Resource Model Updating For Compositional Geometallurgical Variables

Abstract

In the field of mineral resources extraction, one main challenge is to meet production targets in terms of geometallurgical properties. These properties influence the processing of the ore and are often represented in resource modeling by coregionalized variables with a complex relationship between them. Valuable data are available about geometalurgical properties and their interaction with the beneficiation process given sensor technologies during production monitoring. The aim of this research is to update resource models as new observations become available. A popular method for updating is the ensemble Kalman filter. This method relies on Gaussian assumptions and uses a set of realizations of the simulated models to derive sample covariances that can propagate the uncertainty between real observations and simulated ones. Hence, the relationship among variables has a compositional nature, such that updating these models while keeping the compositional constraints is a practical requirement in order to improve the accuracy of the updated models. This paper presents an updating framework for compositional data based on ensemble Kalman filter which allows us to work with compositions that are transformed into a multivariate Gaussian space by log-ratio transformation and flow anamorphosis. This flow anamorphosis, transforms the distribution of the variables to joint normality while reasonably keeping the dependencies between components. Furthermore, the positiveness of those variables, after updating the simulated models, is satisfied. The method is implemented in a bauxite deposit, demonstrating the performance of the proposed approach.

Evaluation of multivariate Gaussian transforms for geostatistical applications

“…Further work is underway to test the methods on different datasets with different complex relationships and to define an open format for the implementation so that an open-source code can be published for the research community. It will also be interesting to explore the application of the proposed techniques within other contexts, such as rapid resource model updating (Li et al, 2021;Prior et al, 2021).…”

“…Unlike PPMT and RBIG, FA is affine equivariant, which many authors consider desirable for conditional simulations and quantile-matching-based transforms. FA is thus a popular method for modelling compositional data (Tolosana-Delgado et al, 2019;Prior et al, 2021), where it is usually paired with log-ratio transformation methods (Pawlowsky-Glahn and Olea, 2004).…”