A universal power-law scaling exponent for fracture apertures in sandstones

A high-resolution data set of kinematic aperture (opening displacement) of opening-mode fractures, from large (up to 2 m long) quartz-cemented sandstone samples, shows that microfractures are ubiquitous and that most natural-fracture sets are better fit by power-law size distributions than by exponential, normal, or log-normal distributions. The data set includes 3822 fractures within 68 scanlines from eight formations on three continents. Kinematic apertures were measured along scanlines using scanning electron microscope-based cathodoluminescence (SEM-CL) and, for field data, using a hand lens. Microtextural evidence from SEM-CL shows that power law-distributed fractures typically have crack-seal texture and are composed of opening increments having a narrow (characteristic) aperture size range. In contrast, rare non-power-law-distributed fracture populations lack crack-seal texture. Power-law exponents, as measured in one dimension, have values of -0.8 approximately 0.1. Most variation among fracture sets results from power-law coefficients, which constitute a scale-invariant measure of fracture intensity. We show how observed scaling patterns can be used to improve estimations of large-fracture spacing in cases where fracture sampling is limited, as by the width of cores. The low (<1) value of the power-law scaling exponent reflects but a gentle increase in fracture frequency with decreasing size, such that microfracture abundances in core are commonly too low for statistically robust sampling. On the other hand, the consistency of the scaling exponent among fracture sets within various tectonic settings is such that the exponent can be assumed, facilitating large-fracture spacing estimations. The assumption of the scaling exponent should be supported by the presence of crack-seal texture within fractures.