Slip-weakening friction on a periodic system of faults: Spectral analysis

Abstract.

We consider the problem of antiplane shearing on a periodic system of collinear faults under a slip-dependent friction law in linear elastodynamics. A spectral analysis is performed in order to characterize the existence of unstable solutions. The structure of the spectrum for the associated eigenvalue problem is obtained. We prove the monotone dependence of the eigenvalues on the friction parameter. The study the static eigenvalue-problem gives the existence of a limit of stability. The eigenvalue problem is reduced to a hyper-singular integral equation, which is solved through a semi-analytical technique. The general eigen-solution consists of a set of eigenfunctions with a physical periodicity which is a multiple of the natural (geometrical) period of the system. The numerical solution allows us to investigate the behavior of the eigenvalues/functions and to conjecture some specific properties of the spectrum.