UDC: 
DOI: 
10.22389/0016-7126-2026-1030-4-56-64
1 Kindeev A.L.
2 Yakushev A.A.
3 Vorobei M.V.
Year: 
№: 
1030
Pages: 
56-64

Belarusian State University

1, 
2, 
3, 
Abstract:
The authors discuss application of geostatistical methods for three-dimensional modeling of the varved clay deposit of "Gaidukovka" (Minsk region, Belarus). The study is based on data from drilling wells, using which a spatial model of clay distribution was built using the empirical Bayesian kriging (EBK 3D) method. This method allows taking spatial correlation into account, reducing the uncertainty of interpolation and selecting the parameters of variograms automatically. The analysis showed that the exponential variogram provides the best results with the minimum values of the root-mean-square error and the optimal alignment of the forecast with the actual data. Cross-checking confirmed the validity of the model and its resistance to the variability of the initial information. The constructed three-dimensional model in voxel layer and iso-surface formats enabled visualizing the distribution of clays and identifying the main zones of industrial value. It was established that about 70 per cent of the deposits are concentrated in the central part of the field at depths of 8,5–22,5 m. The northeastern areas, where the proportion of clay layers exceeds two thirds, are promising for further development. At the same time, the north-western and southeastern zones are considered unpromising due to the low content of clay fractions. The results of the study demonstrate the effectiveness of using EBK 3D to improve the accuracy of reserve assessment and mining planning. The proposed method can be adapted to other types of solid minerals, which expands its scientific and practical significance
References: 
1.   Budrik V. G., Gus'kov O. I., Ezhov A. I., Kushnarev P. P., Markevich V. Yu. Primenenie metodov geostatistiki i gorno-geologicheskikh informatsionnykh tekhnologii pri gosekspertize zapasov rudnykh mestorozhdenii: problemy i resheniya. Nedropol'zovanie XXI vek, 2010, no. 1, pp. 37–43.
2.   Vistelius A. B. Osnovy matematicheskoi geologii. Moskva: Nauka, 1980, 389 p.
3.   Vistelius A. B. Teoreticheskie predposylki stokhasticheskikh modelei i ikh proverka v konkretnykh geologicheskikh usloviyakh. Matematicheskie metody v geologii, Moskva: Nauka, 1968, pp. 7–14.
4.   Kaputin Yu. E., Ezhov A. I., Khenli S. Geostatistika v gorno-geologicheskoi praktike. М.: 1995, 186 p.
5.   Kindeev A. L., Klebanovich N. V. Metodika ucheta pochvenno-agrokhimicheskogo potentsiala dlya optimizatsii struktury zemlepol'zovaniya Volozhinskogo raiona Respubliki Belarus'. Vestnik Moskovskogo universiteta. Ser. 17. Pochvovedenie, 2024, Vol. 79, no. 2, pp. 63–72. DOI: 10.55959/MSU0137-0944-17-2024-79-2-63-72.
6.   Prisyazhnyuk O. N. Primenenie metodov geostatistiki pri postroenii trekhmernoi modeli plasta BS Zapadno-Ust'-Balykskogo neftyanogo mestorozhdeniya (KhMAO). Problemy geologii i osvoeniya nedr: trudy XIX Mezhdunarodnogo simpoziuma im. akad. M. A. Usova studentov i molodykh uchenykh, Tomsk: Izd-vo Tomskogo politekhnicheskogo universiteta, 2015, Vol. 1, pp. 278–280.
7.   Bomeni I. Y., Kenmoe M. R., Nzeugang A. N., Pirard E., Wouatong A. S. L., Fagel N. (2022) Application of geostatistical methods to estimate the mineral contents in the alluvial clay deposit, Monoum plain, West Cameroon. Arabian Journal of Geosciences, Volume 15, no. 24, DOI: 10.1007/s12517-022-11064-8.
8.   Jiménez-Espinosa R., Chica-Olmo M. (1999) Application of geostatistics to identify gold-rich areas in the Finisterre-Fervenza region, NW Spain. Applied Geochemistry, Volume 14, no. 1, pp. 133–145.
9.   Krige D. G. (1951) A statistical approach to some basic mine valuation problems on the Witwatersrand. Journal of the Chemical, Metallurgical and Mining Society of South Africa, no. 51 (b), pp. 119–139.
10.   Lacherade L., Marache A., Denis A., Halfon I., Closset L., Rohmer J., Quesnel F. (2023) Geostatistical modelling of geotechnical properties in the context of a tunneling project: Application to the Grand Paris Express project (France). Expanding Underground – Knowledge and Passion to Make a Positive Impact on the World. CRC Press, pp. 301–309. DOI: 10.1201/9781003348030-37.
11.   Lindagato P., Li. Y., Yang G., Fenghao D., Wang Z. (2018) Application of geostatistical analyst methods in discovering concealed gold and pathfinder elements as geochemical anomalies related to ore mineralization. Geologos, Volume 24, no. 2, pp. 95–109. DOI: 10.2478/logos-2018-0010.
12.   Matheron G. (1973) The intrinsic random functions and their applications. Advances in Applied Probability, no. 5, pp. 439–468.
13.   Matheron G. (1978) The intrinsic random functions and their applications. Centre of Geostatistics, Fontainebleau, 175 p.
14.   Matheron G. (1971) The theory of regionalized variables and its applications. Centre of Geostatistics, Fontainebleau, 212 p.
15.   Olea R. A. (2018) A practical primer on geostatistics. US Geological Survey, 2018. Report No. 2009-1103. DOI: 10.3133/ofr20091103.
16.   Pilz J., Spöck G. (2008) Why do we need and how should we implement Bayesian kriging methods. Stochastic Environmental Research and Risk Assessment, no. 22, pp. 621–632.
17.   Reis A. P., Sousa A. J., Fonseca E. C. (2003) Application of geostatistical methods in gold geochemical anomalies identification (Montemor-O-Novo, Portugal). Journal of Geochemical Exploration, Volume 77, no. 1, pp. 45–63.
Citation:
Kindeev A.L., 
Yakushev A.A., 
Vorobei M.V., 
(2026) Application of geostatistical methods for three-dimensional modeling of varved clay deposits. Geodesy and cartography = Geodeziya i Kartografiya, 87(4), pp. 56-64. (In Russian). DOI: 10.22389/0016-7126-2026-1030-4-56-64
Publication History
Received: 22.09.2025
Accepted: 13.04.2026
Published: 20.05.2026

Content

2026 April DOI:
10.22389/0016-7126-2026-1030-4