Characterization of Fault Roughness at Various Scales: Implications of Three-Dimensional High Resolution Topography Measurements

Accurate description of the topography of active fault surfaces represents an important geophysical issue because this topography is strongly related to the stress distribution along fault planes, and therefore to processes implicated in earthquake nucleation, propagation, and arrest. To date, due to technical limitations, studies of natural fault roughness either performed using laboratory or field profilometers, were obtained mainly from 1-D profiles. With the recent development of Light Detection And Ranging (LIDAR) apparatus, it is now possible to measure accurately the 3-D topography of rough surfaces with a comparable resolution in all directions, both at field and laboratory scales. In the present study, we have investigated the scaling properties including possible anisotropy properties of several outcrops of two natural fault surfaces (Vuache strike-slip fault, France, and Magnola normal fault, Italy) in limestones. At the field scale, digital elevation models of the fault roughness were obtained over surfaces of 0.25 m2 to 600 m2 with a height resolution ranging from 0.5 mm to 20 mm. At the laboratory scale, the 3-D geometry was measured on two slip planes, using a laser profilometer with a spatial resolution of 20 µm and a height resolution less than 1 µm.Several signal processing tools exist for analyzing the statistical properties of rough surfaces with self-affine properties. Among them we used six signal processing techniques: (i) the root-mean-squares correlation (RMS), (ii) the maximum-minimum height difference (MM), (iii) the correlation function (COR), (iv) the RMS correlation function (RMS-COR), (v) the Fourier power spectrum (FPS), and (vi) the wavelet power spectrum (WPS). To investigate quantitatively the reliability and accuracy of the different statistical methods, synthetic self-affine surfaces were generated with azimuthal variation of the scaling exponent, similar to that which is observed for natural fault surfaces. The accuracy of the signal processing techniques is assessed in terms of the difference between the “input” self-affine exponent used for the synthetic construction and the “output” exponent recovered by those different methods. Two kinds of biases have been identified: Artifacts inherent to data acquisition and intrinsic errors of the methods themselves. In the latter case, the statistical results of our parametric study provide a quantitative estimate of the dependence of the accuracy with system size and directional morphological anisotropy. Finally, based on this parametric study, we used the most reliable techniques (RMS-COR, FPS, WPS) to analyze field data. These three methods provide complementary results. The FPS and WPS methods determine a robust characterization of the fault surface roughness in the direction of striations and perpendicular to them. The RMS-COR method allows investigation of the azimuth dependence of the scaling exponent. For both field and laboratory data, the topography perpendicular to the slip direction displays a similar scaling exponent H⊥ = 0.8. However, our analysis indicates that for the Magnola fault surface the scaling roughness exponent parallel to the mechanical striation is identical at large and small scales H// = 0.6–0.7, whereas for the Vuache fault surface it is characterized by two different self-affine regimes at small and large scales. We interpret this cross-over length scale as a witness of different mechanical processes responsible for the creation of fault topography at different spatial scales.