Fractal analyses of fracture network geometry: an example from the Tassili-n-Ajjers area, SE Algeria
Authors
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Réda Samy Zazoun
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1
Abstract
The objective of our study is to analyze the geometry of 2D fracture networks using fractal analysis methods. Three types of analyzes reflecting fractal behaviors, namely monofractal analysis, multifractal analysis and fractal anisotropy analysis are introduced as typical procedures to examine the density, the heterogeneity or the homogeneity, and the spatial-temporal directional relationship between the stress tensor and the fracture pattern generated by the fracture model, respectively. Further, a lacunarity dimension for describing the degree of self-organization is presented. An aerial photographic data set was used to extract fracture network lineaments from the Tassili-n-Ajjers area, Algeria. The scaling and distribution rules that characterize the spatial distribution of fractures were established using classical distribution laws and then revised in the light of Weibull distribution theory. The syn-fault fractures increase in frequency near the faults and we interpret the high fracture densities as a damage zones. The study reveals that multifractal and lacunarity data provides a more comprehensive understanding of the spatial heterogeneity of fracture networks than any monofractal dimension.
