Nanoscale Characterization of Fault Roughness by Atomic Force Microscopy

Abstract:

Frictional properties of laboratory and natural fault surfaces are controlled by the collective behavior of microscopic asperity contacts. A fundamental parameter that determines the spatial distribution and average size of asperity contacts on a fault surface is the roughness at all length scales. Average contact sizes for laboratory friction experiments are inferred to be of order 1 to 10 μm, but contact sizes on natural faults are comparatively unknown. Previous studies have quantified surface roughness of exhumed faults over length scales of microns to tens of meters, but roughness at sub-micron length scales has rarely been determined. For length scales of tens of microns and larger, self-affine roughness is observed, exhibiting anisotropic scaling with a Hurst exponent of 0.6 in the slip-parallel direction and 0.8 in the slip-perpendicular direction (Candela et al., 2012). Using intermittent contact atomic force microscopy (AFM), we have probed natural fault surfaces over profile lengths as large as ~100 μm with nanometer resolution in the slip-parallel and slip-perpendicular directions and sub-nanometer resolution in the third dimension. Surface roughness at length scales of tens of microns and smaller also demonstrates a self-affine character, but characterized by a Hurst exponent of 0.7 in both the slip-parallel and slip-perpendicular directions, in contrast to the different slip-parallel and slip-perpendicular values cited above. Taken together, our data and existing roughness data for several other faults demonstrate self-affine geometry over ~13 orders of magnitude in lateral length scale, to scales as small as 10 nm. Roughness measurements in the sub-micron regime allow us to use contact theory to estimate the real area of contact, the mean pressure, and the distribution of contact stresses on a rough fault surface. Calculations using our measured roughness show that contact stresses for asperities microns and smaller in size are large enough to induce plastic deformation. In addition, we hypothesize that the merging of values of the Hurst exponent for both slip-parallel and slip-perpendicular roughness that occurs below a length scale of tens of microns indicates a transition from predominantly brittle deformation at larger scales to plastic deformation at smaller scales.