The influence of fluid flow in fault zones on patterns of seismicity: A numerical investigation

We present a coupled two-dimensional model of the fluid flow within a tabular fault zone and frictional failure of the fault, incorporating the effects of compaction and dilatancy. The model fault zone is loaded externally, resulting in a constant shear traction along the fault and a constant normal stress τn across it. Nonuniform compaction of the fault material leads to fluid pressure gradients and fluid flow. Frictional failure of element i is triggered when the fluid pressure is sufficiently high that the shear stress exceeds a critical level τci = μi(τn - Pfi), where μi is the frictional coefficient and Pfi is the fluid pressure. Failure of a fault element results in an increase in element porosity and a decrease in fluid pressure. We model the diffusion of fluid pressure using a lattice Bhatnagar-Gross-Krook technique, and frictional failure is simulated by a simple cellular automaton type model. We show that the failure history of the fault is critically dependent on the ratio of the fluid diffusivity of the fault material to the compaction rate. For high diffusivities a power law distribution of failure sizes is observed, but at low diffusivities a non-power law distribution results. High diffusivities promote a cyclic failure history, whereas at low diffusivities the failure occurs at a constant level. Clusters of failed fault elements may be identified with seismic events, and therefore our results place bounds on the range of fault parameters which are permitted in a situation in which seismicity is observed to follow a Gutenberg-Richter distribution.