Articles | Volume 18, issue 14
https://doi.org/10.5194/gmd-18-4469-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/gmd-18-4469-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
SubsurfaceBreaks v. 1.0: a supervised detection of fault-related structures on triangulated models of subsurface homoclinal interfaces
Faculty of Geology, Geophysics and Environmental Protection, AGH University of Science and Technology, Mickiewicza 30, 30-059 Kraków, Poland
Christian Gerhards
Institute of Geophysics and Geoinformatics, TU Bergakademie Freiberg, Gustav-Zeuner-Straße 12, 09599 Freiberg, Germany
Peter Menzel
Institute of Geophysics and Geoinformatics, TU Bergakademie Freiberg, Gustav-Zeuner-Straße 12, 09599 Freiberg, Germany
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Michał P. Michalak, Janusz Morawiec, and Peter Menzel
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This study analyzes geological faults using triangular surface data to model displaced horizons, considering scenarios with and without elevation uncertainties. Formal proofs and computational experiments show that, without elevation errors, identical dip directions occur. Even with uncertainties, the expected dip direction remains consistent. The findings offer insights for predicting fault geometry in data-sparse environments, improving fault modeling with imprecise elevation data.
Michał P. Michalak, Lesław Teper, Florian Wellmann, Jerzy Żaba, Krzysztof Gaidzik, Marcin Kostur, Yuriy P. Maystrenko, and Paulina Leonowicz
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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, 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 megacylinders or megacones.
Michał P. Michalak, Janusz Morawiec, and Peter Menzel
Solid Earth, 16, 1025–1040, https://doi.org/10.5194/se-16-1025-2025, https://doi.org/10.5194/se-16-1025-2025, 2025
Short summary
Short summary
This study analyzes geological faults using triangular surface data to model displaced horizons, considering scenarios with and without elevation uncertainties. Formal proofs and computational experiments show that, without elevation errors, identical dip directions occur. Even with uncertainties, the expected dip direction remains consistent. The findings offer insights for predicting fault geometry in data-sparse environments, improving fault modeling with imprecise elevation data.
Michał P. Michalak, Lesław Teper, Florian Wellmann, Jerzy Żaba, Krzysztof Gaidzik, Marcin Kostur, Yuriy P. Maystrenko, and Paulina Leonowicz
Solid Earth, 13, 1697–1720, https://doi.org/10.5194/se-13-1697-2022, https://doi.org/10.5194/se-13-1697-2022, 2022
Short summary
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, 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 megacylinders or megacones.
Cited articles
An, Y., Guo, J., Ye, Q., Childs, C., Walsh, J., and Dong, R.: Deep convolutional neural network for automatic fault recognition from 3D seismic datasets, Comput. Geosci., 153, 104776, https://doi.org/10.1016/j.cageo.2021.104776, 2021.
Bardziński, W., Lewandowski, J., Więckowski, R., and Zieliński, T.: Objaśnienia do Szczegółowej Mapy Geologicznej Polski w skali 1:50000, ark, Częstochowa (845), Wydawnictwa Geologiczne, Warszawa, 72 pp., 1986.
Bi, Z., Wu, X., Li, Z., Chang, D., and Yong, X.: DeepISMNet: three-dimensional implicit structural modeling with convolutional neural network, Geosci. Model Dev., 15, 6841–6861, https://doi.org/10.5194/gmd-15-6841-2022, 2022.
Bishop, C. M.: Pattern Recognition and Machine Learning (Information Science and Statistics), Springer-Verlag, Berlin, Heidelberg, ISBN-10 0-387-31073-8, ISBN-13 978-0387-31073-2 2006.
CGAL.org: CGAL, Computational Geometry Algorithms Library, https://www.cgal.org (last access: 17 July 2025), 2023.
Childs, C., Manzocchi, T., Walsh, J. J., Bonson, C. G., Nicol, A., and Schöpfer, M. P. J.: A geometric model of fault zone and fault rock thickness variations, J. Struct. Geol., 31, 117–127, https://doi.org/10.1016/j.jsg.2008.08.009, 2009.
Choi, J., Cho, H., Kwac, J., and Davis, L. S.: Toward sparse coding on cosine distance, in: 2014 22nd International Conference on Pattern Recognition, https://doi.org/10.1109/ICPR.2014.757, 2014.
Cracknell, M. J. and Reading, A. M.: Geological mapping using remote sensing data: A comparison of five machine learning algorithms, their response to variations in the spatial distribution of training data and the use of explicit spatial information, Comput. Geosci., 63, 22–33, https://doi.org/10.1016/j.cageo.2013.10.008, 2014.
Dadlez, R., Narkiewicz, M., Stephenson, R. A., Visser, M. T. M., and van Wees, J. D.: Tectonic evolution of the Mid-Polish Trough: modelling implications and significance for central European geology, Tectonophysics, 252, 179–195, https://doi.org/10.1016/0040-1951(95)00104-2, 1995.
Dayczak-Calikowska, K. and Moryc, W.: Rozwój basenu sedymentacyjnego i paleotektonika jury środkowej na obszarze Polski, Geol. Q., 32, 117–136, 1988.
De Berg, M., Cheong, O., Van Kreveld, M., and Overmars, M.: Computational Geometry: Algorithms and Applications, 3rd Edn., Springer, 364 pp., https://doi.org/10.2307/3620533, 2008.
de la Varga, M., Schaaf, A., and Wellmann, F.: GemPy 1.0: open-source stochastic geological modeling and inversion, Geosci. Model Dev., 12, 1–32, https://doi.org/10.5194/gmd-12-1-2019, 2019.
de Oliveira Neto, E. R., Fatah, T. Y. A., Dias, R. M., Freire, A. F. M., and Lupinacci, W. M.: Curvature analysis and its correlation with faults and fractures in presalt carbonates, Santos Basin, Brazil, Mar. Petr. Geol., 158, 106572, https://doi.org/10.1016/j.marpetgeo.2023.106572, 2023.
Fisher, N. I.: Statistical analysis of circular data, Cambridge University Press, 277 pp., https://doi.org/10.1017/cbo9780511564345, 1993.
Fisher, N. I., Huntington, J. F., Jacket, D. R., Willcox, M. E., and Creasey, J. W.: Spatial analysis of two-dimensional orientation data., J. Int. Assoc. Math. Geol., 17, 177–194, https://doi.org/10.1007/BF01033153, 1985.
Garbowska, J.: Interrelation between microfauna and nature of dogger deposits of the Czestochowa Jura (Poland), Acta Palaeontol. Pol., 23, 89–105, 1978.
Guo, J., Xu, X., Wang, L., Wang, X., Wu, L., Jessell, M., Ogarko, V., Liu, Z., and Zheng, Y.: GeoPDNN 1.0: a semi-supervised deep learning neural network using pseudo-labels for three-dimensional shallow strata modelling and uncertainty analysis in urban areas from borehole data, Geosci. Model Dev., 17, 957–973, https://doi.org/10.5194/gmd-17-957-2024, 2024.
Hammah, R. E. and Curran, J. H.: On distance measures for the fuzzy K-means algorithm for joint data, Rock Mech. Rock Eng., 32, 1–27, https://doi.org/10.1007/s006030050041, 1999.
Hermański, S.: Wpływ prac odwadniających kopalnictwa rud żelaza na kształtowanie warunków hydrogeologicznych w rejonie częstochowsko-kłobuckim, Rudy Żelaza, 9–10, 13–16, 1971.
Hermański, S.: Mapa stropu i miąższości warstw kościeliskich, Rejon Żarki-Wieluń. Skala 1:100000, in: Razowska, L., Pacholewski, A., and Zembal, M.: Badania procesów hydrogeochemicznych w obszarach wypełniania się kopalnianych lejów depresyjnych, Centralne Archiwum Geologiczne, 1997.
Hu, X., Bürgmann, R., Xu, X., Fielding, E., and Liu, Z.: Machine-Learning Characterization of Tectonic, Hydrological and Anthropogenic Sources of Active Ground Deformation in California, J. Geophys. Res.-Sol. Ea., 126, e2021JB022373, https://doi.org/10.1029/2021JB022373, 2021.
Jiang, Z., Mallants, D., Gao, L., Munday, T., Mariethoz, G., and Peeters, L.: Sub3DNet1.0: a deep-learning model for regional-scale 3D subsurface structure mapping, Geosci. Model Dev., 14, 3421–3435, https://doi.org/10.5194/gmd-14-3421-2021, 2021.
Jüstel, A., Correira, A. E., Pischke, M., de la Varga, M., and Wellmann, F.: GemGIS – Spatial Data Processing for Geomodeling, J. Open Source Softw., 7, 3709, https://doi.org/10.21105/joss.03709, 2022.
Jüstel, A., de la Varga, M., Chudalla, N., Wagner, J. D., Back, S., and Wellmann, F.: From Maps to Models – Tutorials for structural geological modeling using GemPy and GemGIS, J. Open Source Educ., 6, 185, https://doi.org/10.21105/jose.00185, 2023.
Kaur, H., Zhang, Q., Witte, P., Liang, L., Wu, L., and Fomel, S.: Deep-learning-based 3D fault detection for carbon capture and storage, Geophysics, 88, IM101–IM112, https://doi.org/10.1190/geo2022-0755.1, 2023.
Kopik, J.: Lower and Middle Jurassic of the north-eastern margin of the Upper Silesian Coal Basin, Biul. Państwowego Inst. Geol., 378, 67–129, 1998 (in Polish with English summary).
Kuhn, S., Cracknell, M. J., and Reading, A. M.: Lithologic mapping using Random Forests applied to geophysical and remote-sensing data: A demonstration study from the Eastern Goldfields of Australia, Geophysics, 83, B183–B193, https://doi.org/10.1190/geo2017-0590.1, 2018.
Marynowski, L., Zatoń, M., Simoneit, B., and Otto, A.: Compositions, sources and depositional environments of organic matter from the Middle Jurassic clays of Poland, Appl. Geochem., 22, 2456–2485, https://doi.org/10.1016/j.apgeochem.2007.06.015, 2007.
Mattéo, L., Manighetti, I., Tarabalka, Y., Gaucel, J. M., van den Ende, M., Mercier, A., Tasar, O., Girard, N., Leclerc, F., Giampetro, T., Dominguez, S., and Malavieille, J.: Automatic Fault Mapping in Remote Optical Images and Topographic Data With Deep Learning, J. Geophys. Res.-Sol. Ea., 126, e2020JB021269, https://doi.org/10.1029/2020JB021269, 2021.
Matyja, B. A. and Wierzbowski, A.: Ammonites and stratigraphy of the uppermost Bajocian and Lower Bathonian between Częstochowa and Wieluń Central Poland, Acta Geol. Pol., 50, 191–209, 2000.
Matyszkiewicz, J., Kochman, A., Rzepa, G., Gołębiowska, B., Krajewski, M., Gaidzik, K., and Żaba, J.: Epigenetic silicification of the Upper Oxfordian limestones in the Sokole Hills (Kraków-Częstochowa Upland): Relationship to facies development and tectonics, Acta Geol. Pol., 65, 181–203, https://doi.org/10.1515/agp-2015-0007, 2015.
Michalak, M. P.: SubsurfaceBreaks v. 1.0: A supervised detection of fault-related structures on triangulated models of subsurface homoclinal interfaces: Input and Processed Data, Zenodo [code and data set], https://doi.org/10.5281/zenodo.14589469, 2024.
Michalak, M.: Numerical limitations of the attainment of the orientation of geological planes, Open Geosci., 10, 395–402, https://doi.org/10.1515/geo-2018-0031, 2018.
Michalak, M. P., Bardziński, W., Teper, L., and Małolepszy, Z.: Using Delaunay triangulation and cluster analysis to determine the orientation of a sub-horizontal and noise including contact in Kraków-Silesian Homocline, Poland, Comput. Geosci., 133, 104322, https://doi.org/10.1016/j.cageo.2019.104322, 2019.
Michalak, M. P., Kuzak, R., Gładki, P., Kulawik, A., and Ge, Y.: Constraining uncertainty of fault orientation using a combinatorial algorithm, Comput. Geosci., 154, 104777, https://doi.org/10.1016/j.cageo.2021.104777, 2021.
Michalak, M. P., Teper, L., Wellmann, F., Żaba, J., Gaidzik, K., Kostur, M., Maystrenko, Y. P., and Leonowicz, P.: Clustering has a meaning: optimization of angular similarity to detect 3D geometric anomalies in geological terrains, Solid Earth, 13, 1697–1720, https://doi.org/10.5194/se-13-1697-2022, 2022.
Pedregosa, F., Varoquaux, G., Gramfort, A., Vincent, M., Thirion, B., Grisel, O., Blondel, M., Prettenhofer, P., Weiss, R., Dubourg, V., Vanderplas, J., Passos, A., Cournapeau, D., Brucher, M., Perrot, M., and Duchesnay, É.: Scikit-learn: Machine Learning in Python, J. Mach. Learn. Res., 12, 2825–2830, 2011.
Razowska, L.: Changes of groundwater chemistry caused by the flooding of iron mines (Czestochowa region, southern Poland), J. Hydrol., 244, 17–32, https://doi.org/10.1016/S0022-1694(00)00420-0, 2001.
Razowska, L., Pacholewski, A., and Zembal, M.: Badania procesów hydrogeochemicznych w obszarach wypełniania się kopalnianych lejów depresyjnych, Centralne Archiwum Geologiczne, 1997.
Reichstein, M., Camps-Valls, G., Stevens, B., Jung, M., Denzler, J., Carvalhais, N., and Prabhat, F.: Deep learning and process understanding for data-driven Earth system science, Nature, 566, 195–204, https://doi.org/10.1038/s41586-019-0912-1, 2019.
Shalev-Shwartz, S. and Ben-David, S.: Understanding machine learning: From theory to algorithms, Cambridge University Press, 397 pp., https://doi.org/10.1017/CBO9781107298019, 2013.
Singleton, J. S. and Gans, P. B.: Structural and stratigraphic evolution of the Calico Mountains: Implications for early Miocene extension and Neogene transpression in the central Mojave Desert, California, Geosphere, 4, 459–479, https://doi.org/10.1130/GES00143.1, 2008.
Słonka, Ł. and Krzywiec, P.: Upper Jurassic carbonate buildups in the Miechów Trough, southern Poland – insights from seismic data interpretations, Solid Earth, 11, 1097–1119, https://doi.org/10.5194/se-11-1097-2020, 2020.
Vapnik, V. N.: The nature of statistical learning theory, Statistics for Engineering and Information Science, Springer-Verlag, New York, ISBN 978-1-4419-3160-3, 2000.
Vega-Ramirez, L. A., Spelz, R. M., Negrete-Aranda, R., Neumann, F., Caress, D. W., Clague, D. A., Paduan, J. B., Contreras, J., and Peña-Dominguez, J. G.: A new method for fault-scarp detection using linear discriminant analysis in high-resolution bathymetry data from the alarcón rise and pescadero basin, Tectonics, 40, e2021TC006925, https://doi.org/10.1029/2021TC006925, 2021.
Wang, H., Zhang, L., Yin, K., Luo, H., and Li, J.: Landslide identification using machine learning, Geosci. Front., 12, 351–364, https://doi.org/10.1016/j.gsf.2020.02.012, 2021.
Wang, Y., Ksienzyk, A. K., Liu, M., and Brönner, M.: Multi-geophysical data integration using cluster analysis: Assisting geological mapping in Trøndelag, Mid-Norway, Geophys. J. Int., 225, 1142–1157, https://doi.org/10.1093/gji/ggaa571, 2020.
Więckowski, R., Zieliński, T., Bardziński, W., and Lewandowski, J.: Szczegółowa Mapa Geologiczna Polski w skali 1:50 000 arkusz: Częstochowa, arkusz Częstochowa (845), Państwowy Instytut Geologiczny – Państwowy Instytut Badawczy, 1985.
Xiong, Y. and Zuo, R.: A positive and unlabeled learning algorithm for mineral prospectivity mapping, Comput. Geosci., 147, 104667, https://doi.org/10.1016/j.cageo.2020.104667, 2021.
Yang, J., Xu, J., Lv, Y., Zhou, C., Zhu, Y., and Cheng, W.: Deep learning-based automated terrain classification using high-resolution DEM data, Int. J. Appl. Earth Obs. Geoinf., 118, 103249, https://doi.org/10.1016/j.jag.2023.103249, 2023.
Zhan, J., Xu, P., Chen, J., Wang, Q., Zhang, W., and Han, X.: Comprehensive characterization and clustering of orientation data: A case study from the Songta dam site, China, Eng. Geol., 225, 3–18, https://doi.org/10.1016/j.enggeo.2017.01.010, 2017.
Znosko, J.: Tektonika obszaru częstochowskiego, Przegląd Geol., 8, 418–424, 1960.
Short summary
Using geometric features of synthetic triangulated models of subsurface homoclinal interfaces, we applied machine learning to detect faults. Testing on real borehole data validated its effectiveness across various fault orientations. The supervised approach represents a significant improvement over older methods that relied on simpler clustering techniques which were capable of identifying fewer orientations of potential faults.
Using geometric features of synthetic triangulated models of subsurface homoclinal interfaces,...