191
mean over all the realizations for each block (E-type). The higher the probability to be around
15% of the mean, the lower the uncertainty. The minimum probability to be around 15% of
the mean represents the worst case (highest uncertainty). For the 25 × 25 m data spacing,
the minimum probability to be around 15% of the mean is nearly one hundred (Fig. 7). The
result indicates that the difference between the true and E-type will not be higher than 15%
using the data spacing of 25 × 25 m. As the data spacing increases, the probability to be
around 15% of the mean decreases. The minimum probability around 15% of the mean for
the data spacings of 100 × 100, 200 × 200, 400 × 400, and 800 × 800 m were roughly 84, 82,
82, 80 and 80%. Moreover, the result indicates that the data spacing affects more grade uncertainty at smaller scales. Although large data spacings justify the global resources delineation,
the same may not happen for the prediction of resources in SMU scale.
5 CONCLUSIONS
The sampling density directly affects the uncertainty associated to the mineral resources calculations.
Each type of mineral deposit and commodity studied has its own intrinsic characteristics.
The uncertainty of the mineral resources helps managers make better business decisions. For
instance, if the mining company wants to avoid risks, it may prefer to invest in projects with
little uncertainty.
This paper presents a methodology to evaluate the influence of the data spacing on the
uncertainty of mineral resources. A case study with data derived from a bauxite deposit illustrates the methodology.
REFERENCES
CRIRSCO. (2013, November). crirsco.com. Retrieved from crisco.com: crisco.com/templates/international_reporting_template_november_2013.pdf.
Deutsch, C.V. (1989). DECLUS: A Fortran 77 program for determining optimum spatial declustering
weights. Computers & Geosciences 15(3), 325–332.
Deutsch, C.V. (2002). Geostatistical reservoir modeling. New York: Oxford University.
Deutsch, C.V. (2011). Guide to Best Practice in Geostatistics, Version 1.0. Edmonton, Canada: Centre
for Computational Geostatistics, University of Alberta.
Deutsch, C.V., & Journel, A.G. (1998). GSLIB. Geostatistical Software Library and User’s Guide. New
York: Oxford University Press.
Goovaerts, P. (1997). Geostatistics for Natural Resources Evaluation. New York: Oxford University Press.
Isaaks, E.H. The application of Monte Carlo methods to the analysis of spatially correlated data. USA:
Stanford University, 1990. 213p. (PhD. Thesis).
Isaaks, H.E., & Srivastava, M.R. (1990). An Introduction to Applied Geostatistics. New York: Oxford
University Press.
Journel, A.G., & Kyriakidis, P.C. (2004). Evaluation of mineral. New York, NY: Oxford University Press.
Journel, A.G., & Ying, Z. (2001). The theoretical links between Sequential Gaussian Simulation, Gaussian
Truncated Simulation and Probability Field Simulation. Mathematical Geology, Vol. 33, No. 1, 31–40.
Koppe, V.C., Rubio, R.H., & Costa, J.C. (2017). A Chart for Judging Optimal Sample Spacing for Ore
Grade Estimation. Natural Resources Research (2017) V.26, 191–199.
Manchuk, J.G., & Deutsch, C.V. (2010). Updated Ultimate SGSIM. CCG Annual Report 12, paper 401.
Olea, R.A. (1999). Geostatistics of engineers and earth scientists. Boston. Kluwer Academic Publishers.
Pilger, G.G., Costa, J.F.C.L., & Koppe, J.C. (2001). Additional samples: where they should be locat-ed.
Natural resources research, 10(3), 197–207.
Rubio, H.R., Koppe, V.C., Costa, J.C., & Cherchenevsk, P.K. (2015). How the use of stratigraphic
coordinates improves grade estimation. Fonte: Rem: Rev. Esc. Minas [online]. 2015, vol. 68,
n. 4 [cited 2019-01-07], pp. 471–477:
Sinclair, A.J., & Blackwell, G.H. (2004). Applied mineral inventory estimation. Cambridge: Cambridge
University Press.
Wild, B.J., & Deutsch, C.V. (2013). Methodology for quantifying uncertainty versus data spacing
applied to the oil sands. CIM Journal, p. 211–219.
mean over all the realizations for each block (E-type). The higher the probability to be around
15% of the mean, the lower the uncertainty. The minimum probability to be around 15% of
the mean represents the worst case (highest uncertainty). For the 25 × 25 m data spacing,
the minimum probability to be around 15% of the mean is nearly one hundred (Fig. 7). The
result indicates that the difference between the true and E-type will not be higher than 15%
using the data spacing of 25 × 25 m. As the data spacing increases, the probability to be
around 15% of the mean decreases. The minimum probability around 15% of the mean for
the data spacings of 100 × 100, 200 × 200, 400 × 400, and 800 × 800 m were roughly 84, 82,
82, 80 and 80%. Moreover, the result indicates that the data spacing affects more grade uncertainty at smaller scales. Although large data spacings justify the global resources delineation,
the same may not happen for the prediction of resources in SMU scale.
5 CONCLUSIONS
The sampling density directly affects the uncertainty associated to the mineral resources calculations.
Each type of mineral deposit and commodity studied has its own intrinsic characteristics.
The uncertainty of the mineral resources helps managers make better business decisions. For
instance, if the mining company wants to avoid risks, it may prefer to invest in projects with
little uncertainty.
This paper presents a methodology to evaluate the influence of the data spacing on the
uncertainty of mineral resources. A case study with data derived from a bauxite deposit illustrates the methodology.
REFERENCES
CRIRSCO. (2013, November). crirsco.com. Retrieved from crisco.com: crisco.com/templates/international_reporting_template_november_2013.pdf.
Deutsch, C.V. (1989). DECLUS: A Fortran 77 program for determining optimum spatial declustering
weights. Computers & Geosciences 15(3), 325–332.
Deutsch, C.V. (2002). Geostatistical reservoir modeling. New York: Oxford University.
Deutsch, C.V. (2011). Guide to Best Practice in Geostatistics, Version 1.0. Edmonton, Canada: Centre
for Computational Geostatistics, University of Alberta.
Deutsch, C.V., & Journel, A.G. (1998). GSLIB. Geostatistical Software Library and User’s Guide. New
York: Oxford University Press.
Goovaerts, P. (1997). Geostatistics for Natural Resources Evaluation. New York: Oxford University Press.
Isaaks, E.H. The application of Monte Carlo methods to the analysis of spatially correlated data. USA:
Stanford University, 1990. 213p. (PhD. Thesis).
Isaaks, H.E., & Srivastava, M.R. (1990). An Introduction to Applied Geostatistics. New York: Oxford
University Press.
Journel, A.G., & Kyriakidis, P.C. (2004). Evaluation of mineral. New York, NY: Oxford University Press.
Journel, A.G., & Ying, Z. (2001). The theoretical links between Sequential Gaussian Simulation, Gaussian
Truncated Simulation and Probability Field Simulation. Mathematical Geology, Vol. 33, No. 1, 31–40.
Koppe, V.C., Rubio, R.H., & Costa, J.C. (2017). A Chart for Judging Optimal Sample Spacing for Ore
Grade Estimation. Natural Resources Research (2017) V.26, 191–199.
Manchuk, J.G., & Deutsch, C.V. (2010). Updated Ultimate SGSIM. CCG Annual Report 12, paper 401.
Olea, R.A. (1999). Geostatistics of engineers and earth scientists. Boston. Kluwer Academic Publishers.
Pilger, G.G., Costa, J.F.C.L., & Koppe, J.C. (2001). Additional samples: where they should be locat-ed.
Natural resources research, 10(3), 197–207.
Rubio, H.R., Koppe, V.C., Costa, J.C., & Cherchenevsk, P.K. (2015). How the use of stratigraphic
coordinates improves grade estimation. Fonte: Rem: Rev. Esc. Minas [online]. 2015, vol. 68,
n. 4 [cited 2019-01-07], pp. 471–477:
Sinclair, A.J., & Blackwell, G.H. (2004). Applied mineral inventory estimation. Cambridge: Cambridge
University Press.
Wild, B.J., & Deutsch, C.V. (2013). Methodology for quantifying uncertainty versus data spacing
applied to the oil sands. CIM Journal, p. 211–219.