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 tau(n) 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 tau(c)(i) = mu(i)(tau(n) - P-f(i)), where mu(i) is the frictional coefficient and P-f(i) 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.