Sub-Patch Roughness in Earthquake Rupture Investigations

Fault geometric complexities exhibit fractal characteristics over a wide range of spatial scales (km) and strongly affect the rupture process at corresponding scales. Numerical rupture simulations provide a framework to quantitatively investigate the relationship between a fault's roughness and its seismic characteristics. Fault discretization however introduces an artificial lower limit to roughness. Individual fault patches are planar and sub-patch roughness –roughness at spatial scales below fault-patch size– is not incorporated. Does negligence of sub-patch roughness measurably affect the outcome of earthquake rupture simulations? We approach this question with a numerical parameter space investigation and demonstrate that sub-patch roughness significantly modifies the slip-strain relationship –a fundamental aspect of dislocation theory. Faults with sub-patch roughness induce less strain than their planar-fault equivalents at distances beyond the length of a slipping fault. We further provide regression functions that characterize the stochastic effect sub-patch roughness.