Roughness of fault surfaces over a length-scale range from nano- to milimeters

Fault-surface roughness is one of the primary factors affecting the mechanics of earthquakes and faulting. We report on the topographic roughness measurements on two natural fault surfaces with a continuous length-scale range from 1 nm to 3 mm. The fault surfaces observed in this study include (1) the Corona Heights fault in the Castro Area of San Francisco, detail microstructures reported by Kirkpatrick et al., (2013), and (2) the Itozawa fault in Fukushima prefecture, a fault moved just after the 2011 Off the Pacific Coast of Tohoku earthquake. To measure fault surface to we performed line-measurements both parallel and perpendicular to the slickenlines using two scanner devices; a confocal white-light scanning microscope (measurable range: 0.15 ˜ 3000 μm) and a scanning probe microscope (1 ˜ 50000 nm). The topographic properties of the measured surfaces were expressed either as a Hurst exponent (H) which are calculated from Power Spectrum Density (PSD) of topography data.

The measurements revealed that the Corona Heights fault and the Itozawa fault exhibit a similar geometrical property, a linear behavior on a log-log plot where axes are PSD and spatial length scale. A slope of the log-log plot, H, of the Corona Heights fault and the Itozawa fault shows H_N = 0.76 ± 0.01 perpendicular to the slickenslide and H_P = 0.84 ± 0.01 parallel to it, and H_N = 0.88 ± 0.01 and H_P = 0.91 ± 0.01, respectively. The measurements on both faults show H_P are higher than H_N, which is inconsistent with previous results that H_P is small compared to H_N because surface roughness in the slip direction becomes less pronounced selectively with progressive displacement. (e.g., Sagy et al., 2007). There is a hypotheses that explain the difference that H_P and H_N are undifferentiated with displacement in the length-scale range from 1 nm to 3 mm．

Candela et al., (2012) measured roughness of 13 earthquake fault surfaces and suggested that the fault geometry can be expressed as a single geometrical description (i.e., single H) over a range of scales from 50 μm to 50 km. Our data, at least H_N = 0.88 ± 0.01 perpendicular to the slickenlines, is approximately consistent with their universal H_N = 0.81 ± 0.04. The geometric complexity of fault surfaces in nature can be maintained over length-scales from nm- to km and be described as the single H.