Application of multi-point statistics to irregular core sampling data in modeling of copper-porphyry deposits
Ilya O. Panichkin, Georgy O. Abramyan
National University of Science and Technology “MISIS”, Moscow, Russian Federation
Mining Industry Journal (Gornaya Promyshlennost) №5/ 2026 p. 159-163
Summary: The article discusses a procedure for adapting multi-point statistics to interval-based core sampling data obtained from a copper-porphyry system. The procedure uses irregular borehole sampling and generates local category-based patterns within an anisotropic ellipsoidal neighborhood of a point. The calculation includes the geological domain, lithological rock type, composite type, and aggregated class of the ore potential. Single-layer and multi-layer patterns, distance-weighted and balanced variants of multi-point statistics, indicative kriging, and hybrid schemes were compared for verification. The quality was assessed using a post-hoc validation against the borehole data, employing the proportion of the correct answers, the balanced proportion of the correct answers and the macro-averaged F1 score. For the geological domains, the best result was achieved by a hybrid variant combining multi-point statistics and indicative kriging: the macro-F1 score was 0.401, and the proportion of the correct answers was 0.495. For the lithological types, the best macro-F1 score was obtained by jointly considering the domain, lithological, and composite contexts. For the composite type and the aggregated ore potential class, the best macro-F1 scores were achieved using a distance-weighted approach with class balancing. The results show that the multilayer and distance-weighted templates improve the accuracy of category-based modeling and can be used to refine a geological model.
Keywords: copper-porphyry system, interval data, core sampling, multi-point statistics, indicative kriging, category-based modeling, geological domain, lithological type, composite type, macro-averaged F1 score
For citation: Panichkin Ilya O., Abramyan Georgy O. Application of multi-point statistics to irregular core sampling data in modeling of copper-porphyry deposits. Mining Industry Journal (Gornaya Promyshlennost). 2026;(5):159–163. https://doi.org/10.30686/1609-9192-2026-5-159-163
Article info
Received: 03.06.2026
Revised: 09.07.2026
Accepted: 16.07.2026
Authors info
Panichkin Ilya O. – Postgraduate Student, Department of Geology and Mine Surveying, College of Mining, National University of Science and Technology “MISIS”, Moscow, Russian Federation; e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
Abramyan Georgy O. – Cand. Sci. (Eng.), Associate Professor, Department of Geology and Mine Surveying, College of Mining, National University of Science and Technology “MISIS”, Moscow, Russian Federation; https://orcid.org/0000-0002-0493-6290; e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
References
1. Guardiano F.B., Srivastava R.M. Multivariate geostatistics: Beyond bivariate moments. In: Soares A. (eds) Geostatistics Tróia ’92. Dordrecht: Springer; 1993. Vol. 1, pp. 133–144. https://doi.org/10.1007/978-94-011-1739-5_12
2. Strebelle S. Conditional simulation of complex geological structures using multiple-point statistics. Mathematical Geology . 2002;34(1):1–21. https://doi.org/10.1023/A:1014009426274
3. Mariethoz G., Caers J. Multiple-point geostatistics: Stochastic modeling with training images. John Wiley & Sons; 2015. 376 p. https://doi.org/10.1002/9781118662953
4. Høyer A.-S., Vignoli G., Hansen T.M., Vu L.T., Keefer D.A., Jørgensen F. Multiple-point statistical simulation for hydrogeological models: 3-D training image development and conditioning strategies. H ydrology and Earth System Sciences . 2017;21(12):6069–6089. https://doi.org/10.5194/hess-21-6069-2017
5. Hansen T.M., Vu L.T., Bach T. MPSLIB: A C++ class for sequential simulation of multiple-point statistical models. SoftwareX . 2016;5:127–133. https://doi.org/10.1016/j.softx.2016.07.001
6. Tahmasebi P. Multiple point statistics: A review. In: Daya Sagar B., Cheng Q., Agterberg F. (eds) Handbook of Mathematical Geosciences . Cham: Springer; 2018, pp. 613–643. https://doi.org/10.1007/978-3-319-78999-6_30
7. Zuo C., Pan Z., Yin Z., Guo C. A nearest neighbor multiple-point statistics method for fast geological modeling. Computers & Geosciences. 2022;167:105208. https://doi.org/10.1016/j.cageo.2022.105208
8. Jóhannsson Ó.D., Hansen T.M. Multiple-point statistics and non-colocational soft data integration. Computers & Geosciences . 2023;172:105280. https://doi.org/10.1016/j.cageo.2022.105280
9. Zhexenbayeva A., Madani N., Renard P., Straubhaar J. Using multiple-point geostatistics for geomodeling of a vein-type gold deposit. Applied Computing and Geosciences . 2024;23:100177. https://doi.org/10.1016/j.acags.2024.100177
10. Guo J., Zheng Y., Liu Z., Wang X., Zhang J., Zhang X. Pattern-based multiple-point geostatistics for 3D automatic geological modeling of borehole data. . 2025;34(1):149–169. https://doi.org/10.1007/s11053-024-10405-6
11. Kantemirov V.D., Yakovlev A.M., Titov R.S. Estimation of quality indicators of mineral resources using geoinformation technologies of block modeling. Geoinformatika. 2020;(3):29–37. (In Russ.) https://doi.org/10.47148/1609-364X-2020-3-29-37
12. Kantemirov V.D., Iakovlev A.M., Titov R.S. Applying geoinformation technologies of block modelling to improve the methods of assessing quality indicators of minerals. Izvestiya Vysshikh Uchebnykh Zavedeniy. Gornyy Zhurnal . 2021;(1):63–73. (In Russ.) https://doi.org/10.21440/0536-1028-2021-1-63-73
13. Yakovlev I.M. Testing of algorithms for automated processing of geological databases in mineral quality control flowcharts. Mining Informational and Analytical Bulletin . 2021;(5-1):248–257. (In Russ.) https://doi.org/10.25018/0236_1493_2021_51_0_248



