Geostatistical modelling of grades in mineral deposits often requires the simulation of multiple related variables that have sum and fraction constraints. Sum constraints occur when the sum of some variables may not exceed or must equal a given constant. Fraction constraints occur when a variable may not exceed another variable. In this case, the geostatistical simulations should reproduce the histograms, variograms, multivariate relationships and honour the constraints. We present a methodology for the geostatistical simulation of multiple related variables that considers sum and fraction constraints. The methodology is illustrated in a case study. The data were obtained from a bauxite deposit. First, the original variables were re-expressed as ratios. Second, the variables were transformed using the Projection Pursuit Multivariate Transform (PPMT). Then the PPMT transformed variables were simulated independently using sequential Gaussian simulation and back-transformed. The simulations reproduced the histograms, variograms and bivariate relationships and honoured the sum and fraction constraints.

The classification of mineral resources is crucial for public disclosure and is used to evaluate the risk associated with the mineral deposit, enabling informed decisions. To address this need, this study proposes the use of a multi-layer scorecard workflow (MLSW) for mineral resource classification that considers multiple factors from different disciplines. This approach is highly flexible as the competent user may adapt the scorecard workflow to the particularities of each deposit. In this paper, we considered classical metrics for resource classification, such as the number of samples, the slope of regression, kriging efficiency, and kriging variance, combinedwith more modern ones (Risk Index), which contemplates the combination of the estimation error, and geological continuity by a probabilistic approach. The methodology can also incorporate qualitative information such as the geological complexity. The proposed workflow has been applied in two different databases, demonstrating its transparency, auditability, and applicability.

The definition of the search neighbourhood in kriging can have a significant impact on the resulting estimates. Stationary domains are usually estimated using a unique search strategy for the entire domain. However, the use of a global search neighbourhood ignores the local variations within each domain, i.e. all blocks are interpolated using a unique search strategy. In this paper, localised kriging parameter optimisation (LKPO) is proposed as an alternative methodology that considers the best ‘local estimation parameter settings’ block by block. The optimisation process is based on absolute error minimisation obtained in cross-validation. Two datasets are presented, the first is a synthetic mineral deposit (2D) and the second is a gold deposit (3D). A wide variety of validation checks show that the use of local kriging parameters significantly improves the grade estimation, obtaining more precise and accurate results than the methodologies currently available in the geostatistical literature.