Faults smooth gradually as a function of slip

Geometry and roughness of fault surfaces plays a central role in the dynamics and kinematics of faulting. Faults smooth with increasing slip, but the degree of the smoothing has not previously been well-constrained for natural faults. We measure the roughness as a function of displacement for a suite of 16 faults with cumulative offsets ranging from 0.1 m to approximately 500 m. We find that slip parallel roughness evolves gradually with slip. For instance, for segments of length 0.5 m, H ≈ 2 × 10−3 D−0.1 where H is the RMS roughness and D is the displacement on the fault strand with both quantities measured in meters. The gradual nature of the smoothing is robust to varying lithology and erosion. The weak function implies a decrease in the rate of gouge formation for a model with increasing slip for a model in which gouge is generated by abrading an asperity tip. The relatively gradual evolution of roughness could be explained by lubrication by the accumulated gouge that mitigates the abrasional smoothing that occurs during slip and/or re-roughening processes.