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
Tectonic work done on the external boundaries of the models (Wext) is partitioned into frictional work (Wfric), gravitational work (Wgrav), and internal elastic strain energy (Wint). Results show that Wext and Wint are smallest for a perfectly planar fault, and steadily increase with increasing β. The opposite is true for Wgrav and Wfric. While the dependence of work on β is greater than H, Wgrav and Wfric increase with increasing H, while Wint and Wext 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.