Clustering has a meaning: optimization of angular similarity to detect 3D geometric anomalies in geological terrains

The geological potential of sparse subsurface data is not being fully exploited since the available workflows are not specifically designed to detect and interpret 3D geometric anomalies hidden in the data. We develop a new unsupervised machine learning framework to cluster and analyze the spatial distribution of orientations sampled throughout a geological interface. Our method employs Delaunay triangulation and clustering with the squared Euclidean distance to cluster local unit orientations, which results in minimization of the within-cluster cosine distance. We performed the clustering on two representations of the triangles: normal and dip vectors. The classes resulting from clustering were attached to a geometric center of a triangle (irregular version). We also developed a regular version of spatial clustering which allows the question to be answered as to whether points from a grid structure can be affected by anomalies. To illustrate the usefulness of the combination between cosine distance as a dissimilarity metric and two cartographic versions, we analyzed subsurface data documenting two horizons: (1) the bottom Jurassic surface from the Central European Basin System (CEBS) and (2) an interface between Middle Jurassic units within the Krakow-Silesian Homocline (KSH), which is a part of the CEBS. The empirical results suggest that clustering normal vectors may result in near-collinear cluster centers and boundaries between clusters of similar trend, thus pointing to axis of a potential megacylinder. Clustering dip vectors, on the other hand, resulted in near-co-circular cluster centers, thus pointing to a potential megacone. We also show that the linear arrangements of the anomalies and their topological relationships and internal structure can provide insights regarding the internal structure of the singularity, e.g., whether it may be due to drilling a nonvertical fault plane or due to a wider deformation zone composed of many smaller faults.