A three-dimensional fluid-controlled earthquake model: Behavior and implications

We describe the behavior of a three-dimensional, fluid-controlled fault model that couples the dominant mechanical effects of fluid within a cellular fault zone with shear stress accumulation from constant plate motion applied at the downward continuation of the fault. Improvements from a previous model include long-term plate motion loading and porosity creation through dilatant slip, which allow the model to evolve to its steady state dynamic equilibrium. The examined results include slip and slip-deficit accumulation, pore pressure buildup and release, stress states, the emergence of seismic scaling relationships, and frequency-size statistics of model earthquakes. We find that asperities develop naturally within the model, reflecting the disorganization of the evolving stress state in Mohr space. The dynamical interaction of shear stress and effective normal stress perturbs the initial uniform stress state to a complex state that produces transient asperity development along the fault. These "Mohr-space" asperities spontaneously evolve, disintegrate, reemerge, and migrate along the fault plane. The general model behavior is independent of the state of the fluid pressure. In four examined cases, which span the range of possible fault zone overpressures, the equilibrium condition is that which occupies all of the available Mohr space. Maximum slip deficits along the fault depend on the degree of fault weakness, ranging from about 3 m for a weak fault to over 30 m for a strong fault after 4000 years of model evolution. For events that breach the surface the seismic moment scales with the cube of the source dimension M-o similar to L-3, which reflects the slipped area times the depth extent of the rupture. This scaling crosses isolines of stress drop. For confined events, M-o similar to L-2 along isolines of stress drop, but no general scaling emerges. Clusters emerge between stress drop versus seismic moment and stress drop versus source dimension, with large events converging to average stress drops of about 8 MPa for a weak fault and about 20 MPa for a strong fault.