Multivariate Imputation of Unequally Sampled Geological Variables

Unequally sampled data pose a practical and significant problem for geostatistical modeling. Multivariate transformations are frequently applied in modeling workflows to reproduce the multivariate relationships of geological data. Unfortunately, these transformations may only be applied to data observations that sample all of the variables. In the case of unequal sampling, practitioners must decide between excluding incomplete observations and imputing (inferring) the missing values. While imputation is recommended by missing data theorists, the use of deterministic methods such as regression is generally discouraged. Instead, techniques such as multiple imputation (MI) are advocated to increase the accuracy, decrease the bias, and capture the uncertainty of imputed values. As missing data theory has received little attention within geostatistical literature and practice, MI has not been adapted from its conventional form to be suitable for geological data. To address this, geostatistical algorithms are integrated within an MI framework to produce parametric and non-parametric methods. Synthetic and geometallurgical case studies are used to demonstrate the feasibility of each method, where techniques that use both spatial and colocated information are shown to outperform the alternatives.