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Optimally locating additional drill holes in three dimensions using grade and simulated annealing

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Journal of the Geological Society of India

Abstract

Average kriging variance is a standard tool used in optimization of the location of additional drill holes. However, this tool cannot distinguish between areas with different priorities. This limitation could be eliminated by using weighted average kriging variance. This paper extends the problem of optimal location to three dimensional cases, use grade as a weight and search optimum locations by simulated annealing. Weighted average kriging variance is used as objective function. The method is applied to a copper deposit. Results have shown that weighting of the estimation variance with “grade” is effective only when the difference among the grades estimated for different blocks is considerable.

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References

  • Aarts, E. and Korst, J. (1989) Simulated Annealing and Boltzmann Machines. Wiley, New York, NY.

    Google Scholar 

  • Bogaert, P. and Russo, D. (1999) Optimal sampling design for the estimation of the variogram based on a least squares approach. Water Resour. Res., v.35(4), pp.1275–1289.

    Article  Google Scholar 

  • Burger, H. and Birkenhake, F. (1994) Geostatistics and the polygonal method: a re-examination. In: International Association for Mathematical Geology (IAMG 95) Annual Conference, pp.50–55.

  • Chou, D. and Schenk, D.E. (1983) Optimum Locations for Exploratory Drill Holes. Int. Jour. Min. Engg., v.1, pp.343–355.

    Article  Google Scholar 

  • Cressie, N. (1991) Statistics for Spatial Data. Wiley, New York, USA.

    Google Scholar 

  • Deutsch, C.V. (1993) Kriging in a finite domain. Math. Geol., v.25, pp.41–52.

    Article  Google Scholar 

  • Gershon, M., Allen, L.E. and Manley, F. (1998) Application of a new approach for drillholes location optimization. Int. Jour. Min. Reclamat. Environ., v.2, pp.27–31.

    Article  Google Scholar 

  • Ghaderi, M., Hezarkhani, A. and Talebi, M. (2007) The use of litho-geochemical data and fluid inclusions in the study of Iju porphyry copper deposit, Northwest of Shahr-e-Babak. AmirKabir Jour., v.67, pp.135–150.

    Google Scholar 

  • Hassanipak, A.A. and Sharafodin, M. (2003) GET: a function for preferential site selection of additional borehole drilling. Explor. Min. Geol., v.13, pp.1–8.

    Google Scholar 

  • Journel, A.G. and Huijbregts, C.H. (1978) Mining Geostatistics, Academic Press London.

  • Kalai, A.T. and Vempala, S. (2006) Simulated annealing for convex optimization. Math. Oper. Res., v.31, pp.253–266.

    Article  Google Scholar 

  • Lark, R.M. (2002) Optimized spatial sampling of soil for estimation of the variogram by maximum likelihood. Geoderma, v.105, pp.49–80.

    Article  Google Scholar 

  • Muller, W.G. and Zimmerman, D.L. (1999) Optimal designs for variogram estimation. Environmetrics, v.10(1), pp.23–37.

    Article  Google Scholar 

  • Rogerson, P.A., Delmelle, E.M., Batta, R., Akella, M.R., Blatt, A. and Wilson, G. (2004) Optimal sampling design for variables with varying spatial importance. Geogr. Anal., v.36, pp.177–194.

    Google Scholar 

  • Soltani, S. and Hezarkhani, A. (___) Determination of realistic and statistical value of the information gathered from exploratory drilling, Natural Resource Research, v.4, no.4, pp.207–211

  • Szidarovszky, F. (1983)Multiobjective observation network design for regionalized variables. Int. Jour. Min. Engg., v.1, pp.331–342.

    Article  Google Scholar 

  • van Groenigen, J.W., Pieters, G. and Stein, A. (2000) Optimizing spatial sampling for multivariate contamination in urban areas. Environmetrics, v.11, pp.227–244.

    Article  Google Scholar 

  • van Groenigen J.W., Siderius W. and Stein, A. (1999) Constrained optimisation of soil sampling for minimisation of the kriging variance. Geoderma, v.87, pp.239–259.

    Article  Google Scholar 

  • Walton, D.R. and Kauffman, P.W. (1982) Some practical considerations in applying geostatistics to coal reserve estimation. In: SME-AIME, Dallas.

    Google Scholar 

  • Zhao, T., Debba, P. and Stein, A. (2008) Geochemical sampling scheme optimization on mine wastes based on hyperspectral data. In: The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, XXXVII, pp.1529–1532.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mining Engineering, University of Kashan, Kashan, I. R. Iran

    Saeed Soltani Mohammadi

  2. Department of Mining and Metallurgy Engineering, Amirkabir University of Technology, Tehran, Iran

    Ardeshir Hezarkhani

  3. Department of Mining Engineering, Hacettepe University, Ankara, Turkey

    A. Erhan Tercan

Authors
  1. Saeed Soltani Mohammadi
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  2. Ardeshir Hezarkhani
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  3. A. Erhan Tercan
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Correspondence to Saeed Soltani Mohammadi.

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Mohammadi, S.S., Hezarkhani, A. & Erhan Tercan, A. Optimally locating additional drill holes in three dimensions using grade and simulated annealing. J Geol Soc India 80, 700–706 (2012). https://doi.org/10.1007/s12594-012-0195-8

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  • DOI: https://doi.org/10.1007/s12594-012-0195-8

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