). Wavelets. From theory to practice. Moscow: SALON-R Publ 448 p. (in Russian).Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • Nikolay A. Makhutov
    • 1
  • Rasim S. Akhmetkhanov
    • 1
  • Dmitry O. Reznikov
    • 1
  1. 1.Mechanical Engineering Research Institute of the RASMoscowRussia

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