Managing Complex Multivariate Relations in the Presence of Incomplete Spatial Data

Abstract

Evaluating the process performance of mining and petroleum operations requires numerical geological models of many related rock properties or variables. Taken together, they provide a characterization of the geologic deposit that forms the basis for engineering design and decision making. Complex multivariate features such as compositional constraints and non-linearity often exist between geological variables and may have a large impact on process performance. This poses a problem for geostatistical modeling, where popular techniques do not capture complex relations. The data could be transformed to be suitable for modeling before using back-transformations to reintroduce the original complexity. Unfortunately, no sequence of available transforms will consistently remove all complex features from a large number of variables. The first contribution of this thesis is a transformation for removing complexity and correlation from data of practical size and dimension. This facilitates independent geostatistical modeling, before the back-transform restores the original relations. Multivariate transformations may only be applied to data observations that sample all of the variables under consideration. This creates another significant challenge, as it is common for geological data to sample subsets of the variables. Practical solutions will exclude the incomplete observations from transformations, or use basic regression to infer (impute) the missing variables. These approaches usually have consequences, however, in terms of global bias, local accuracy and the reproduction of key properties. The second contribution of this thesis is methodology for the effective imputation and geostatistical modeling of incomplete data. Missing data theory is integrated with geostatistical algorithms to develop imputation methods that are suitable for geological data. Uncertainty of the imputed values is transferred through a modified geostatistical workflow. These two contributions cumulatively simplify and improve the modeling of potentially complex and unequally sampled geological variables. Their value is demonstrated using real geometallurgical data and associated mine project decision making.