22 Jul 2022
22 Jul 2022
Status: this preprint is open for discussion.

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

Michał Michalak1,2, Lesław Teper1, Florian Wellmann3, Jerzy Żaba1, Krzysztof Gaidzik1, Marcin Kostur4, Yuriy Maystrenko5, and Paulina Leonowicz6 Michał Michalak et al.
  • 1Institute of Earth Sciences, Faculty of Natural Sciences, University of Silesia in Katowice, Będzińska 60, 41-205 Sosnowiec, Poland
  • 2Faculty of Geology, Geophysics and Environmental Protection, AGH University of Science and Technology, Mickiewicza 30, 30-059 Cracow, Poland
  • 3Computational Geoscience and Reservoir Engineering, RWTH Aachen, Wüllnerstr. 2, 52056 Aachen, Germany
  • 4Faculty of Science and Technology, University of Silesia in Katowice, 75. Pułku Piechoty, 41-500 Chorzów, Poland
  • 5The Geological Survey of Norway (NGU), Leiv Eirikssons vei 39, 7040 Trondheim, Norway
  • 6Faculty of Geology, University of Warsaw, Żwirki i Wigury 93, PL-02-089 Warszawa, Poland

Abstract. 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/attitude which results in minimizing 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 centre of a triangle (irregular version). We developed also a regular version of spatial clustering which allows to answer whether points from a grid structure can be affected by anomalies. To illustrate the usefulness of the combination between cosine distance as 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 Kraków-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 megafold. Clustering dip vectors resulted on the other hand in near co-circular cluster centers, thus pointing to a potential megacone. We also show that the linear arrangements of the anomalies, 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.

Michał Michalak et al.

Status: open (until 12 Sep 2022)

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Michał Michalak et al.

Model code and software

GeoAnomalia Michał Michalak

Michał Michalak et al.


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Short summary
When characterizing geological/geophysical surfaces, various geometric attributes are calculated such as dip angle (1D) or dip direction (2D). However, the boundaries between specific values may be subjective and without optimization significance as resulting from using default color palletes. This study proposes minimizing cosine distance among within-cluster observations to detect 3D anomalies. Our results suggest that the method holds promise for identification of megafolds or megacones.