Quantifying karstic geomorphologies using Minkowski tensors and graph theory: Applications to SLAM Lidar data from carbonate caves in Northern Bavaria (Germany)

Karstification is a ubiquitous feature in carbonate rocks. The origins can be hypogenic or epigenic based on the source of the reacting fluids. The presence of karstified lithologies and their spatial heterogeneity poses a major risk in subsurface energy utilization goals (hydrocarbons, geothermal etc). Such dissolution features tend to organize as spatial networks, with their evolution controlled by a complex interplay of several factors, including natural mineralogical variations in host rocks, effects of pre-existing structures, directional history of palaeo-flow paths, and competition between convective transport and dissolution. Accurate quantification of the spatial distribution of karst is difficult owing to resolution issues in 3D data such as seismic and ground penetrating radar. Recent advances in Simultaneous Location and Mapping (SLAM) Lidar technology have made possible to acquire karst cave passage geometries at very high-resolution with relative ease compared to conventional terrestrial lidar. In this contribution, we present a unique dataset of more than 80 caves, scanned using SLAM lidar, in Jurassic carbonates from northern Bavaria, Germany. We introduce a methodology for robustly deriving morphometrics of karstic caves using Minkowski tensors and spatial graph theory. The method is based on a combination representation of cave passage skeletons as spatial graphs and 2D passage cross-sections using Minkowski functionals. The enriched topological representation enables detailed analysis of internal spatial variation within a single cave and also comparison with cave geometries from other caves. We derive a typology of cave systems based on the degree of structural control on karstification using the database.