Nanoscale Roughness of Natural Fault Surfaces Controlled by Scale‐Dependent Yield Strength

Many natural fault surfaces exhibit remarkably similar scale‐dependent roughness, which may reflect the scale‐dependent yield strength of rocks. Using atomic force microscopy (AFM), we show that a sample of the Corona Heights Fault exhibits isotropic surface roughness well‐described by a power law, with a Hurst exponent of 0.75 +/− 0.05 at all wavelengths from 60 nm to 10 μm. The roughness data and a recently proposed theoretical framework predict that yield strength varies with length scale as λ ‐0.25+/−0.05 . Nanoindentation tests on the Corona Heights sample and another fault sample whose topography was previously measured with AFM (the Yair Fault) reveal a scale‐dependent yield stress with power‐law exponents of −0.12 +/− 0.06 and −0.18 +/− 0.08, respectively. These values are within one to two standard deviations of the predicted value, and provide experimental evidence that fault roughness is controlled by intrinsic material properties, which produces a characteristic surface geometry.