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Quantification of Fracture Roughness by Change Probabilities and Hurst Exponents

Gutjahr, Tim; Hale, Sina ORCID iD icon; Keller, Karsten; Blum, Philipp; Winter, Steffen

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 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.


Verlagsausgabe §
DOI: 10.5445/IR/1000141582
Veröffentlicht am 02.01.2022
Originalveröffentlichung
DOI: 10.1007/s11004-021-09985-3
Scopus
Zitationen: 1
Web of Science
Zitationen: 1
Dimensions
Zitationen: 2
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte Geowissenschaften (AGW)
Institut für Stochastik (STOCH)
Publikationstyp Zeitschriftenaufsatz
Publikationsjahr 2022
Sprache Englisch
Identifikator ISSN: 1874-8961, 0020-5958, 0882-8121, 1573-8868, 1874-8953
KITopen-ID: 1000141582
Erschienen in Mathematical Geosciences
Verlag Springer-Verlag
Band 54
Seiten 679–710
Nachgewiesen in Dimensions
Scopus
Web of Science
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