Paper No. 5
Presentation Time: 9:20 AM

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


NEWMAN, Patrick J., Department of Geology and Environmental Science, University of Akron, Akron, OH 44325-4101 and GRIFFITH, W. Ashley, Earth and Environmental Sciences, University of Texas at Arlington, Geoscience Building Room 107, 500 Yates St. Box 19049, Arlington, TX 76019, wagriff@uta.edu

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 (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.