Abstract
Mineral industry contributes a major part of economical growth to a nation. Therefore, it is important to understand the concentration measurement of minerals in different locations of earth’s crust. The concentration refers to as the grade values of minerals. A block model is a simplified geometrical representation of a mineral deposit. There are several methods to find out the grade values of each block, such as, inverse distance method, copula, krigging etc. Krigging is a popular method to find out the grade values. However, number of mathematical calculations increase with the increasing number of sample points and thus the computational complexity becomes high. Here, we use a mathematical tool, cellular automata (CAs) where each cell is represented as a block. Using cellular automata, we here find out the grade values with much less computations. 2 dimensional CAs are used in this study where the local rule is the ordinary krigging estimator function using spherical variogram model. Also, in this study we deal with multiple horizontal slices of 3 dimensional mineral deposits. It can be seen that the CA based estimation is same as ordinary krigging based estimation, however, in a much simpler way.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Burks, A.W.: Essays on Cellular Automata. University of Illinois Press (1970)
Das, S.: Theory and Applications of Nonlinear Cellular Automata In VLSI Design. Ph.D. thesis, Bengal Engineering and Science University, Shibpur, India (2007)
Gardner, M.: The fantastic combinations of John Conway’s new solitaire game ‘Life’. Sci. Am. 223, 120–123 (1970)
Kim, Y.C.: Introductory Geostatistics and Mine Planning. University of Wollongong, Key Centre for Mines (1991)
Krige, D.G.: A statistical approach to some basic mine valuation problems on the Witwatersrand. J. S. Afr. Inst. Min. Metall. 52, 201–203 (1951)
Martins, A.C., Nader, B., De Tomi, G.: A novel application of cellular automata for the evaluation and modelling of mineral resources. Int. J. Min. Miner. Eng. 3(4), 303–315 (2011)
Matheron, G.: Principles of geostatistics. Econ. Geol. 58(8), 1246–1266 (1963)
Matheron, G.: The theory of regionalized variables and its applications, vol. 5. Paris: École National Supérieure des Mines, p. 211 (1971)
Moore, E.F.: Machine models of self-reproduction. In: Proceedings of Symposia in Applied Mathematics, vol. 14, pp. 17–33. American Mathematical Society (1962)
Ulam, S.: On some mathematical problems connected with patterns of growth of figures. In: Proceedings of Symposia in Applied Mathematics, vol. 14, pp. 215–224. American Mathematical Society (1962)
von Neumann, J.: The Theory of Self-reproducing Automata, Burks, A.W. ed. University of Illinois Press, Urbana and London (1966)
Zhang, J., Yao, N.: The geostatistical framework for spatial prediction. Geo-spat. Inf. Sci. 11(3), 180–185 (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Paty, S., Kamilya, S. (2022). Grade Estimation of Mineral Resources: An Application of Cellular Automata. In: Das, S., Martinez, G.J. (eds) Proceedings of First Asian Symposium on Cellular Automata Technology. ASCAT 2022. Advances in Intelligent Systems and Computing, vol 1425. Springer, Singapore. https://doi.org/10.1007/978-981-19-0542-1_4
Download citation
DOI: https://doi.org/10.1007/978-981-19-0542-1_4
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-19-0541-4
Online ISBN: 978-981-19-0542-1
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)