Methodological framework for implicit modeling of solid mineral deposits in automated design

The conventional delineation of three-dimensional geological boundaries largely depends on the time-consuming manual digitizing process. This modeling method can be best described as the modeling of a surface as the complex geometry of an ore body with regard to cutoff grades is constructed by means of triangulation. However, with the advent of fast 3D interpolation, construction of geological surfaces using the functions of volume became an efficient alternative to the explicit surface modeling. This article discusses the application of FastRBF™ and statistical analysis of geological data in 3D implicit modeling of solid mineral deposits. The stages of the geological model of a solid mineral deposit and the features of the numerical modeling using FastRBF™ are described. The implicit modeling allows assessment of the condition of solid mineral deposits, enables standardized digitizing when designing in mining and geology software systems, and provides more complete knowledge about the quality and quantity of a georesource potential of a mine. The high productivity of the implicit modeling is illustrated. It is also proved that the implicit modeling using FastRBF™ is a breakthrough in the interpolation of RBF. Using these functions, designers can solve problems connected with interpolation and smoothing of large data arrays in mining and geology software systems.

Keywords: mine, 3D geomodeling, geotechnical systems, implicit modeling, implication, statistical analysis, 3D mineral deposit models, data interpolation, indicator kriging, radial basis functions, fast radial basis functions, FastRBF™.
For citation:

Stadnik D. A., Stadnik N. M., Zhilin A. G., Lopushnyak E. V. Methodological framework for implicit modeling of solid mineral deposits in automated design. MIAB. Mining Inf. Anal. Bull. 2023;(5-1):185-197. [In Russ]. DOI: 10.25018/0236_1493_2023_51_0_185.

Issue number: 5
Year: 2023
Page number: 185-197
ISBN: 0236-1493
UDK: 622.272; 622.45
DOI: 10.25018/0236_1493_2023_51_0_185
Article receipt date: 27.02.2023
Date of review receipt: 29.03.2023
Date of the editorial board′s decision on the article′s publishing: 10.04.2023
About authors:

D.A. Stadnik1, Dr. Sci. (Eng.), Professor, e-mail:, 
N.M. Stadnik1, Cand. Sci. (Eng.), Assistant Professor, e-mail:,
A.G. Zhilin, Technical Director, Green Solutions, 050006, Almaty, Republic of Kazakhstan, e-mail:,
E.V. Lopushnyak1, Student, e-mail:,
1 North Caucasian Institute of Mining and Metallurgy (State Technological University), 362021, Vladikavkaz, Russia.


For contacts:

D.A. Stadnik, e-mail:


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