Investigating Spatial Heterogeneity within Fracture Networks using Hierarchical Clustering and Graph Distance Metrics

Abstract. We investigate the spatial variation of 2D fracture networks digitized from the well-known Lilstock limestone pavements, Bristol Channel, UK. By treating fracture networks as spatial graphs, we utilize a novel approach combining graph similarity measures and hierarchical clustering to identify spatial clusters within fracture networks and quantify spatial variation. We use four graph similarity measures: fingerprint distance, D-measure, NetLSD, and portrait divergence to compare fracture graphs. The technique takes into account both topological relationship and geometry of the networks and is applied to three large fractured regions consisting of nearly 300,000 fractures spread over 14,200 sq.m. The results indicates presence of spatial clusters within fracture networks with that vary gradually over distances of tens of metres. One region is not influenced by faulting but still displays variation in background fracturing. Variation in fracture development in the other two regions are interpreted to be primarily influenced by proximity to faults that gradually gives way to background fracturing. Comparative analysis of the graph similarity-derived clusters with fracture persistence measures indicate that there is a general correspondence between patterns; however, additional variations are highlighted that is not obvious from fracture intensity and density plots. The proposed method provides a quantitative way to identify spatial variations in fracture networks which can be used to guide stochastic and geostatistical approaches to fracture network modelling.