Lucile Bruhat, Yann Klinger, Amaury Vallage, Eric M Dunham 

Field studies characterized early on natural faults as rough, i.e. non-planar at all scales. Fault roughness induces local stress perturbations, which dramatically affect rupture behavior, resulting in slip heterogeneity. The relation between fault roughness and produced slip remains, however, a key knowledge gap in current numerical and field studies. In this study, we analyze numerical simulations of earthquake rupture to determine how roughness influences final slip profiles. Using a rupture catalog of thousands dynamic rupture simulations on non-planar fault profiles with varying roughness and background shear stress levels, we demonstrate that fault roughness affects the spectral characteristics of the resulting slip distribution. In particular, slip distributions become increasingly more self-affine, i.e. containing more short wavelength at smaller scale, with higher fault roughness, despite self-similar initial fault profiles. We also show that, at very short wavelength (<1km), the fractal dimension of the slip distributions dramatically changes with increasing roughness, background shear stress, and rupture behavior (e.g., sub-Rayleigh vs. supershear). The existence of a critical wavelength around 1km, under which more short wavelength are either preserved or created, suggests the role of rupture process and dynamic effects, together with fault geometry, in resulting slip distributions. The same spectral analysis is finally performed on high-resolution coseismic slip distributions from real strike-slip earthquakes. Compared to numerical simulations, all events present slip distributions that are much more self-affine than the profiles from numerical simulations. A different critical wavelength, here around 5-6km, appears, potentially informing about a critical asperity length. While we show here that the relation between fault roughness and produced slip distribution is much more complex than expected, this study is a first attempt at using statistical analyses of numerical simulations on rough faults to investigate observed coseismic slip distributions.