Entropy production and self-organized (sub)criticality in earthquake dynamics

Main, Ian; Naylor, Mark

doi:10.1098/rsta.2009.0206

Cited by 40 publications

(10 citation statements)

References 42 publications

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“…Moments, spatial and temporal distributions then scale as power laws 54 . For stick–slip asperities at Rhonegletscher, the lack of strong mechanical coupling between the asperities prohibits these large-scale failures resulting in moment dependent recurrence times revealing a memory of past events and a sub-critical state of self-organization 55 , whereas for a super-critical asperity density, randomness in recurrence times is expected 52 . On the other hand, critical asperity density could be a failure criterion for catastrophic glacial collapses 7 .…”

Section: Discussionmentioning

confidence: 99%

Changing friction at the base of an Alpine glacier

Gräff

Walter

2021

Sci Rep

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Repeating earthquakes are a global phenomenon of tectonic faults. Multiple ruptures on the same fault asperities lead to nearly identical waveforms characteristic for these seismic events. We identify their microseismic counterparts beneath an Alpine glacier, where basal sliding accounts for a significant amount of ice flow. In contrast to tectonic faults, Alpine glacier beds are subject to large variations in sliding velocity and effective normal stresses. This leads to inter- and sub-seasonal variations in released seismic moment from stick–slip asperities, which we explain with the rate-and-state friction formalism. During summer, numerically modelled effective normal stresses at asperities are three times higher than in winter, which increases the local shear resistance by the same factor. Stronger summer asperities therefore tend to form in bed regions well connected to the efficient subglacial drainage system. Moreover, asperities organise themselves into a state of subcriticality, transferring stresses between each other. We argue that this seismic stick–slip behavior has potentially far-reaching consequences for glacier sliding and in particular for catastrophic failure of unstable ice masses.

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Section: Discussionmentioning

confidence: 99%

Changing friction at the base of an Alpine glacier

Gräff

Walter

2021

Sci Rep

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“…The range of the parameter α where the maximum of the entropy production rate is achieved corresponds to the subcritical regime of the OFC model. A critical point was suggested to exist at α = 0.25 with a diverging correlation length and average avalanche sizes [41].…”

Section: The Olami-feder-christensen (Ofc) Modelmentioning

confidence: 99%

Record-breaking avalanches in driven threshold systems

2013

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Record-breaking avalanches generated by the dynamics of several driven nonlinear threshold models are studied. Such systems are characterized by intermittent behavior, where a slow buildup of energy is punctuated by an abrupt release of energy through avalanche events, which usually follow scale-invariant statistics. From the simulations of these systems it is possible to extract sequences of record-breaking avalanches, where each subsequent record-breaking event is larger in magnitude than all previous events. In the present work, several cellular automata are analyzed, among them the sandpile model, the Manna model, the Olami-Feder-Christensen (OFC) model, and the forest-fire model to investigate the record-breaking statistics of model avalanches that exhibit temporal and spatial correlations. Several statistical measures of record-breaking events are derived analytically and confirmed through numerical simulations. The statistics of record-breaking avalanches for the four models are compared to those of record-breaking events extracted from the sequences of independent and identically distributed (i.i.d.) random variables. It is found that the statistics of record-breaking avalanches for the above cellular automata exhibit behavior different from that observed for i.i.d. random variables, which in turn can be used to characterize complex spatiotemporal dynamics. The most pronounced deviations are observed in the case of the OFC model with a strong dependence on the conservation parameter of the model. This indicates that avalanches in the OFC model are not independent and exhibit spatiotemporal correlations.

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“…Moreover, Main & Al-Kindy [77] used equation (2.16) to investigate the proximity of global seismicity to criticality, characterized by the dissipated seismic energy E and the entropy S. The authors defined a subcritical state for positive θ and a supercritical state for negative θ and concluded that global seismicity is in a near-critical state, in which large fluctuations are dominated by fluctuations in θ rather than β and large seismic energy fluctuations can occur for smaller entropy fluctuations [77]. The hypothesis that the Earth's lithosphere is in a state of thermodynamically driven maximum entropy production and SOC was tested by Main & Naylor [78,80]. The authors explored this hypothesis using the Olami-Feder-Christensen (OFC) model [81] …”

Section: (B) the Classical Statistical Mechanics Approachmentioning

confidence: 99%

“…BG statistical mechanics has been applied to earthquake physics in a series of works, which address the theory as a variational principle for deriving the large-scale properties of earthquake populations [11,75] or to investigate the thermodynamic state of the crust [76][77][78]. One of the first studies that applied statistical mechanics to earthquakes was that of Berrill & Davis [79].…”

Section: (B) the Classical Statistical Mechanics Approachmentioning

confidence: 99%

Generalized statistical mechanics approaches to earthquakes and tectonics

2016

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Despite the extreme complexity that characterizes the mechanism of the earthquake generation process, simple empirical scaling relations apply to the collective properties of earthquakes and faults in a variety of tectonic environments and scales. The physical characterization of those properties and the scaling relations that describe them attract a wide scientific interest and are incorporated in the probabilistic forecasting of seismicity in local, regional and planetary scales. Considerable progress has been made in the analysis of the statistical mechanics of earthquakes, which, based on the principle of entropy, can provide a physical rationale to the macroscopic properties frequently observed. The scale-invariant properties, the (multi) fractal structures and the long-range interactions that have been found to characterize fault and earthquake populations have recently led to the consideration of non-extensive statistical mechanics (NESM) as a consistent statistical mechanics framework for the description of seismicity. The consistency between NESM and observations has been demonstrated in a series of publications on seismicity, faulting, rock physics and other fields of geosciences. The aim of this review is to present in a concise manner the fundamental macroscopic properties of earthquakes and faulting and how these can be derived by using the notions of statistical mechanics and NESM, providing further insights into earthquake physics and fault growth processes.

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Entropy production and self-organized (sub)criticality in earthquake dynamics

Cited by 40 publications

References 42 publications

Changing friction at the base of an Alpine glacier

Changing friction at the base of an Alpine glacier

Record-breaking avalanches in driven threshold systems

Generalized statistical mechanics approaches to earthquakes and tectonics

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