Mean-field solution of a block-spring model of earthquakes

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 4, with a cut-off Δ max ∼ (σ r -σ) -1 as the stress σ→σ r and 2) a run away occurring at a well-defined stress threshold σ r