Abstract

Understanding the spatial distribution of elements in mine tailing deposits is fundamental for resource reprocessing, economic feasibility studies, and environmental sustainability. Multivariate geostatistical simulation, commonly known as cosimulation or joint simulation, is a powerful method for capturing spatial variability and cross-correlation in these deposits. The accuracy of the modeling is strongly influenced by the inferred spatial cross-correlation structure, which reflects the complexity of tailings formed through variations in deposition processes, particle settling, and postdepositional modifications. Properly accounting for these nested structures ensures a more accurate representation of spatial dependence and multivariate relationships. Among the available techniques, sequential Gaussian cosimulation (SGCS) remains widely used, largely because of its integration into commercial software packages. However, its computational performance becomes a limitation when it is applied to large datasets involving multiple variables, as a full cokriging system must be solved for each variable at every simulation location. To address these challenges, decorrelation techniques have been introduced to streamline cosimulation workflows. Principal component analysis (PCA) and minimum/maximum autocorrelation factors (MAF) are commonly applied, but their effectiveness is constrained by structural limitations in the linear model of coregionalization (LMC). PCA guarantees decorrelation only for single-structure LMCs, whereas MAF is limited to at most two structures. Thus, both methods are inadequate for datasets with the nested spatial continuity characteristic of mine tailing deposits. The projection pursuit multivariate transform (PPMT) provides a more flexible alternative, effectively removing cross-correlations at a lag distance of zero. However, residual correlations may persist at larger lag distances, requiring additional transformations such as MAF, which remains limited by the number of structures in the LMC. This study develops a joint simulation algorithm that integrates the PPMT with cosimulation via coregionalization analysis to develop a factorization-based decorrelation technique across all nested LMC structures. Unlike traditional PCA, MAF, and PPMT-MAF, this approach is not restricted by the number of nested structures, making it a more adaptable solution for complex multivariate datasets. The proposed approach is tested on the Haveri mine tailing deposit, where Cu, Au, Fe, and S are jointly simulated to evaluate its effectiveness in handling decorrelation challenges in multivariate geostatistical simulations. The results confirm that this method provides a computationally efficient and flexible alternative to traditional cosimulation techniques, ensuring better preservation of global statistics and spatial continuity while maintaining the multivariate relationships essential for resource assessment.