Dynamics of earthquake faults

Carlson, Jean M.; Langer, J. S.; Shaw, Bruce E.

doi:10.1103/revmodphys.66.657

Cited by 350 publications

(280 citation statements)

References 30 publications

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“…Clearly, the dynamics of the system will significantly depend on the particular choice of the friction law. Recently, a lot of results were presented on the dynamics of the Burridge-Knopoff model in the case of velocity-weakening friction law [9,10,[12][13][14][15][16]. A characteristic feature of the Burridge-Knopoff model with this form of friction is its highly chaotic dynamics that occurs on all length scales down to the smallest length scale a and therefore, the absence of the proper continuum limit [12].…”

Section: Modelmentioning

confidence: 99%

“…Both experimental observations and numerical simulations show that such systems are capable of supporting steadily propagating solitary waves in the form of shocks [7][8][9][10]. These systems are also of special interest because they are used for modeling the dynamics of earthquakes [7][8][9][10][11][12][13][14][15][16][17]. It is clear that systems exhibiting stick-slip motion have both necessary ingredients of excitable systems.…”

Section: Introductionmentioning

confidence: 99%

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Traveling wave solutions in the Burridge-Knopoff model

Muratov

1999

Phys. Rev. E

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The slider-block Burridge-Knopoff model with the Coulomb friction law is studied as an excitable medium. It is shown that in the continuum limit the system admits solutions in the form of the self-sustained shock waves traveling with constant speed which depends only on the amount of the accumulated stress in front of the wave. For a wide class of initial conditions the behavior of the system is determined by these shock waves and the dynamics of the system can be expressed in terms of their motion. The solutions in the form of the periodic wave trains and sources of counterpropagating waves are analyzed. It is argued that depending on the initial conditions the system will either tend to synchronize or exhibit chaotic spatiotemporal behavior.

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Section: Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Traveling wave solutions in the Burridge-Knopoff model

Muratov

1999

Phys. Rev. E

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“…Recently, the concepts of information content and entropy of order α ∈ R were proposed [32,54], inspired on fractional calculus. These generalizations of the classical definitions are given by: (6) where D α (·) is the derivative of order α and Γ (·) and ψ (·) represent the gamma and digamma functions, respectively.…”

Section: Entropymentioning

confidence: 99%

“…In fact, tectonic plates on the Earth's surface move with respect to each other, due to the convection currents that exist within the mantle [48]. The asperities between the plates cause friction and stick-slip motion [5,6,11]. Such behavior increases stress, while strain energy accumulates around the fault surfaces.…”

Section: Introductionmentioning

confidence: 99%

Integer and fractional-order entropy analysis of earthquake data series

Lopes

Machado

2015

Nonlinear Dyn

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This paper studies the statistical distributions of worldwide earthquakes from year 1963 up to year 2012. A Cartesian grid, dividing Earth into geographic regions, is considered. Entropy and the Jensen-Shannon divergence are used to analyze and com-pare real-world data. Hierarchical clustering and multi-dimensional scaling techniques are adopted for data visualization. Entropy-based indices have the advan-tage of leading to a single parameter expressing the relationships between the seismic data. Classical and generalized (fractional) entropy and JensenShannon divergence are tested. The generalized measures lead to a clear identification of patterns embedded in the data and contribute to better understand earthquake distrib-utions.

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“…Neighbouring plates are separated by large fault zones and, when moving along the fault surfaces, exhibit friction and stick-slip behaviour [2][3][4]. Asperities between the plates may increase stress, leading to strain energy accumulation around the fault surface.…”

Section: Introductionmentioning

confidence: 99%

Fractional dynamics and MDS visualization of earthquake phenomena

Lopes¹,

Machado²,

Pinto³

et al. 2013

Computers & Mathematics with Applications

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This paper analyses earthquake data in the perspective of dynamical systems and frac-tional calculus (FC). This new standpoint uses Multidimensional Scaling (MDS) as a power-ful clustering and visualization tool. FC extends the concepts of integrals and derivatives to non-integer and complex orders. MDS is a technique that produces spatial or geometric representations of complex objects, such that those objects that are perceived to be similar in some sense are placed on the MDS maps forming clusters. In this study, over three million seismic occurrences, covering the period from January 1, 1904 up to March 14, 2012 are analysed. The events are characterized by their magnitude and spatiotemporal distri-butions and are divided into fifty groups, according to the Flinn-Engdahl (F-E) seismic regions of Earth. Several correlation indices are proposed to quantify the similarities among regions. MDS maps are proven as an intuitive and useful visual representation of the com-plex relationships that are present among seismic events, which may not be perceived on traditional geographic maps. Therefore, MDS constitutes a valid alternative to classic visu-alization tools for understanding the global behaviour of earthquakes.

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Dynamics of earthquake faults

Cited by 350 publications

References 30 publications

Traveling wave solutions in the Burridge-Knopoff model

Traveling wave solutions in the Burridge-Knopoff model

Integer and fractional-order entropy analysis of earthquake data series

Fractional dynamics and MDS visualization of earthquake phenomena

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