Anisotropy quantification: the application of fractal geometry methods on tectonic fracture patterns of a Hercynian fault zone in NW Sardinia

Three different fractal geometry methods for pattern analysis are applied on a quartz-filled late-Hercynian fracture zone in NW Sardinia. Fragment–size distribution analysis and the box-counting method offer the possibility to (i) detect self-similarity of patterns and, therefore, argue for a specific pattern forming process, and (ii) allow the quantification of the patterns and their comparison with other patterns from similar natural and artificial environments. The failure of these methods in analyzing pattern anisotropies can be overcome by the Cantor-dust method, direction-related and based on the analysis of 1-D distribution of material in relation to its 2-D orientation. With the aid of fractal-dimension orientation diagrams (DOD), a specific parameter, the azimuthal anisotropy of fractal dimension (AAD), can be determined. It quantifies the pattern anisotropy and, consequently, provides the basis for analyzing the pattern-forming processes. In addition, the Cantor-dust method shows the existence of two different pattern-forming processes.