Stick, slip, and opening of wavy frictional faults: A numerical approach in two dimensions

摘要

We use a two-dimensional displacement discontinuity method (DDM) for quasi-static boundary value problems to investigate sinusoidal faults of finite length in an otherwise homogeneous and isotropic elastic material.The DDM incorporates a complementarity algorithm to enforce appropriate contact boundary conditions along the model fault.The numerical solution for the model sinusoidal fault converges to the analytical solution for a straight fault of finite length as the ratio amplitude/wavelength goes to zero.It does not converge to the analytical solution for an infinite sinusoidal interface as the ratio distance/wavelength goes to zero.We provide stick,slip,and opening distributions along wavy faults with a range of uniform coefficients of friction,amplitude/wavelength ratios,and wave numbers.As the number of sinusoidal waves or the amplitude/wavelength is increased,mean slip decreases.Additionally,the fault geometry causes slip to deviate significantly from the elliptical distribution of a planar fault.We demonstrate that the displacement discontinuity of wavy faults cannot be prescribed a priori.This necessitates implementation of the complemcntarity algonthm and precludes an analytical solution.We employ the terms lee and stoss instead of releasing and restraining bends because a local minimum in slip may occur along lee sides,as well as stoss sides.In some cases,lee sides stick while stoss sides slip. Trends in the slip perturbation can be explained by the angular relationship between the local fault trace and the orientation of the remote principal stresses;however,the displacement discontinuity along a wavy model fault cannot be explained by this relationship alone.