Fault Roughness Records Strength

Abstract:

Fault roughness is commonly ~0.1-1% at the outcrop exposure scale. More mature faults are smoother than less mature ones, but the overall range of roughness is surprisingly limited which suggests dynamic control. In addition, the power spectra of many exposed fault surfaces follow a single power law over scales from millimeters to 10’s of meters. This is another surprising observation as distinct structures such as slickenlines and mullions are clearly visible on the same surfaces at well-defined scales.

We can reconcile both observations by suggesting that the roughness of fault surfaces is controlled by the maximum strain that can be supported elastically in the wallrock. If the fault surface topography requires more than 0.1-1% strain, it fails.

Invoking wallrock strength explains two additional observations on the Corona Heights fault for which we have extensive roughness data. Firstly, the surface is isotropic below a scale of 30 microns and has grooves at larger scales. Samples from at least three other faults (Dixie Valley, Mount St. Helens and San Andreas) also are isotropic at scales below 10’s of microns. If grooves can only persist when the walls of the grooves have a sufficiently low slope to maintain the shape, this scale of isotropy can be predicted based on the measured slip perpendicular roughness data. The observed 30 micron scale at Corona Heights is consistent with an elastic strain of 0.01 estimated from the observed slip perpendicular roughness with a Hurst exponent of 0.8. The second observation at Corona Heights is that slickenlines are not deflected around meter-scale mullions. Yielding of these mullions at centimeter to meter scale is predicted from the slip parallel roughness as measured here.

The success of the strain criterion for Corona Heights supports it as the appropriate control on fault roughness. Micromechanically, the criterion implies that failure of the fault surface is a continual process during slip. Macroscopically, the fundamental nature of the control means that 0.1 to 1% roughness should be ubiquitous on faults and can generally be used for simulating ground motion. An important caveat is that the scale-dependence of strength may result in a difference in the yield criterion at large-scales. The commonly observed values of the Hurst exponent below 1 may capture this scale-dependence.