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 mu m to 50 km. We used three scanner devices (LiDAR, laser profilometer, white light interferometer), spanning complementary scale ranges from 50 mu 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-parallel to = 0.58 +/- 0.07 in the slip direction and H-perpendicular to = 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.