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

TL;DR

This paper develops a phenomenological stick-slip model linking earthquake interevent times with crustal shear strength, deriving Weibull and log-Weibull distributions, and analyzing deviations due to sampling biases and fault heterogeneity.

Contribution

It introduces a stochastic stick-slip model that explains the Weibull distribution of earthquake interevent times and generalizes it for fault systems with heterogeneity.

Findings

Weibull ITD derived for power-law stress accumulation.

Logarithmic stress accumulation leads to log-Weibull ITD.

Deviations from Weibull can occur due to sampling bias and fault heterogeneity.

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.