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The statistics of recurrence times in broad areas have been reported to obey universal scaling laws, both for single homogeneous regions (Corral, 2003) and when averaged over multiple regions (Bak et al.,2002). These unified scaling laws…

Geophysics · Physics 2007-12-04 A. Saichev , D. Sornette

Crackling noise is observed in many disordered non-equilibrium systems in response to slowly changing external conditions. Examples range from Barkhausen noise in magnets to acoustic emission in martensites to earthquakes. Using the…

Statistical Mechanics · Physics 2009-11-07 A. Travesset , R. A. White , K. A. Dahmen

Declustering aims to divide earthquake catalogs into independent events (mainshocks), and dependent (clustered) events, and is an integral component of many seismicity studies, including seismic hazard assessment. We assess the effect of…

Geophysics · Physics 2021-02-17 Leila Mizrahi , Shyam Nandan , Stefan Wiemer

Ground motion scenarios exists for most of the seismically active areas around the globe. They essentially correspond to shaking level maps at given earthquake return times which are used as reference for the likely areas under threat from…

Applications · Statistics 2020-04-02 Luigi Lombardo , Hakan Tanyas

Upon employing a natural time window of fixed length sliding through a time series, an explicit interrelation between the variability $\beta$ of the variance $\kappa_1$($=< \chi^2 > - < \chi >^2$) of natural time $\chi$ and events'…

Statistical Mechanics · Physics 2015-08-06 N. V. Sarlis , P. V. Varotsos , E. S. Skordas

We propose a new physically-based ``multifractal stress activation'' model of earthquake interaction and triggering based on two simple ingredients: (i) a seismic rupture results from activated processes giving an exponential dependence on…

Statistical Mechanics · Physics 2007-05-23 G. Ouillon , D. Sornette

Fundamentally related to the UV divergence problem in Physics, conventional wisdom in seismology is that the smallest earthquakes, which are numerous and often go undetected, dominate the triggering of major earthquakes, making the…

Geophysics · Physics 2021-05-12 Shyam Nandan , Guy Ouillon , Didier Sornette

We present simulations of static model sandpiles in two dimensions (2D) and focus on the stress distribution in such arrays made of discrete particles. We use the simplest possible model, i.e. spherical particles with a linear spring and a…

Disordered Systems and Neural Networks · Physics 2009-10-30 S. Luding

We propose a new version of the ETAS model, which we also analyze theoretically. As for the standard ETAS model, we assume the Gutenberg-Richter law as a probability density function for background events' magnitude. Instead, the magnitude…

Probability · Mathematics 2015-04-23 Ilaria Spassiani , Giovanni Sebastiani

The determination of confidence intervals of stress orientation is a crucial element in the discussion of homogeneity or heterogeneity of the stress field under study. The error estimates provided by the grid search method Focal Mechanism…

Geophysics · Physics 2010-08-04 Stefan A. Revets

Evidence derived primarily from physical models has identified saltwater disposal as the dominant causal factor that contributes to induced seismicity. To complement physical models, statistical/machine learning (ML) models are designed to…

Applications · Statistics 2025-10-21 Yuchen Xiao , Corwin Zigler , Peter H. Hennings , Alexandros Savvaidis

Avalanche statistics of various threshold activated dynamical systems are known to depend on the magnitude of the drive, or stress, on the system. Such dependencies exist for earthquake size distributions, in sheared granular avalanches,…

Statistical Mechanics · Physics 2019-01-07 Soumyajyoti Biswas , Lucas Goehring

The key parameter for describing frictional strength at the onset of sliding is the static friction coefficient. Yet, how the static friction coefficient emerges at the macroscale from contacting asperities at the microscale is still an…

Soft Condensed Matter · Physics 2025-05-09 Liang Peng , Thibault Roch , Daniel Bonn , Bart Weber

In the region between two closely located stiff inclusions, the stress, which is the gradient of a solution to the Lam\'{e} system with partially infinite coefficients, may become arbitrarily large as the distance between interfacial…

Analysis of PDEs · Mathematics 2021-09-15 Zhiwen Zhao , Xia Hao

Even the most regular stick-slip frictional sliding is always stochastic, with irregularity in both the intervals between slip events and the sizes of the associated stress drops. Applying small-amplitude oscillations to the shear force, we…

Soft Condensed Matter · Physics 2015-05-27 Rosario Capozza , Shmuel M. Rubinstein , Itay Barel , Michael Urbakh , Jay Fineberg

Nearly all aspects of earthquake rupture are controlled by the friction along the fault that progressively increases with tectonic forcing, but in general cannot be directly measured. We show that fault friction can be determined at any…

A recently proposed unified scaling law for interoccurrence times of earthquakes [P. Bak et al., Phys. Rev. Lett. {\bf 88}, 178501 (2002)] is analyzed, both theoretically and with data from Southern California. We decompose the…

Condensed Matter · Physics 2009-11-10 Alvaro Corral

Recently A. Gusev suggested and numerically investigated the doubly stochastic earthquake source model. The model is supposed to demonstrate the following features in the far-field body waves: 1) the omega-square high-frequency (HF)…

Geophysics · Physics 2015-06-11 G. Molchan

We study the distributions of earthquake numbers in two global catalogs: Global Centroid-Moment Tensor and Preliminary Determinations of Epicenters. These distributions are required to develop the number test for forecasts of future seismic…

Applications · Statistics 2017-10-11 Yan Y. Kagan

We report moment distribution results from a laboratory earthquake fault experiment consisting of sheared elastic plates separated by a narrow gap filled with a two dimensional granular medium. Local measurement of strain displacements of…

Soft Condensed Matter · Physics 2014-10-23 Drew A. Geller , Robert E. Ecke , Karin A. Dahmen , Scott Backhaus