Avalanches and epidemic models of fracturing in earthquakes

Lomnitz-Adler, J.; Knopoff, L.; Martnez-Mekler, G

doi:10.1103/physreva.45.2211

Cited by 40 publications

(11 citation statements)

References 25 publications

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“…The results obtained are similar to those reported in Ref. [15], where the dynamics of a sandpile-like model was investigated, and with those of Ref. [14].…”

Section: Non-soc Behavioursupporting

confidence: 91%

Self-organized criticality in a fibre-bundle-type model

Moreno

Gómez

Pacheco

1999

Physica A: Statistical Mechanics and its Applications

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The dynamics of a fibre-bundle type model with equal load sharing rule is numerically studied. The system, formed by N elements, is driven by a slow increase of the load upon it which is removed in a novel way through internal transfers to the elements broken during avalanches. When an avalanche ends, failed elements are regenerated with strengths taken from a probability distribution. For a large enough N and certain restrictions on the distribution of individual strengths, the system reaches a self-organized critical state where the spectrum of avalanche sizes is a power law with an exponent τ ≃ 1.5.

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“…The results obtained are similar to those reported in Ref. [15], where the dynamics of a sandpile-like model was investigated, and with those of Ref. [14].…”

Section: Non-soc Behavioursupporting

confidence: 91%

Self-organized criticality in a fibre-bundle-type model

Moreno

Gómez

Pacheco

1999

Physica A: Statistical Mechanics and its Applications

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“…266, which is very close to what we measure (α = 2.23 ± 0.03). Therefore, we can relate our results on uncorrelated landscapes to the subcritical point-to-point invasion percolation process [19] and to the mass distribution of avalanches that occur during the IP-cluster growth [20][21][22].…”

mentioning

confidence: 95%

Impact of Perturbations on Watersheds

et al. 2011

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We find that watersheds in real and artificial landscapes can be strongly affected by small, local perturbations like landslides or tectonic motions. We observe power-law scaling behavior for both the distribution of areas enclosed by the original and the displaced watershed as well as the probability density to induce, after perturbation, a change at a given distance. Scaling exponents for real and artificial landscapes are determined, where in the latter case the exponents depend linearly on the Hurst exponent of the applied fractional Brownian noise. The obtained power laws are shown to be independent on the strength of perturbation. Theoretical arguments relate our scaling laws for uncorrelated landscapes to properties of invasion percolation.

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“…72-73]. A characteristic peak in the size distribution at large length scales is reminiscent of a first-order phase transition[Lomnitz-Adler et al, 1992;Ceva and Perazzo, 1993].…”

mentioning

confidence: 99%

Statistical physics, seismogenesis, and seismic hazard

Main¹

1996

Reviews of Geophysics

408

325

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The scaling properties of earthquake populations show remarkable similarities to those observed at or near the critical point of other composite systems in statistical physics. This has led to the development of a variety of different physical models of seismogenesis as a critical phenomenon, involving locally nonlinear dynamics, with simplified rheologies exhibiting instability or avalanche‐type behavior, in a material composed of a large number of discrete elements. In particular, it has been suggested that earthquakes are an example of a “self‐organized critical phenomenon” analogous to a sandpile that spontaneously evolves to a critical angle of repose in response to the steady supply of new grains at the summit. In this stationary state of marginal stability the distribution of avalanche energies is a power law, equivalent to the Gutenberg‐Richter frequency‐magnitude law, and the behavior is relatively insensitive to the details of the dynamics. Here we review the results of some of the composite physical models that have been developed to simulate seismogenesis on different scales during (1) dynamic slip on a preexisting fault, (2) fault growth, and (3) fault nucleation. The individual physical models share some generic features, such as a dynamic energy flux applied by tectonic loading at a constant strain rate, strong local interactions, and fluctuations generated either dynamically or by fixed material heterogeneity, but they differ significantly in the details of the assumed dynamics and in the methods of numerical solution. However, all exhibit critical or near‐critical behavior, with behavior quantitatively consistent with many of the observed fractal or multifractal scaling laws of brittle faulting and earthquakes, including the Gutenberg‐Richter law. Some of the results are sensitive to the details of the dynamics and hence are not strict examples of self‐organized criticality. Nevertheless, the results of these different physical models share some generic statistical properties similar to the “universal” behavior seen in a wide variety of critical phenomena, with significant implications for practical problems in probabilistic seismic hazard evaluation. In particular, the notion of self‐organized criticality (or near‐criticality) gives a scientific rationale for the a priori assumption of “stationarity” used as a first step in the prediction of the future level of hazard. The Gutenberg‐Richter law (a power law in energy or seismic moment) is found to apply only within a finite scale range, both in model and natural seismicity. Accordingly, the frequency‐magnitude distribution can be generalized to a gamma distribution in energy or seismic moment (a power law, with an exponential tail). This allows extrapolations of the frequency‐magnitude distribution and the maximum credible magnitude to be constrained by observed seismic or tectonic moment release rates. The answers to other questions raised are less clear, for example, the effect of the a priori assumption of a Poisson process in a system with s...

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Avalanches and epidemic models of fracturing in earthquakes

Cited by 40 publications

References 25 publications

Self-organized criticality in a fibre-bundle-type model

Self-organized criticality in a fibre-bundle-type model

Impact of Perturbations on Watersheds

Statistical physics, seismogenesis, and seismic hazard

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