Abstract. We consider a system made of n coplanar faults and study the conditions under which it may originate a sequence of n seismic events of similar magnitudes. The system is placed in an elastic half-space and is subject to a constant and uniform strain rate by tectonic motions. The state of the system is described by n variables that are the Coulomb stresses of the faults. Coulomb stresses increase steadily during the interseismic intervals and change suddenly in connection with seismic events. A permutation of the first n integers can be associated with each state of the system, expressing the order of Coulomb stresses according to their magnitudes. The permutation controls the evolution of the system. The state space can be divided into n! subsets corresponding to each of the n! permutations. The representative point of the system moves continuously in one of the subsets during the interseismic intervals and switches to a different subset in connection with seismic events. The order of events in a sequence can be also expressed as a permutation of the first n integers, so that the number of possible sequences is equal to n!. The order of events is determined by the initial stress state, the stress drops and the stress transfers associated with each event. If the sequence is made of n similar events and the differences between Coulomb stresses are always greater than the mutual stress transfers, the order is given by the initial permutation. However, the order implicit in the initial permutation is generally modified during the sequence, due to changes in the differences between Coulomb stresses and to different stress drops of the events. The model allows the retrieval of the stress states of a fault system from the observation of a seismic sequence. As an example, the model is applied to the 2012 Emilia (Italy) seismic sequence and enlightens the complex interplay between the fault dislocations that produced the observed order of events.

Abstract. 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. We treat the fault as a discrete dynamical system with three degrees of freedom: the slip deficits of the asperities and the variation of their difference due to viscoelastic deformation. The dynamics of the system is described in terms of one sticking mode and three slipping modes. We consider the effect of stress transfers connected to earthquakes produced by neighbouring faults. The perturbation 5 is studied in terms of a vector in the state space, whose components are the changes in the state variables of the system. 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, 10California, earthquake, which we model as a two-mode event associated with the consecutive failure of two asperities.Copyright statement. All authors have approved the manuscript for submission. The content of the manuscript has not been published or submitted elsewhere.

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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 twomode event associated with the consecutive failure of two asperities.

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 twomode event associated with the consecutive failure of two asperities.