Analysis of Spatially Distributed Fracture Attributes: Normalized Lacunarity Ratio

ABSTRACT Most fracture data analysis techniques for attributes such as dip and aperture, treat the attributes independently of their respective spatial locations. A power‐law cumulative frequency for fracture apertures, for example, tells us nothing about their spatial distribution. Lacunarity is a technique for analyzing multi‐scale binary and non‐binary data and is ideally suited for analysis that relates an attribute (e.g., aperture) to its spatial distribution. In a previous study, we showed that scale‐dependent heterogeneity of fracture spacing can be analyzed using lacunarity in order to identify whether fractures occur in clusters. To determine if such clusters contain the largest fractures that control fluid flow through a fracture network, it is imperative that size attribute data be integrated with information about fracture spacing. Here we introduce the novel concept of lacunarity ratio (LR), which is the lacunarity of a given non‐binary data set normalized to the lacunarity of its random counterpart. This technique can delineate the relationship between attributes and spatial clustering by determining scale‐dependent changes in persistence and anti‐persistence. LR is implemented to test if large fractures are statistically found within fracture clusters or if they are randomly distributed at a given scale of observation. The technique is then applied to five different data sets with spacing values together with aperture, length and dip values respectively. The LR‐technique thus developed can help in identifying the occurrence of large or steep fractures with respect to fracture clusters, which in turn, can help improve modeling strategies. Key Points Lacunarity ratio can allow for analyzing data on fracture spacing integrated with their size attributes Such analysis is based on delineating scale‐dependent persistence/anti‐persistence of data The results can identify the statistical presence or absence of large fractures within fracture clusters