Block Cokriging of a whole composition
Faculty of Health, Engineering and Science
School of Engineering/Natural Resources Modelling and Simulation Research Group
An accurate prediction of benefit for some types of ore may require not just the ore grade, but a whole compositional characterization of the mining block composition: its mineral composition, including waste composition and nuisance trace elements, i.e. An example is banded iron formation, where Fe content must be complemented by estimates of chert, shale and ore proportions, or P and Mn abundances. This is often obtained with block (co)kriging. However, linear geostatistics applied to compositional data may yield spurious and inconsistent results as a consequence of the constant sum constraint. The log-ratio approach avoids spurious correlations and removes the constant sum constraint. Analogous to Gaussian anamorphosis, the approach proposes a three-step procedure: (1) data are mapped to a set of logarithms of ratios of components, e.g. the additive lognormal transformation (alr); (2) transformed scores are modelled; and (3) results are back-transformed to the original units. However, upscaling to a mass-unbiased block estimate is not straightforward, because of the nonlinearity of the log-ratio transformation. Under the assumption that the alr transformed data on a certain support come from a Gaussian random field, Monte Carlo simulation can provide an upscaling. The target block is partitioned into units of that support, and LU simulation on the discretised block is applied conditional on the available data. Simulated values are back-transformed with the inverse alr, and scores obtained are averaged to obtain a simulated block mean composition. Multiple simulations then provide the distribution of the block mean composition.