We consider a plane fault with two asperities embedded in a shear zone, subject to a uniform strain rate owing to tectonic loading. After an earthquake, the static stress field is relaxed by viscoelastic deformation in the asthenosphere. We treat the fault as a discrete dynamical system with 3 degrees of freedom: the slip deficits of the asperities and the variation of their difference due to viscoelastic deformation. The evolution of the fault is described in terms of inter-seismic intervals and slip episodes, which may involve the slip of a single asperity or both. We consider the effect of stress transfers connected to earthquakes produced by neighbouring faults. The perturbation alters the slip deficits of both asperities and the stress redistribution on the fault associated with viscoelastic relaxation. The interplay between the stress perturbation and the viscoelastic relaxation significantly complicates the evolution of the fault and its seismic activity. We show that the presence of viscoelastic relaxation prevents any simple correlation between the change of Coulomb stresses on the asperities and the anticipation or delay of their failures. As an application, we study the effects of the 1999 Hector Mine, California, earthquake on the post-seismic evolution of the fault that generated the 1992 Landers, California, earthquake, which we model as a two-mode event associated with the consecutive failure of two asperities.
