[1] We report on the topographic roughness measurements of five exhumed faults and thirteen surface earthquake ruptures over a large range of scales: from 50 mm to 50 km. We used three scanner devices (LiDAR, laser profilometer, white light interferometer), spanning complementary scale ranges from 50 mm 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 k = 0.58 AE 0.07 in the slip direction and H ? = 0.81 AE 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.

-Accurate description of the topography of active faults surfaces represents an 23 important geophysical issue because this topography is strongly related to the stress 24 distribution along fault planes, and therefore to processes implicated in earthquake nucleation, 25 propagation, and arrest. 26Up to know, due to technical limitations, studies of natural fault roughness either performed 27 using laboratory or field profilometers, were obtained mainly from 1D profiles. With the 28 recent development of Light Detection And Ranging (LIDAR) apparatus, it is now possible to 29 measure accurately the 3D topography of rough surfaces with a comparable resolution in all 30 directions, both at field and laboratory scales. In the present study, we have investigated the 31 scaling properties including possible anisotropy properties of several outcrops of two natural 32 fault surfaces (Vuache strike-slip fault, France, and Magnola normal fault, Italy) in 33 limestones. At the field scale, digital elevation models of the fault roughness were obtained 34 over surfaces of 0.25 m 2 to 600 m 2 with a height resolution ranging from 0.5 mm to 20 mm. 35At the laboratory scale, the 3D geometry was measured on two slip planes, using a laser 36 profilometer with a spatial resolution of 20 μm and a height resolution less than 1 μm. 37

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