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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.
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Makhutov, N. A., Petrov, V. P., & Akhmetkhanov, R. S. (2004). Natural-technogenic-social systems and risks. Problems of safety and emergency situations (pp. 3–28). No 3. (in Russian).
Akhmetkhanov, R. S. (2006). Fractal theory and risks. Problems of safety and emergency situations (pp. 22–36). No 4. (in Russian).
Akhmetkhanov R. S. (2009). Application of fractal theory and wavelet analysis for identification of singularities of time series in system diagnostics. Herald of scientific and technical development (pp. 26–31). No 1. (in Russian).
Pavlov, A. N., & Anishchenko, V. S. (2007). Multifractal. Analysis of complex signals. Advances in Physical Sciences, 177(8), 859–876 (in Russian).
Dikonov, V. P. (2002). Wavelets. From theory to practice. Moscow: SALON-R Publ 448 p. (in Russian).
- Application of Fractal Theory Methods for Seismogram Analysis
Nikolay A. Makhutov
Rasim S. Akhmetkhanov
Dmitry O. Reznikov
- Chapter 25
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