A mechanical model for deformation and earthquakes on strike-slip faults

A two-dimensional model for stress accumulation and earthquake instability associated with strike-slip faults is considered. The model consists of an elastic lithosphere overlying a viscous asthenosphere, and a fault of finite width with an upper brittle zone having an elastoplastic response and a lower ductile zone having an elastoviscoplastic response. For the brittle, or seismic, zone the behavior of the fault material is assumed to be governed by a relation which involves strain hardening followed by a softening regime, with strength increasing with depth. For the fault material in the ductile, or aseismic, section, the viscous effect is included through use of a nonlinear creep law, and the strength is assumed to decrease with depth. Hence, because of the lesser strength and the viscous effect, continuous flow occurs at great depths, causing stress accumulation at the upper portion of the fault and leading to failure at the bottom of the brittle zone. The failure is initially due to localized strain softening but, with further flow, the material above the softened zone reaches its maximum strength and begins to soften. This process accelerates and may result in an unstable upward rupture propagation.Relations are developed for the history of deformation within the lithosphere, specifically for the velocity of particles within the fault and at the ground surface. The boundary-element method is used for a quantitative study, and numerical results are obtained and compared with the recorded surface deformation of the San Andreas fault. The effects of geometry and material properties on instability, on the history of the surface deformation, and on the earthquake recurrence time are studied. The results are presented in terms of variations of ground-surface shear strain and shear strain rate, and velocity of points within the fault at various times during the earthquake cycle.It is found that the location of rupture initiation, the possibility of a sudden rupture as opposed to stable creep, and also the ground deformation pattern and its history, all critically depend on the mechanical response of the material within the fault zone, especially that of the brittle section. Shorter earthquake recurrence times are obtained for shallower brittle zones and for a stiffer lithosphere. Lower viscosities of the aseismic zone and the absence of asthenospheric coupling tend to suppress instability and promote stable creep. The model results thus suggest that the overall viscosity of the ductile creeping zone must exceed a minimum value for a sudden upward propagating rupture to take place within the seismic section.