Statistical distribution of static stress resolved onto geometrically-rough faults

The in-situ stress state within fault zones is technically challenging to characterize, requiring the use of indirect methods to estimate. Most work to date has focused on understanding average properties of resolved stress on faults, but fault non-planarity should induce spatial variations in resolved static stress on a single fault. Assuming a particular stochastic model for fault geometry (band-limited fractal) gives an approximate analytic solution for the probability density function (PDF) on fault stress that depends on the mean fault orientation, mean stress ratio, and roughness level. The mean stress is shown to be equal to the planar fault value, while deviations are described by substituting a second-order polynomial expansion of the stress ratio into the inverse distribution on fault slope. The result is an analytical expression for the PDF of shear-to-normal stress ratio on 2-D rough faults in a uniform background stress field. Two end-member distributions exist, one approximately Gaussian when all points on the fault are well away from failure, and one reverse exponential, which occurs when the mean stress ratio approaches the peak. For the range of roughness values expected to apply to crustal faults, stress deviations due to geometry can reach nearly 100% of the background stress level. Consideration of such a distribution of stress on faults suggests that geometric roughness and the resulting stress deviations may play a key role in controlling earthquake behavior.