Mechanics of normal fault networks subject to slip-weakening friction

Abstract

International audienceWe seek to understand how the stress interactions and the slip-weakening process combine within a non-coplanar, normal fault network to allow a slip instability to develop, and shape the final slip distribution on the system. In a first part, we perform a non-linear spectral analysis to investigate the conditions of stability and the process of slip initiation in an antiplane non-coplanar fault system subject to a slip-dependent friction law. That numerical model allows determining the zones that are able to slip within a fault network, as well as the location of the stress singularities. The resulting slip profiles on the faults show only a few different shapes, some of them with long, linear sections. This leads to formulate a general classification of slip profiles that can be used to infer the degree of fault interaction within any non-coplanar system. In a second part of work, we use our modelling to try reproducing the cumulative slip profiles measured on three real normal interacting faults forming a large-scale en echelon system. For that, we assume that cumulative slip profiles can be compared to the first static modal solution of our conceptual model. We succeed reproducing the profiles quite well using a variable weakening along the faults. Overall, the weakening rate decreases in the direction of propagation of the fault system. Yet, modelling the slip along the propagating, isolated termination segment of the system requires an unlikely distribution of weakening. This suggests that factors not considered in our analysis may contribute to slip profile shaping on isolated, propagating faults

Interaction of faults under slip‐dependent friction. Non‐linear eigenvalue analysis

“…Examples of curved faults were investigated in Reference [14]. The friction coe cient is piecewise linear, as suggested in (2), with D c ; S; s and d constant.…”

“…Hence, in modelling the initiation of friction instabilities, the nonlinear eigenvalue problem has to be considered. As reported in Reference [14], where fault systems of realistic geometries were analysed, there is an important gap between the ÿrst eigenvalues of the linear and non-linear problems.…”

“…The non-linear eigenvalue method presented in this paper and the above algorithm were used in Reference [14] for some geophysical applications, in particular to explain the slip patterns of normal faults in Afar (East Africa). In all our tests and applications, we found that the algorithm is convergent; but the proof of the convergence is beyond the scope of the present paper.…”

“…Consider, as in References [7,8,12,14], the anti-plane shearing on a system of ÿnite faults under a slip-dependent friction in a linear elastic domain (see Figure 1). Let ⊂ R 2 be a domain, not necessarily bounded, containing a ÿnite number of cuts.…”

“…References [1,2]) and it has been 79 physical signiÿcance through a stability analysis and to ÿnd an e cient numerical algorithm able to compute it together with the corresponding eigenfunction. The non-linear eigenvalue method presented in this paper is used in Reference [14] for some geophysical applications, in particular the slip patterns of normal faults in Afar (East Africa).…”