Journal ArticleDOI
Discrete scale invariance, complex fractal dimensions, and log‐periodic fluctuations in seismicity
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In this article, the Sierpinsky gasket is described by a complex fractal dimension whose imaginary part is a simple function (inverse of the logarithm) of the discrete scaling factor, and a set of simple physical systems (spins and percolation) on hierarchical lattices is analyzed to exemplify the origin of different terms in the discrete renormalization group formalism introduced to tackle this problem.Abstract:
We discuss in detail the concept of discrete scale invariance and show how it leads to complex critical exponents and hence to the log-periodic corrections to scaling exhibited by various measures of seismic activity close to a large earthquake singularity. Discrete scale invariance is first illustrated on a geometrical fractal, the Sierpinsky gasket, which is shown to be fully described by a complex fractal dimension whose imaginary part is a simple function (inverse of the logarithm) of the discrete scaling factor. Then, a set of simple physical systems (spins and percolation) on hierarchical lattices is analyzed to exemplify the origin of the different terms in the discrete renormalization group formalism introduced to tackle this problem. As a more specific example of rupture relevant for earthquakes, we propose a solution of the hierarchical time-dependent fiber bundle of Newman et al. [1994] which exhibits explicitly a discrete renormalization group from which log-periodic corrections follow. We end by pointing out that discrete scale invariance does not necessarily require an underlying geometrical hierarchical structure. A hierarchy may appear “spontaneously” from the physics and/or the dynamics in a Euclidean (nonhierarchical) heterogeneous system. We briefly discuss a simple dynamical model of such mechanism, in terms of a random walk (or diffusion) of the seismic energy in a random heterogeneous system.read more
Citations
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Journal ArticleDOI
An observational test of the critical earthquake concept
TL;DR: In this paper, the authors test the concept that seismicity prior to a large earthquake can be understood in terms of the statistical physics of a critical phase transition and find the critical region before all earthquakes along the San Andreas system since 1950 with M ≥ 6.5.
Journal ArticleDOI
Collective behavior of earthquakes and faults: Continuum-discrete transitions, progressive evolutionary changes, and different dynamic regimes
TL;DR: In this article, the authors point to three general dynamic regimes of individual fault zones, which are associated with broad range of heterogeneities, little dynamic weakening, power law frequency-size statistics, temporal clustering of intermediate and large events, and accelerated seismic release before large earthquakes.
Journal ArticleDOI
Statistical physics approach to understanding the multiscale dynamics of earthquake fault systems
John B. Rundle,Donald L. Turcotte,Robert Shcherbakov,William Klein,William Klein,Charles G. Sammis +5 more
TL;DR: In this paper, the authors argue that the occurrence of earthquakes is a problem that can be attacked using the fundamentals of statistical physics, and they apply statistical physics associated with phase changes and critical points to a variety of cellular automata models.
Journal ArticleDOI
Evolving towards a critical point : A review of accelerating seismic moment/energy release prior to large and great earthquakes
S. C. Jaume,Lynn R. Sykes +1 more
TL;DR: In the critical point model for regional seismicity, a region of the earth's crust is truly in or near a "self-organized critical" (SOC) state, such that small earthquakes are capable of cascading into much larger events.
Book ChapterDOI
Fault interaction by elastic stress changes: New clues from earthquake sequences
TL;DR: In this paper, the authors present a theoretical framework for earthquake cycles based on calculating the stress changes caused by one event and assessing where and what mechanism of earthquakes these changes may promote, which is different from investigating the dynamic rupture growth requiring the reconstruction of the spatiotemporal evolution of the stress on the fault plane.
References
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TL;DR: In this paper, a scaling solution for the Bethe lattice is proposed for cluster numbers and a scaling assumption for cluster number scaling assumptions for cluster radius and fractal dimension is proposed.
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TL;DR: The connection between faults and the seismicity generated is governed by the rate and state dependent friction laws -producing distinctive seismic styles of faulting and a gamut of earthquake phenomena including aftershocks, afterslip, earthquake triggering, and slow slip events.
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The Potts model
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Journal ArticleDOI
Fault behavior and characteristic earthquakes: Examples from the Wasatch and San Andreas Fault Zones
TL;DR: In this article, an analysis of scarp-derived colluvium in trench exposures across the Wasatch fault provides estimates of the timing and displacement associated with individual surface faulting earthquakes.
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