Stress-transfer efficiency in presence of sub-patch fault roughness

Abstract:

It is well known that faults are not planar surfaces. Instead, their geometry exhibits fractal properties that span a wide range of scales (sub-micrometer to tens-of-kilometer). This “geometric fault roughness” has a distinct impact on the amount and distribution of stress that is induced in the medium when a fault slips. Although this is well known, large portions of this roughness are ignored in numerical simulations (even though they aim to understand the effect of roughness on seismic behavior): individual fault patches –the incremental elements that build the fault surface in the respective computer models– are planar and fault roughness at this and lower spatial scales is not considered. As a result, the fault-patch stress-transfer efficiency may be systematically too large in those numerical simulations with respect to the “actual” efficiency level. This defeats to some extend the purpose of those investigations that aim to constrain the effect of fault roughness on seismic behavior.

Here, we investigate the effect of sub-patch fault geometric complexity on fault-patch stress-transfer efficiency. We sub-divide a circular fault patch (1km radius) into a large number of triangular sub-patches (using different levels sub-patch discretizations to confirm convergence of our results), emplace them in an elastic full space, and determine the amount of induced stress as a function of fault roughness. For each level of sub-patch discretization we generate 10,000 random fault geometries that obey the fractal properties mentioned above. The corresponding stress values are normalized with a nominal stress value that is due to slip along a planar fault(patch), providing scaling factors and their variability for stress transfer efficiency.The presented work therefore provides the means to implement sub-patch fault roughness into (numerical) investigations that adopot fault-patch interaction schemes.