Quantification of fracture networks in non-layered, massive rock using synthetic and natural data sets

Two quantitative measures – correlation dimension and maximum Lyapunov exponent – are investigated for quantifying fracture spacing in massive, non-layered rock. The correlation dimension, a measure of fractal dimension, characterizes some aspects of fracture distribution. Relative to other fractal methods used in structural geology, the correlation dimension provides a more rigorous mathematical calculation of the fractal dimension and is particularly robust in cases where data is limited. The maximum Lyapunov exponent calculation also provides quantification of observed distributions of fracture spacing, emphasizing variations in adjacent spacing measurements. The two methods are tested on two different synthetic data sets, to elucidate their usefulness in distinguishing between different distributions, and their sensitivity to population size, average fracture spacing, and standard deviation. Both methods provide accurate results for small population sizes and for a range of average fracture spacings. These methods are then used together to quantify two different fracture sets in the granitoids of the Sierra Nevada Batholith. The results indicate that the different fracture sets – inferred to form from different tectonic processes – have distinctive and quantifiable differences in patterns of fracture spacing.

Research highlights
► Two fracture set quantifications are presented: the correlation dimension and λmax.
► The two quantifications can be used in the absence of mechanical layering.
► The correlation dimension can be used to approximate the fractal dimension.
► λmax can be used to quantify irregularity in an array of fractures.
► The methodologies may have predictive capability where outcrop is limited.