Self Organized Criticality and/or Low Dimensional Chaos in Earthquake Processes: Theory and Practice in Hellenic Region

Pavlos, G. P.; Iliopoulos, A. C.; Athanasiu, M. A.

doi:10.1007/978-0-387-34918-3_14

Cited by 7 publications

(4 citation statements)

References 138 publications

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“…In a series of papers [5,[60][61][62] results were presented concerning seismogenesis in different Hellenic regions (land and sea of Greece), applying nonlinear analysis to various earthquake time series, such as magnitude, inter-event times, longitude and latitude time series. For the analysis, the model of the dripping faucet was used as a physical interpretation of the seismic process.…”

Section: Seismogenesismentioning

confidence: 99%

“…Under appropriate conditions, the energy stored in the Earth's crust is released in a "bursting" mode, namely the earthquakes. Therefore, the interaction between the lithosphere and the mantle convection indicates the fact that plate tectonics and lithospheric internal dynamics, related with seismogenesis, constitute an input-output driven process [5]. This paper is summarized as follows: In chapter 2, the phenomenology and the basic characteristics of complex systems are presented, while in chapter 3 an overview of models used frequently in the study of complex systems is given.…”

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confidence: 99%

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Complex Systems: Phenomenology, Modeling, Analysis

Iliopoulos¹

2016

Int J Appl Exp Math

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In this paper a short overview on complex systems and their basic features, as well as the models and mathematical tools developed for their analysis, is given. This review is formed according to the related experience, activity and scientific interests of the author, namely focused on mainly in nonlinear time series analysis and statistics and their applications on different physical systems. In particular, rough outlines are given concerning the phenomenology of complex systems, e.g. far from equilibrium thermodynamics and Tsallis statistics, power law scaling, multi-fractality, low dimensional chaos, SOC, strange kinetics and anomalous diffusion and turbulent intermittency. In addition, a non-complete list of models, based on equations or agent based, is briefly described such as Kuramoto -Sivashinsky equation, cubic complex Ginzburg-Landau Equation, reaction-diffusion Equation, fractional equations, cellular automata, complex networks and artificial neural networks. A more extended review is provided concerning the nonlinear time series analysis complex systems, describing tools like mutual information, flatness coefficient, structure functions, Tsallis q-triplet, correlation dimension and Lyapunov exponents in the reconstructed phase space, which can provide valuable information for the complex system's dynamics. Finally, applications of nonlinear time series analysis on various physical systems, such as earthquakes, Earth's magnetosphere, solar plasma and solar wind, plastic deformation of materials, epilepsy, economical indices and DNA structure, are provided. Mini ReviewOpen Access Complex SystemsIn general, even though there is no precise definition of complex systems, a complex system can be thought of as a collection of nonlinearly interacting elements summing up as a whole which is characterized by novel large scale effects. These effects arise as emergent properties related with nonlinear-complex behavior, which is the most distinguishing feature of complex systems [1]. A nonexhaustive list of complex systems contains among others (in fact most systems can be considered as complex systems): geophysical processes (earthquakes), biophysics (brain dynamics, DNA), space plasmas (solar wind, solar flares, Earth's magnetosphere), plastic deformation of materials, economy (stock indices), socio-technical systems and many others. The aforementioned complex systems, even though they are completely different in many aspects (e.g. different elements), share common characteristics such as:1. They consist of a large number of interacting elements. This fact allows the description of these systems in two different hierarchical levels, namely microscopic and macroscopic. 2. Their subsystems and their interactions are nonlinear. 3. They exhibit emergent behavior, namely a self-organizing collective behavior, which is not predictable from the knowledge of the element's behavior. 4. These systems are open, namely they interact with their environment. This allows these systems to be driven to metastable state...

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Section: Seismogenesismentioning

confidence: 99%

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confidence: 99%

Complex Systems: Phenomenology, Modeling, Analysis

Iliopoulos¹

2016

Int J Appl Exp Math

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“…Seismic events are complex spatial-temporal phenomena [Turcotte 1993, Sornette 1999, Pavlos et al 2007, Vecchio et al 2008, Sornette and Werner 2009, since they occur in clusters and exhibit scale-invariant characteristics. The most typical description in such cases is the division of the earthquakes into foreshocks, main quakes and aftershocks.…”

Section: Aftershocks Spatial Distributionmentioning

confidence: 99%

Analysis of the spatial distribution between successive earthquakes in aftershocks series

Marekova

2014

Annals of Geophysics

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<p>The earthquake spatial distribution is being studied, using catalogs for different recent aftershock series. The quality of the available data, taking into account the completeness of the magnitude, is examined. Based on the analysis of the catalogs, it was determined that the probability densities of the inter-event distance distribution collapse into a single curve when the data were rescaled. The collapse of the data provides a clear illustration of aftershock-occurrence self-similarity in space.</p>

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“…A number of autoregressive schemes to the dataset at hand were fitted relying on the statistical significance of their components and selecting their complexity by the use of the AIC. 4 A complete review concerning the methodology of nonlinear time series analysis and its application in various geophysical time series can be found inAthanasiu and Pavlos (2001),Pavlos et al (2007),Iliopoulos et al (2008) andIliopoulos and Pavlos (2010). 5 A similar study on daily stock indices has been conducted byWilley (1992).…”

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confidence: 99%

Time series analysis of Earth's Northern Hemisphere temperature reconstructions using non-linear tools and statistical tests

Halkos

Tsilika

Iliopoulos

2018

IJISD

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This paper presents results concerning the non-linear analysis of the Earth's Northern Hemisphere mean annual land temperature reconstructions for the time period of 713-2004. The non-linear analysis consists of the application of several filtering methods, the estimation of geometrical and dynamical characteristics in the reconstructed phase space, techniques of discrimination between non-linear low-dimensional and linear high-dimensional (stochastic) dynamics and tests for serial dependence and non-linear structure. The results of this study indicate the efficiency of the filtering methods in revealing non-linear structures and correlations in short noisy time series, such as Earth's Northern Hemisphere temperature reconstructions. No low-dimensional chaotic behaviour evidence was found from the analysis.

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Self Organized Criticality and/or Low Dimensional Chaos in Earthquake Processes: Theory and Practice in Hellenic Region

Cited by 7 publications

References 138 publications

Complex Systems: Phenomenology, Modeling, Analysis

Complex Systems: Phenomenology, Modeling, Analysis

Analysis of the spatial distribution between successive earthquakes in aftershocks series

Time series analysis of Earth's Northern Hemisphere temperature reconstructions using non-linear tools and statistical tests

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