@article{aa730e90144f40728eef04f834f572fa,

title = "Probabilistic model of waiting times between large failures in sheared media",

abstract = "Using a probabilistic approximation of a mean-field mechanistic model of sheared systems, we analytically calculate the statistical properties of large failures under slow shear loading. For general shear F(t), the distribution of waiting times between large system-spanning failures is a generalized exponential distribution, ρT(t)=λ(F(t))P(F(t))exp-∫0tdτλ(F(τ))P(F(τ)), where λ(F(t)) is the rate of small event occurrences at stress F(t) and P(F(t)) is the probability that a small event triggers a large failure. We study the behavior of this distribution as a function of fault properties, such as heterogeneity or shear rate. Because the probabilistic model accommodates any stress loading F(t), it is particularly useful for modeling experiments designed to understand how different forms of shear loading or stress perturbations impact the waiting-time statistics of large failures. As examples, we study how periodic perturbations or fluctuations on top of a linear shear stress increase impact the waiting-time distribution.",

author = "Brinkman, {Braden A.W.} and Leblanc, {Michael P.} and Uhl, {Jonathan T.} and Yehuda Ben-Zion and Dahmen, {Karin A.}",

note = "Funding Information: Natural Sciences and Engineering Research Council of Canada http://dx.doi.org/10.13039/501100000038 Conseil de Recherches en Sciences Naturelles et en G{\'e}nie du Canada NSERC http://sws.geonames.org/6251999/ National Science Foundation http://dx.doi.org/10.13039/100000001 NSF http://sws.geonames.org/6252001/ http://sws.geonames.org/6254928/ EAR-0529922 U.S. Geological Survey http://dx.doi.org/10.13039/100000203 USGS http://sws.geonames.org/6252001/ http://sws.geonames.org/6254928/ 07HQAC0026 National Science Foundation http://dx.doi.org/10.13039/100000001 NSF http://sws.geonames.org/6252001/ http://sws.geonames.org/6254928/ NSF DMR 1005209 NSF DMS 1069224 B.A.W.B. thanks NSERC for a PGS D scholarship and the Southern California Earthquake Center (SCEC), based on NSF Cooperative Agreement No. EAR-0529922 and USGS Cooperative Agreement No. 07HQAC0026, for financial support. K.A.D. and M.L. thank MGA, Grants No. NSF DMR 1005209 and No. NSF DMS 1069224 for support. We thank Don Turcotte for helpful discussions and Ilya Zaliapin and Kam Harris for helpful comments on the manuscript. Publisher Copyright: {\textcopyright} 2016 American Physical Society.",

year = "2016",

month = jan,

day = "29",

doi = "10.1103/PhysRevE.93.013003",

language = "English (US)",

volume = "93",

journal = "Physical Review E",

issn = "2470-0045",

publisher = "American Physical Society",

number = "1",

}