Quantification of fracture roughness by change probabilities and Hurst exponents

TL;DR

This paper introduces a novel method called 'change probabilities' to quantify fracture roughness and anisotropy, linking it to Hurst exponents for improved surface profile analysis.

Contribution

The study presents a new, flexible approach for quantifying and visualizing fracture roughness and anisotropy using change probabilities and their relation to Hurst exponents.

Findings

Change probabilities effectively quantify surface roughness.

The method reveals anisotropy and scale dependence in fracture surfaces.

Relation to Hurst exponents enhances modeling capabilities.

Abstract

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