Earthquake nucleation in a stochastic fault model of globally coupled units with interaction delays

• Stochastic fault model with time delay is for the first time proposed and analyzed.
• Surrogate testing of real data implies predominant stochastic nature of fault motion.
• Numerical analysis of mean-field system indicates an occurrence of local bifurcation.
• Jerky motion near the bifurcation arises due to effect of noise or global attractor.
• Irregular oscillations obey power-law behavior similar to real observed dynamics.

In present paper we analyze dynamics of fault motion by considering delayed interaction of 100 all-to-all coupled blocks with rate-dependent friction law in presence of random seismic noise. Such a model sufficiently well describes a real fault motion, whose prevailing stochastic nature is implied by surrogate data analysis of available GPS measurements of active fault movement. Interaction of blocks in an analyzed model is studied as a function of time delay, observed both for dynamics of individual faults and phenomenological models. Analyzed model is examined as a system of all-to-all coupled blocks according to typical assumption of compound faults as complex of globally coupled segments. We apply numerical methods to show that there are local bifurcations from equilibrium state to periodic oscillations, with an occurrence of irregular aperiodic behavior when initial conditions are set away from the equilibrium point. Such a behavior indicates a possible existence of a bi-stable dynamical regime, due to effect of the introduced seismic noise or the existence of global attractor. The latter assumption is additionally confirmed by analyzing the corresponding mean-field approximated model. In this bi-stable regime, distribution of event magnitudes follows Gutenberg–Richter power law with satisfying statistical accuracy, including the b-value within the real observed range.