Quantification of Fracture Roughness by Change Probabilities and Hurst Exponents

The objective of the current study is to utilize an innovative method called 'change probabilities' for describing fracture roughness. In order detect and visualize anisotropy rock joint surfaces, roughness one-dimensional profiles taken in different directions quantified. central quantifiers, probabilities', are based on counting monotone changes discretizations a profile. These probabilities, which usually varying with scale, can be reinterpreted as scale-dependent Hurst exponents. For large class Gaussian stochastic processes change probabilities shown directly related classical exponent, generalizes relationship known fractional Brownian motion. While being this measure, proposed more generally applicable, increasing therefore flexibility modeling investigating surface profiles. particular, it allows quick efficient visualization detection scale dependence