Scale Effects in Simple Models for the Dynamics of Faults

Although the evidence for complexity is overwhelming, the dynamics of faulting is still poorly understood. Whilst it has long been known that discreteness in numerical earthquake models produces complexity, the mathematical structure and form of this complexity has never been fully established. Using a simple 1D nonlinear fault model we show how complexity can arise in discrete models through the presence of nonlinear, scale-dependent (or mesh-dependent) terms. We show that scale-dependencies may be a significant factor in the generation of slip complexity and pulse-like rupture over multiple earthquake cycles. We demonstrate that the introduction of length scales in discrete earthquake models implies that both strongly weakening friction and scale-dependent processes may be necessary in generating the pulse-like rupture mode and earthquake complexity over multiple earthquake cycles.