Lacunarity Analysis of Fracture Networks

Lacunarity is a relatively new parameter for quantifying the spatial variability of patterns at different scales. In simple terms, it can be considered to be a measure of the degree of clustering of the elements of interest in a given pattern. Although originally developed for studying fractal entities, lacunarity is also applicable to non-fractal patterns which include a variety of data sets in the geosciences. In the present study, we investigate the use of this parameter for distinguishing between different fracture networks with the same fractal dimension (D) but different visual appearances. The gliding-box algorithm was employed for computing the normalized lacunarity, L*, as a function of the box-size, r. Normalized lacunarity curves were constructed for a suite of synthetic fractal fracture patterns with a known D value, as well as for a set of 7 nested natural fracture maps with similar D values ranging from 1.80±0.05 to 1.84±0.04. Our results show that differences between synthetic patterns with the same fractal dimension and fracture porosity were most pronounced when L* values were determined at intermediate box sizes. Although the natural patterns had similar fractal dimensions their “fracture porosities” varied between 5.73 and 10.09%. Estimates of L* indicate that natural fractures are more clustered at smaller scales. Further research is needed to explore the mechanistic implications of this finding.