SMOOTH OPERATORS? ANALYSIS OF THE WORK BUDGET OF ROUGH FRICTIONAL FAULTS SUGGESTS THAT IT IS MECHANICALLY EFFICIENT FOR FAULTS TO MAINTAIN SOME DEGREE OF SELF-AFFINE ROUGHNESS

Rough faults become smoother parallel to the slip direction with increasing slip due to various wear processes. This well-documented observation is consistent with the expectation that natural systems evolve to their lowest energy configurations, yet all natural faults, regardless of maturity, have measurable roughness at many scales and never become perfectly smooth. We address this apparent conundrum by analyzing the work budget of synthetic frictional faults representing a range of prescribed fractal roughness. We utilize the boundary element method to model the response of these faults to external tectonic loading. Model faults are generated with known fractal roughness parameters, including the root mean square slope (β), a measure of roughness amplitude, and the Hurst exponent (H), a measure of geometric self-similarity.

Tectonic work done on the external boundaries of the models (W_ext) is partitioned into frictional work (W_fric), gravitational work (W_grav), and internal elastic strain energy (W_int). Results show that W_ext and W_int are smallest for a perfectly planar fault, and steadily increase with increasing β. The opposite is true for W_grav and W_fric. While the dependence of work on β is greater than H, W_grav and W_fric increase with increasing H, while W_int and W_ext decrease across the same range, suggesting that faults become more efficient with increasing self-similarity. Remarkably, however, for a narrow range of roughness amplitudes commonly measured along natural faults, the total work of the system remains approximately constant, while only slightly larger than the total work of a planar fault. Faults evolve toward the most mechanically efficient configuration; therefore we argue that the constant total work observed across this range of roughness amplitudes may represent an energy barrier, preventing faults from removing asperities and evolving to smooth, planar discontinuities. Furthermore, simulations in which fault depth is varied show that shallower faults have larger energy barriers, and can maintain constant mechanical efficiency at higher roughness amplitudes. Therefore, fault roughness should increase with decreasing fault depth.