Mathematical Geology

, Volume 38, Issue 4, pp 489–501 | Cite as

Theoretical Estimation of the Critical Sampling Size for Homogeneous Ore Bodies with Small Nugget Effect

  • K. Modis
  • K. Papaodysseus


The aim of this work is to investigate whether it is possible to determine a critical sampling grid density for a given ore body, above which further improvement in the accuracy of the estimated ore reserves would be small or negligible. The methodology employed is based on the theory of information. First, it is proven that the range of influence, when appears in the variogram function, is a measure of the maximum variability frequency observed in the ore body. Then, a simple application of the well-known sampling theorem shows that, under certain assumptions, it is possible to define a critical sampling density as mentioned before. An approximate rule of thumb can then be stated: that critical sampling grid size is half the range of influence observed in the variogram.


Geostatistics sampling density accuracy of estimation sampling theorem 


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  1. Adamides, N. G., 2001, The geology of Phoenix with an estimate of available resource: Internal Report, Hellenic Copper Mines Ltd, Nicosia, 26 p.Google Scholar
  2. Brooker, P. E., 1975, Avoiding unnecessary drilling: Proceedings, Australasian Institute of Mining and Metallurgy, No. 253, p. 21–23.Google Scholar
  3. Brooker, P. E., 1977, Block estimation at various stages of deposit development: Proceedings, 14th APCOM Symposium, American Institute of Mining, Metallurgical and Petroleum Engineers, p. 995–1003.Google Scholar
  4. Christakos, G., 2000, Modern spatiotemporal geostatistics: Oxford University Press, Oxford, 288 p.Google Scholar
  5. David, M., 1976, What Happens If?—Some Remarks on Useful Geostatistical Concepts in the Design of Sampling Patterns: Proceedings, Australasian Institute of Mining and Metallurgy, Symposium on Sampling Practices in the Minerals Industry, p. 1–15.Google Scholar
  6. Dowd, P. A., and Milton, D. W., 1987, Geostatistical estimation of a section of the perseverance nickel deposit, in G. Matheron and Armstrong M., eds., Geostatistical case studies, Reidel, Dordrecht, p. 39–67.Google Scholar
  7. Dunlop, J. S. F., 1979, Geostatistical modeling of an Australian Iron Ore body: Proceedings, 16th APCOM Symposium, American Institute of Mining, Metallurgical and Petroleum Engineers, p. 226–239.Google Scholar
  8. Jain, A. K., 1989, Fundamentals of digital image processing: Prentice Hall, Englewood Cliff, NJ, 569 p.Google Scholar
  9. Journel, A. G., and Huijbregts, Ch. J., 1978, Mining geostatistics: Academic Press, London, 600 p.Google Scholar
  10. Lloyd, S. P., 1959, A sampling theorem for stationary (wide sense) stochastic processes: Trans. Am. Math. Soc., v. 92, p. 1–12.CrossRefGoogle Scholar
  11. Matheron, G., 1970, La Theorie des Variables Regionalisees et ses Application: Les Cahiers du Centre de Morphologie Mathematique, Fasc. 5, CGMM Fontainebleau, 212 p.Google Scholar
  12. Peterson, D. P., and Middleton, D., 1962, Sampling and reconstruction of wave number limited functions in N-dimensional Euclidean spaces: Inform. Contr., v. 5, p. 279–323.CrossRefGoogle Scholar
  13. Shannon, C. E., 1949, Communications in the presence of noise: Proc. IRE v. 37, p. 10–21.Google Scholar
  14. Whittaker, E. T., 1915, On the functions, which are represented by the expansions of the interpolation theory: Proc. Roy. Soc., Edinburgh, Section A 35, p. 181–194.Google Scholar
  15. Xydas, K., Vattis, D., Georgaki-Ilia, K., Lamprou, V., and Triandafyllou, M., 2000, The use of information technology for the design of an intensive excavation program at the “Phoenix” copper deposit in Cyprus: Proceedings of the 3d Hellenic Conference for the mineral Wealth-Part B, Athens, p. 55–62, (in Greek).Google Scholar

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© International Association for Mathematical Geology 2006

Authors and Affiliations

  1. 1.School of Mining and Metallurgical EngineeringNational Technical University of AthensAthensGreece
  2. 2.School of Electrical and Computer EngineeringNational Technical University of AthensAthensGreece

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