Abstract
A mean field version of the Burridge-Knopoff block-spring stick-slip model of earthquake faults is mapped onto a cycled generalization of the democratic fiber bundle model (DFM). This provides an exactly soluble model which describes the set of earthquakes preceding a major earthquake. We find the coexistence of 1) a differential Gutenberg-Richter distribution d(Δ)∼Δ-3/2 of bursts of size Δ, with a cut-off Δmax ∼(σr-σ)-1 as the stress σ↦σr and 2) a run away occurring at a well-defined stress threshold σr. The total number of bursts of size Δ up to the run away scales as D(Δ)∼Δ-5/2. The exponent 5/2 reflects the occurrence of larger and larger events when approaching the run away instability (Omori's law for foreshocks). The Gutenberg-Richter and Omori power laws are not associated with a stationary criticality but to fluctuations accompanying the nucleation of the run away. Introducing long range correlations in the model lead to a continuous dependence of the above exponents as a function of the correlation exponent