Sensitivity of a simple earthquake nucleation model to small parameter perturbation: Conditions for the occurrence of deterministic chaos

Abstract

A new mechanism that may account for the onset of chaotic dynamics of earthquake faults is proposed and analyzed. The concept is to build on the Burridge-Knopoff model, which integrates the spring-block setup with the Dieterich-Ruina's rate- and state-dependent friction law to interpolate for the key aspects of earthquake episodes, including the seismic nucleation, fracture propagation and arrest, as well as the rupture healing. Results obtained indicate that deterministic chaos occur in case frictional parameters exhibit small oscillations about their equilibrium values. Based on the construction of appropriate phase portraits, power spectra and the Lyapunov exponents it could be concluded that a single time-dependent parameter is sufficient for the chaotic behavior to emerge, while the fully developed chaos is found when two perturbed parameters are brought into play.