Comparing Fracture Networks Across Scales: The Minkowski Fingerprint Distance

We introduce a novel method of representing and comparing fracture networks across scales that incorporates geometry and topology of fracture patterns. The Minkowski Fingerprint is a unique representation of a fracture network built on the spatial graph abstraction of fracturing where fracture intersections form graph nodes and connecting segments form edges. The partitioning of space within the edge connections in such a spatial graph can be represented as sets of connected tessellations to which morphometric analysis is applied. In particular, we use Minkowski tensor-based morphometric quantification to the tessellations, deriving multi-scale probability distributions and forming a unique fingerprint of any fracture network. We derive a similarity metric known as the Minkowski Fingerprint Distance that can compare a pair of networks. The MFD is then used to quantify variations in large-scale fracture patterns using hierarchical clustering. Examples of such intra-network and inter-network fracturing variations are showcased from limestone outcrops of the Franconian Alb.