A HIERARCHICAL SEQUENTIAL GAUSSIAN CO-SIMULATION ALGORITHM WITH ACCEPTANCE-REJECTION SAMPLING TECHNIQUE FOR MINE TAILINGS EVALUATION

Abstract

Despite the environmental impacts, it can be acknowledged that mine tailings may contain large amount of valuable and critical minerals for re-valorization or re-processing. However, evaluation of the same tailings poses a major challenge while dealing with multiple elements in the composition. Conventional methods may not appropriately capture the essence of the bivariate relationship between components of interest. To address this challenge, our research investigates the hierarchical sequential Gaussian co-simulation approach with acceptance-rejection sampling methods. This algorithm is designed towards the fulfillment of the linearity constraints dealing with two major elements among which are copper and gold. Both hierarchical and conventional co-simulation approaches were employed in the study, highlighting differences in data reproduction based on the obtained results. Notably, our findings showed that the effectiveness of the proposed algorithm is superior to those of conventional methods due to the more accurate reproduction of the linearity constraints. By using an acceptance-rejection sampling technique, the proposed technique guarantees the replication of values based on the identified linearity requirements. To apply this algorithm initially, regression analysis was performed to check the validity of linearity between copper and gold in the dataset and to obtain the coefficients of a formula which represents the required linearity constraint. Thereafter, the obtained formula with the linearity constraint was used to co-simulate the values of the copper and gold conditions to their bivariate linearity relations by either accepting or rejecting the simulated values based on whether they meet the predefined constraint. Thus, the proposed algorithm provides more accurate and reliable results in the bivariate relationships of copper and gold than the conventional co-simulation approach that does not take into account the linearity constraint. Nonetheless, the use of hierarchical Gaussian co-simulation is restricted to the chemical elements, which show a poor correlation between them.