Skip to main content
SpringerLink
Log in

A Chart for Judging Optimal Sample Spacing for Ore Grade Estimation: Part II

  • Original Paper
  • Published:
Natural Resources Research Aims and scope Submit manuscript

Abstract

Resources of mineral deposits are commonly estimated using data extracted from rock cores obtained by drilling. Information of good quality and quantity is essential to achieve good estimates (unbiased and precise). Frequently, the geomodeller is required to provide an estimate of the grade of each block to be mined. Some deposits have more erratic spatial grade distributions than others, and therefore a better understanding of closely spaced samples is required. Given the importance of samples, due to their influence on the precision and accuracy of the model built from these collected data, it is deemed important to optimize their spacing (or sampling grid). The idea is to obtain information which will lead to the desired model precision while minimizing the overall sampling cost. Commonly, mineral deposit regions with high grade variability require closely spaced samples. In this paper, the variability is measured by the grades’ coefficient of variation. A chart relating the sample spacing to the estimation error for various data coefficients of variation and block geometries of three different deposits is proposed. A case study illustrates the results obtained for a copper grade, an iron grade, and an aluminum oxide grade. The aim of this paper is to establish a fast and reliable way to obtain the maximum error for a given sample spacing that may be used for short-term geological modeling and mine planning at different ore deposits.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7

Similar content being viewed by others

References

  • Emery, X., Hernández, J., Corvalán, P., & Montaner, D. (2008). Developing a cost-effective sampling design for forest inventory. In J. M. Ortiz, & X. Emery (Eds.), Proceedings of the eighth international geostatistics congress (Vol. 2, pp. 1001–1010). Santiago: Gecamin.

    Google Scholar 

  • Goovaerts, P. (2001). Geostatistical modelling of uncertainty in soil science. Geoderma,103, 3–26.

    Article  Google Scholar 

  • Isaaks, E. D., & Srivastava, R. M. (1989). An introduction to applied geostatistics. New York: Oxford University Press.

    Google Scholar 

  • Koppe, V. C., Costa, J. F. C. L., Peroni, R. L., & Koppe, J. C. (2011). Choosing between two kind of sampling patterns using geostatistical simulation: Regularly spaced or at high uncertainty locations? Natural Resources Research,20(2), 131–142.

    Article  Google Scholar 

  • Koppe, V. C., Rubio, R. H., & Costa, J. F. C. L. (2017). A chart for judging optimal sample spacing for ore grade estimation. Natural Resources Research,26(2), 191–199.

    Article  Google Scholar 

  • Li, S., Dimitrakopoulos, R., Scott, J., & Dunn, D. (2004). Quantification of geological uncertainty and risk using stochastic simulation and applications in the coal mining industry. In Orebody modelling and strategic mining planning (pp. 233–240). Melbourne: The Australasian Institute of Mining and Metallurgy.

  • Machado, J. L., Leal, R. S., Koppe, V. C., Peroni, R. L., & Capponi, L. N. (2016). Short-term sampling space optimization. In 24th World mining congress proceedings—surface mining, e-book (pp. 218–230). IBRAM. ISBN: 978-85-61993-11-5.

  • Matheron, G. (1973). The intrinsic random functions and their applications. Advances in Applied Probability, 5, 439–468. Retrieved December 8, 2006 from http://cg.ensmp.fr/bibliotheque/index.html.

    Article  Google Scholar 

  • Pilger, G. G., Costa, J. F. C. L., & Koppe, J. C. (2001). Additional samples: Where they should be located. Natural Resources Research,10(3), 197–207.

    Article  Google Scholar 

Download references

Acknowledgments

The authors thank CAPES (Brazilian government research agency) for providing financial support to this research and the Mining Planning and Mineral Research Laboratory at Federal University of Rio Grande do Sul for providing computational facilities. The authors also thank the anonymous reviewers for their constructive comments, which helped us to improve the quality of our paper.

Author information

Authors and Affiliations

  1. Mining Engineering Department, Federal University of Rio Grande do Sul - UFRGS, Porto Alegre, Rio Grande do Sul, Brazil

    David Alvarenga Drumond, Flávio Azevedo Neves Amarante, Vanessa Cerqueira Koppe & João Felipe Coimbra Leite Costa

Authors
  1. David Alvarenga Drumond
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Flávio Azevedo Neves Amarante
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Vanessa Cerqueira Koppe
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. João Felipe Coimbra Leite Costa
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to David Alvarenga Drumond.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Drumond, D.A., Amarante, F.A.N., Koppe, V.C. et al. A Chart for Judging Optimal Sample Spacing for Ore Grade Estimation: Part II. Nat Resour Res 29, 551–560 (2020). https://doi.org/10.1007/s11053-019-09481-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11053-019-09481-w

Keywords

Search

Navigation