## Stochastic Stick - Slip Model Linking Crustal Shear Strength and Earthquake Interevent Times

### Abstract

The current understanding of the earthquake interevent times distribution (ITD) is incomplete. The Weibull distribution is often used to model the earthquake ITD. We link the earthquake ITD on single faults with the Earth's crustal shear strength distribution by means of a phenomenological stick - slip model. We obtain Weibull ITD for power-law stress accumulation, i.e., $\sigma(t) = \alpha t^{\beta}$, where $\beta >0$ for single faults or systems with homogeneous strength statistics. We show that logarithmic stress accumulation leads to the log-Weibull ITD. For the Weibull ITD, we prove that (i) $m= \beta m_s$, where $m$ and $m_s$ are, respectively, the ITD and crustal shear strength Weibull moduli and (ii) the time scale $\tau_s = (S_s/\alpha)^{1/\beta}$ where $S_s$ is the scale of crustal shear strength. We generalize the ITD model for fault systems. We investigate deviations of the ITD tails from the Weibull due to sampling bias, magnitude selection, and non-homogeneous strength parameters. Assuming the Gutenberg - Richter law and independence of $m$ on the magnitude threshold, $M_{L,c},$ we deduce that $\tau_s \propto e^{- \rho_{M} M_{L,c}},$ where $\rho_M \in [1.15, 3.45]$ for seismically active regions. We demonstrate that a microearthquake sequence conforms reasonably well to the Weibull model. The stochastic stick - slip model justifies the Weibull ITD for single faults and homogeneous fault systems, while it suggests mixtures of Weibull distributions for heterogeneous fault systems. Non-universal deviations from Weibull statistics are possible, even for single faults, due to magnitude thresholds and non-uniform parameter values.Comment: 32 pages, 11 figures Version 2; minor correction

Topics: Physics - Geophysics, Condensed Matter - Materials Science, Condensed Matter - Statistical Mechanics, Nonlinear Sciences - Adaptation and Self-Organizing Systems, Physics - Data Analysis, Statistics and Probability
Publisher: 'Elsevier BV'
Year: 2012
DOI identifier: 10.1016/j.physa.2012.09.011
OAI identifier: oai:arXiv.org:1201.2253

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