Roughness of fault surfaces over nine decades of length scales

We report on the topographic roughness measurements of five exhumed faults and thirteen surface earthquake ruptures over a large range of scales: from 50 μ m to 50 km. We used three scanner devices (LiDAR, laser profilometer, white light interferometer), spanning complementary scale ranges from 50 μ m to 10 m, to measure the 3‐D topography of the same objects, i.e., five exhumed slip surfaces (Vuache‐Sillingy, Bolu, Corona Heights, Dixie Valley, Magnola). A consistent geometrical property, i.e., self‐affinity, emerges as the morphology of the slip surfaces shows at first order, a linear behavior on a log‐log plot where axes are fault roughness and spatial length scale, covering five decades of length‐scales. The observed fault roughness is scale dependent, with an anisotropic self‐affine behavior described by four parameters: two power law exponents H , constant among all the faults studied but slightly anisotropic ( H ∥ = 0.58 ± 0.07 in the slip direction and H ⊥ = 0.81 ± 0.04 perpendicular to it), and two pre‐factors showing variability over the faults studied. For larger scales between 200 m and 50 km, we have analyzed the 2‐D roughness of the surface rupture of thirteen major continental earthquakes. These ruptures show geometrical properties consistent with the slip‐perpendicular behavior of the smaller‐scale measurements. Our analysis suggests that the inherent non‐alignment between the exposed traces and the along or normal slip direction results in sampling the slip‐perpendicular geometry. Although a data gap exists between the scanned fault scarps and rupture traces, the measurements are consistent within the error bars with a single geometrical description, i.e., consistent dimensionality, over nine decades of length scales.