The critical slip distance for seismic and aseismic fault zones of finite width;

We present a conceptual model for the effective critical friction distance for fault zones of finite width. A numerical model with 1D elasticity is used to investigate implications of the model for shear traction evolution during dynamic and quasi-static slip. The model includes elastofrictional interaction of multiple, parallel slip surfaces, which obey rate and state friction laws with either Ruina (slip) or Dieterich (time) state evolution. A range of slip acceleration histories is investigated by imposing perturbations in slip velocity at the fault zone boundary and using radiation damping to solve the equations of motion. The model extends concepts developed for friction of bare surfaces, including the critical friction distance L, to fault zones of finite width containing wear and gouge materials. We distinguish between parameters that apply to a single frictional surface, including L and the dynamic slip weakening distance do, and those that represent slip for the entire fault zone, which include the effective critical friction distance, Dcb, and the effective dynamic slip weakening distance Do. A scaling law for Dcb is proposed in terms of L and the fault zone width. Earthquake source parameters depend on net slip across a fault zone and thus scale with Dcb, Do, and the slip at yield strength Da. We find that Da decreases with increasing velocity jump size for friction evolution via the Ruina law, whereas it is independent of slip acceleration rate for the Dieterich law. For both laws, Da scales with fault zone width and shear traction exhibits prolonged hardening before reaching a yield strength. The parameters Dcb and Do increase roughly linearly with fault zone thickness. This chapter and Chapter 7 in the volume discuss the problem of reconciling laboratory measurements of the critical friction distance with theoretical and field-based estimates of the effective dynamic slip weakening distance.