Nonlinear dynamics of a continuous spring-block model of earthquake faults

The continuous one-dimensional Burridge-Knopoff model is generalized by introducing plastic creep in addition to rigid sliding. The resulting equations, for an order parameter (sliding rate) and a control parameter (driving force), exhibit a velocity-strengthening and a velocity-softening instability. In the former regime, reminiscent of self-organized criticality in continuum systems, anomalous diffusion is described by a nonlinear diffusion equation. The latter regime, characteristic of deterministic chaos, is described by a time-dependent Ginzburg-Landau equation. Implications of the model with respect to earthquake predictability are discussed.