Smoothing of Fault Slip Surfaces by Scale Invariant Wear

Fault slip surface roughness plays a determining role in the overall strength, friction, and dynamic behavior of fault systems. Previous wear models and field observations suggest that roughness decreases with increasing displacement. However, measurements have yet to isolate the effect of displacement from other possible controls, such as lithology or tectonic setting. In an effort to understand the effect of displacement, we present comprehensive qualitative and quantitative description of the evolution of fault slip surfaces in and around the San-Rafael Desert, S.E. Utah, United States. In the study area, faults accommodated regional extension at shallow (1 to 3 km) depth and are hosted in the massive, well-sorted, high-porosity Navajo and Entrada sandstones. Existing displacement profiles along with tight displacement controls readily measureable in the field, combined with uniform lithology and tectonic history, allowed us to isolate for the effect of displacement during the embryonic stages of faulting (0 to 60 m in displacement). Our field observations indicate a clear compositional and morphological progression from isolated joints or deformation bands towards smooth, continuous, and mirror-like fault slip surfaces with increasing displacement. We scanned pristine slip surfaces with a white light interferometer, a laser scanner, and a ground-based LiDAR. We produce and analyses more than 120 individual scans of fault slip surfaces. Results for the surfaces with the best displacement constraints indicate that roughness as defined by the power spectral density at any given length scale decreases with displacement according to a power law with an exponent of -1. Roughness measurements associated with only maximum constraints on displacements corroborate this result. Moreover, maximum roughness for any given fault is bounded by a primordial roughness corresponding to that of joint surfaces and deformation band edges. Building upon these results, we propose a multi-scale wear model to explain the evolution of faults with displacement. We suggest that together, asperity failure as a scale invariant process, and the stochastic strength of host rocks are consistent with qualitative and quantitative observational constraints made in this study.