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Fractal and Multifractal Properties of the Spatial Distribution of Natural Fractures—Analyses and Applications
Author(s) -
Jiandong XU,
Guosheng QU,
JACOBI Robert D.
Publication year - 1999
Publication title -
acta geologica sinica ‐ english edition
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.444
H-Index - 61
eISSN - 1755-6724
pISSN - 1000-9515
DOI - 10.1111/j.1755-6724.1999.tb00857.x
Subject(s) - multifractal system , fractal , fractal dimension , fracture (geology) , box counting , scaling , mathematics , fractal analysis , field (mathematics) , geology , geometry , statistical physics , mathematical analysis , physics , geotechnical engineering , pure mathematics
The Cantor's dust theory is applied to investigate the scaling properites of the spatial distribution of natural fractures obtained from detailed scanline surveys of 27 field sites in the Appalachian Plateau of western New York, USA. The results obtained in this study indicate: 1) fracture spacing is characterized by fractal and multifractal properties. On small scales analyses yield an average fractal dimension of 0.15, which suggests a very high degree of clustering. In contrast, on large scales, fractures tend to be more regular and evenly distributed with an average fracture dimension of 0.52; 2) fractal dimension varies with different sets in different orientations, which can be attributed to interactions between pre‐existing fractures and younger ones, as well as variations of the intensity of the stresses under which the fractures were formed; 3) a time sequence of fracture set formation can be proposed based on fractal and multifractal analyses, which consists of (from old to young): N‐S, NW, ENE, and NE‐striking sets. This time sequence is confirmed by the study of the abutting relationships of different fracture sets observed in the field.