Non-Monotonic Transformation for Gaussianization of Regionalized Variables: Modeling Aspects

This paper proposes an extension of the traditional multigaussian model, where a regionalized variable measured on a continuous quantitative scale is represented as a transform of a stationary Gaussian random field. Such a model is popular in the earth and environmental sciences to address both spatial prediction and uncertainty assessment problems. The novelty of our proposal is that the transformation between the original variable and the associated Gaussian random field is not assumed to be monotonic, which offers greater versatility to the model. A step-by-step procedure is presented to infer the model parameters, based on the fitting of the marginal distribution and the indicator direct and cross-covariances of the original variable. The applicability of this procedure is illustrated with a case study related to grade control in a porphyry copper-gold deposit, where the fit of the gold grade distribution is shown to outperform the one obtained with the traditional multigaussian model based on a monotonic transformation. This translates into a better assessment of the uncertainty at unobserved locations, as proved by a split-sample validation.