Ordinary Cokriging of Additive Log-Ratios for Estimating Grades in Iron Ore Deposits

Boezio, M.N.M.
Costa, J.F.C.L.
Koppe, J.C.
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Risk assessment and economic evaluation of mining projects are mainly affected by the determination of grades and tonnages. In the case of iron ore, multiple variables must be determined for ore characterization which estimation must satisfy the original mass balances and stoichiometry among granulometric fractions and chemical species. Models of these deposits are generally built from estimates obtained using ordinary kriging or cokriging, most time using solely the global grades and determining the ones present at different granulometric partitions by regression. Alternative approaches include determining the totality of the chemical species and distributing the closing error or leaving one variable aside and determining it by difference afterwards, adding up the error of previous determinations. Furthermore, the estimates obtained are outside the interval of the original variables or even exhibiting negative values. These inconsistencies are generally overridden by post-processing the estimates to satisfy the closed sum condition and positiveness. In this paper, cokriging of additive log-ratios (alr) is implemented to determine global grades of iron, silica, alumina, phosphorous, manganese and loss by ignition and masses of three different granulometric partitions, providing better results than the ones obtained through cokriging of the original variables, with all the estimates within the original data values interval and satisfying the considered mass balances ​
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