Abstract : We model the processes of unstable slip, considering the complex geometry of fault systems and some friction law deduced from laboratory experiments. We define faults as interfaces of discontinuity in a perfect elastic body - the crust - and we use a slip weakening friction law, assuming that, as the slip grows, the medium's resistance decreases from the static to the dynamic threshold.
We propose two numerical methods. The first one models the spontaneous evolution of a fault network which is initially submitted to a given stress field, and to which we apply an initial velocity perturbation. A Newmark time scheme is used, together with a finite element mesh and a domain decomposition method. The model reveals to be efficient to capture slip instabilities, and in particular the initiation phase which occurs before the phase of rupture propagation and is characterized by a self-similar shape and an exponential growth with time of the slip. Numerical experiments show that fault interaction, on fault segments having a significant overlap, reveals through the existence of "shadow zones" in which the slip is inhibited by stress drop. In the case of two fault segments with an important overlap, slip profiles are strongly asymmetric as one of the stress singularities vanishes at one of the fault tips.
The second numerical scheme handles the nonlinear spectral analysis of the initiation problem, "pseudo-linearized" in the vicinity of the equilibrium position where the fault system is initially homogeneously at the static resistance threshold. The nonlinearity of the problem comes from the existence of shadow zones, which geometry is a priori unknown. Through this analysis, we find the eigenmode bearing the signature of initiation, i.e. the self-similar shape mentioned above. The static version of this modal analysis leads to the definition of a stability criterion for fault networks, i.e. the critical value of the weakening rate : beyond this value, an episode of stable slip will give rise to a seismic event.
We assume that the nonlinear static mode, characterizing a weakening behavior at the stability limit, can be used to describe the cumulative slip at tectonic time scale on a particular system of normal faults in Afar, knowing the slip profiles measured at the surface. We show a good fit between the observed slip patterns and the static mode, assuming a particular choice of the weakening profile. We draw some conclusions in terms of interaction, propagation and/or branching of the fault segments. Finally, we describe two additional physical applications of our modeling :
1) the influence of secondary fracturing (damage) on the slip patterns
2) the optimal geometrical parameters that favor the branching of two fault segments propagating toward each other.