TY  - JOUR
A1  - Gutjahr, Tim
A1  - Hale, Sina
A1  - Keller, Karsten
A1  - Blum, Philipp
A1  - Winter, Steffen
T1  - Quantification of Fracture Roughness by Change Probabilities and Hurst Exponents
Y1  - 2021-12-17
VL  - 54
IS  - 4
SP  - 679
EP  - 710
JF  - Mathematical Geosciences
DO  - 10.1007/s11004-021-09985-3
PB  - Springer Berlin Heidelberg
N2  - 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 monotonic changes in discretizations of a profile. These probabilities, which usually vary 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 related to this classical roughness measure, the proposed method is more generally applicable, therefore increasing 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.
UR  - http://resolver.sub.uni-goettingen.de/purl?gldocs-11858/11046
ER  -