Abstract: |
Evaluation of process performance within mining operations requires geostatistical modeling of many related variables. These variables are a combination of grades and other rock properties, which together provide a characterization of the deposit that is necessary for optimizing plant design, blending and stockpile planning. Complex multivariate relationships such as stoichiometric constraints, non-linearity and heteroscedasticity are present when considering the variables that characterize a mineral deposit. Conventional covariance-based techniques do not capture these multivariate features; nevertheless, these complexities influence decision making and should be reproduced in geostatistical models. There are non-linear transforms that help bridge the gap between complex geologic relationships and practical geostatistical modeling tools. Logratios, principal component analysis, normal score, and stepwise conditional transformation are a few of the available transforms. In many circumstances these transforms are used in sequence to model the variables for a given deposit. As each technique possesses its own intrinsic limitations, challenges may arise in choosing the appropriate transforms, the order in which they are applied, and subjective decisions which must be made in their implementation. These practical challenges will be examined in detail, along with a discussion of potential solutions and considerations. Included in these solutions is a new technique named conditional standardization, which is introduced for the improved performance of transforms that would not otherwise capture non-linear and heteroscedastic multivariate features. A number of example applications show how these techniques are used in practice. Common problems such as bias and lack of histogram reproduction are illustrated in case studies, followed by a demonstration of corrective measures. |
