Joint simulation of cross-correlated ore grades and geological domains: an application to mineral resource modeling

Abstract

Spatial modeling of ore grades is frequently impacted by the local variation in geological domains such as lithological characteristics, rock types, and geological formations. Disregarding this information may lead to biased results in the final ore grade block model, subsequently impacting the downstream processes in a mining chain project. In the current practice of ore body evaluation, which is known as stochastic cascade/hierarchical geostatistical modeling, the geological domain is first characterized, and then, within the geological model, the ore grades of interest are evaluated. This practice may be unrealistic in the case when the variability in ore grade across the boundary is gradual, following a smooth transition. To reproduce such characteristics, the cross dependence that exists between the ore grade and geological formations is considered in the conventional joint simulation between continuous and categorical variables. However, when using this approach, only one ore variable is considered, and its relationship with other ore grades that may be available at the sample location is ignored. In this study, an alternative approach to jointly model two cross-correlated ore grades and one categorical variable (i.e., geological domains) with soft contact relationships that exist among the geological domains is proposed. The statistical and geostatistical tools are provided for variogram inference, Gibbs sampling, and conditional cosimulation. The algorithm is also tested by applying it to a Cu deposit, where the geological formations are managed by the local and spatial distribution of two cross-correlated ore grades, Cu and Au, throughout the deposit. The results show that the proposed algorithm outperforms other geostatistical techniques in terms of global and local reproduction of statistical parameters.

Graphical abstract

Keywords

geostatistical simulation / categorical variable / continuous variable / geological domain / variogram inference

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Acknowledgment

The first author is thankful to Nazarbayev University for funding this work via “Faculty Development Competitive Research Grants for 2018–2020 under Contract No. 090118FD5336 and 2021–2023 under Contract No. 021220FD4951”. This work is supported by Faculty Development Competitive Research Grants for 2018–2020 under Contract No. 090118FD5336 and 2021–2023 under Contract No. 021220FD4951.

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