Rocks and Ores comprising of multicomponent of minerals (Group I) contain chemical molecules (Group II) which further contain (Group III). Man has exploited these valuable constituents for industrial, economic, and social growth causing serious depletion of high-grade ores at surface and shallow depths. Sustainable growth now requires exploitation of low-grade ores and those occurring at depth which imply optimal and most efficient mining efforts based on spatial, temporal, and spatiotemporal distribution of these constituents. The optimal decisions resulting in profit maximization is possible by obtaining precise and accurate parameters of these distributions. Sample size required for such estimations must be at least representative elementary volume (REV) of the rocks/ores, but the data matrix is not full-rank for statistical analyses and sample mean (x; 0 < x < 1) must be transformed to Gaussian to apply standard univariate (UND)/multivariate (MND) statistical techniques. A log(x/(1−x)) or ln(x/(1−x)) transform is shown to be an appropriate pre-transformation that eliminates the twin problems of full-rank, and spurious negative correlations as well as makes the distribution Gaussian for major, minor, and trace components. Mining applications using the univariate and/or Multivariate Normal Theory of pre-transformed sample mean (x) in rocks/ores is optimal for anomaly detection, drilling site selection, global reserve and grade estimations, mine planning, ore mineral liberation, blending, sustainable mine developments and maximization of profits computed on net profit value (NPV) basis to present time.
Part of the book: Minerals