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Keywords = Projection Pursuit Multivariate Transform (PPMT)

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25 pages, 21082 KB  
Article
Probabilistic Modeling of Lateritic Nickel Mineral Resources
by Roberto Rolo, Jafar Arief and Selvi Yuminti
Minerals 2026, 16(5), 551; https://doi.org/10.3390/min16050551 - 20 May 2026
Viewed by 1061
Abstract
Lateritic nickel deposits exhibit complex weathering-driven geometries, strong vertical variability, and complex multivariate geochemical relationships. These characteristics challenge conventional deterministic resource modeling. This paper presents a unified probabilistic workflow for lateritic nickel mineral resource modeling that integrates lithology and grade simulation within a [...] Read more.
Lateritic nickel deposits exhibit complex weathering-driven geometries, strong vertical variability, and complex multivariate geochemical relationships. These characteristics challenge conventional deterministic resource modeling. This paper presents a unified probabilistic workflow for lateritic nickel mineral resource modeling that integrates lithology and grade simulation within a consistent geostatistical framework. The methodology combines unfolding, plurigaussian simulation, multivariate imputation of incomplete datasets, projection pursuit multivariate transformation (PPMT) for decorrelation, and conditional simulation using the Turning Bands algorithm. Application to an Indonesian lateritic nickel deposit demonstrates reproduction of lithological proportions, spatial continuity, marginal distributions, and complex multivariate relationships. The proposed workflow enables explicit quantification of geological and grade uncertainty, providing a basis for uncertainty assessment in recoverable resource estimation and supporting downstream applications such as resource classification and drillhole spacing analysis. Full article
(This article belongs to the Special Issue Geostatistical Methods and Practices for Specific Ore Deposits)
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22 pages, 13954 KB  
Article
Multivariate Simulation in Non-Stationary Domains: A Framework for Accurate Data Reproduction
by Rita M Teal, João Felipe Costa and Navid Mojtabai
Minerals 2025, 15(11), 1145; https://doi.org/10.3390/min15111145 - 31 Oct 2025
Cited by 1 | Viewed by 839
Abstract
Accurate multivariate Gaussian simulation is critical for resource assessment and mine planning, especially in polymetallic deposits where strong trends, data bias, and multivariate outliers introduce complexity. In this scenario, standard workflows applied to non-stationary domains may result in undesirable data statistics reproduction, especially [...] Read more.
Accurate multivariate Gaussian simulation is critical for resource assessment and mine planning, especially in polymetallic deposits where strong trends, data bias, and multivariate outliers introduce complexity. In this scenario, standard workflows applied to non-stationary domains may result in undesirable data statistics reproduction, especially the multivariate relationships between variables. This study proposes an enhanced simulation framework that integrates data standardization, multivariate outlier detection, trend modeling and removal, and a dual application of the Projection Pursuit Multivariate Transform (PPMT). The approach is demonstrated within a high-grade mineralized breccia domain of the Peñasquito deposit, utilizing data from diamond core and reverse circulation (RC) drill holes, including Au, Ag, Pb, and Zn. Bias in RC data was corrected using data standardization, and multivariate outliers were identified through the application of a robust Mahalanobis distance. Trend modeling was performed using a moving window average and was removed using the Gaussian Mixture Model and Stepwise Conditional Transform. PPMT was applied both before and after trend modeling in order to improve decorrelation and simulation performance. Results show improved data reproduction through histograms, variograms, and complex relationships, as well as correlation coefficients. Cross-validation confirms reduced bias and improved accuracy. This research highlights the importance of treating multivariate outliers and applying PPMT both before and after trend modeling. The study demonstrates that applying PPMT twice is more effective for managing persistent non-stationary features, especially in high-grade domains. Full article
(This article belongs to the Special Issue Geostatistical Methods and Practices for Specific Ore Deposits)
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27 pages, 14975 KB  
Article
Stochastic Modeling of Chemical Compounds in a Limestone Deposit by Unlocking the Complexity in Bivariate Relationships
by Nurassyl Battalgazy and Nasser Madani
Minerals 2019, 9(11), 683; https://doi.org/10.3390/min9110683 - 4 Nov 2019
Cited by 9 | Viewed by 4240
Abstract
Modeling multivariate variables with complexity in a cross-correlation structure is always applicable to mineral resource evaluation and exploration in multi-element deposits. However, the geostatistical algorithm for such modeling is usually challenging. In this respect, projection pursuit multivariate transform (PPMT), which can successfully handle [...] Read more.
Modeling multivariate variables with complexity in a cross-correlation structure is always applicable to mineral resource evaluation and exploration in multi-element deposits. However, the geostatistical algorithm for such modeling is usually challenging. In this respect, projection pursuit multivariate transform (PPMT), which can successfully handle the complexity of interest in bivariate relationships, may be particularly useful. This work presents an algorithm for combining projection pursuit multivariate transform (PPMT) with a conventional (co)-simulation technique where spatial dependency among variables can be defined by a linear model of co-regionalization (LMC). This algorithm is examined by one real case study in a limestone deposit in the south of Kazakhstan, in which four chemical compounds (CaO, Al2O3, Fe2O3, and SiO2) with complexity in bivariate relationships are analyzed and 100 realizations are produced for each variable. To show the effectiveness of the proposed algorithm, the outputs (realizations) are statistically examined and the results show that this methodology is legitimate for reproduction of original mean, variance, and complex cross-correlation among the variables and can be employed for further processes. Then, the applicability of the concept is demonstrated on a workflow to classify this limestone deposit as measured, indicated, or inferred based on Joint Ore Reserves Committee (JORC) code. The categorization is carried out based on two zone definitions, geological, and mining units. Full article
(This article belongs to the Special Issue Novel Methods and Applications for Mineral Exploration)
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