Process and signature of initiation on a finite fault system: a spectral approach

Abstract

We present a numerical approach, based on a spectral analysis, for the initiation of the unstable slip on a finite fault region. First we focus on one fault model. We study the relationship between the weakening parameter and the largest positive eigenvalue of the dynamic spectral problem. Since the numerical approach based on the integral equations proposed by Dascalu et al. (2000) is appropriate only for small eigenvalues we use a finite element method which permits accurate computations for large eigenvalues. We show the relation between fault length and the first eigenvalue that governs the duration of initiation duration. The value of the weakening rate can be evaluated from the strain field in the elastic medium over a domain of confidence. A specific pattern of deformation represents the signature of the initiation phase. The spectral analysis and the numerical methods used for the single fault model remain valid for more complex fault systems. The interaction between two faults is examined. Finally, we introduce the concept of spectral equivalence between a heterogeneous fault system and a homogeneous fault with renormalized friction law.