Lacunarity Analysis of Fracture Networks: Evidence for Scale-Dependent Clustering

Previous studies on fracture networks have shown that fractures contained within distinct mechanical units (“stratabound”) are regularly spaced while those that terminate within the rock mass are clustered (“non-stratabound”). Lacunarity is a parameter which can quantify the distribution of spaces between rock fractures. When normalized to account for differences in fracture abundance, lacunarity characterizes the distribution of spaces as the degree of clustering in the fracture network. Normalized lacunarity curves, L∗(r), computed using the gliding-box algorithm and plotted as a function of box-size, r, were constructed for natural fracture patterns from Telpyn Point, Wales and the Hornelen basin, Norway. The results from analysis of the Telpyn Point fractures indicate that such curves are sensitive to differences in the clustering of different fracture sets at the same scale. For fracture networks mapped at different scales from the Hornelen basin, our analysis shows that clustering increases with decreasing spatial scale. This trend is attributed to the transition from a “stratabound” system at the scale of sedimentary cycles (100–200m) that act as distinct mechanical units to a “non-stratabound” fracture system geometry at the finer 10’s of meters thick bedding scale.