Self-organized criticality and deterministic chaos in a continuous spring-block model of earthquake faults
Starting from the relationship between time-dependent friction and velocity softening, this paper presents a generalization of the continuous version of the one-dimensional homogeneous, deterministic Burridge-Knopoff (BK) model by allowing for displacements by plastic creep and rigid sliding. The evolution equations describe the coupled dynamics of an order parameter-like field variable (the sliding rate) and a control parameter field (the driving force). In addition to the velocity-softening instability and deterministic chaos known from the BK model, the model exhibits a velocity-strengthening regime at low displacement rates which is characterized by anomalous diffusion and which is interpreted as a continuum analogue of self-organized criticality (SOC). The governing evolution equations for both regimes (a generalized time-dependent Ginzburg-Landau equation and a nonlinear diffusion equations, respectively) are derived and implications with regard to fault dynamics and power-law scaling of event-size distributions are discussed.
Bibliographic Reference: Article: Physical Review E (1997)
Record Number: 199711034 / Last updated on: 1997-09-16
Original language: en
Available languages: en