Geostatistical simulation methods are important in mineral resources estimation. However, applying such methods to simulate the grades of metals that are strongly correlated within a deposit remains challenging because it requires preserving the statistical properties and inter-variable dependencies. For this challenge, multivariate data transformations, such as minimum/maximum autocorrelation factors (MAF) and projection pursuit multivariate transform (PPMT), are widely applied in the field of geosciences to handle the global inter-variable correlations before independent simulation. Therefore, it is important to evaluate existing multivariate transformation methods in independent simulation framework to determine how these transformations behave statistically when used within independent simulation framework. This study evaluated the performance of PPMT and MAF within the turning bands simulation method (TBSIM) using Fe and Al 2 O 3 data from the Carajás deposits in Brazil, where these variables exhibit strong negative Pearson correlation. The assessments focused on the ability of each transformation to reproduce the univariate statistical characteristics and evaluate inter-variable dependency after back-transformation. Performance was evaluated using summary statistics, histogram reproduction, global inter-variable correlation, direct variogram, spatial cross-correlation, and computational efficiency between Fe and Al 2 O 3 . However, due to the use of TBSIM, global inter-variable correlations and spatial cross-correlation were not preserved after simulation and back-transformation. MAF reproduced the statistical characteristics of Fe more consistently, particularly its mean, whereas PPMT showed better reproduction of Al 2 O 3 but less reliable performance for Fe. Overall, the findings indicate that although both MAF and PPMT transformations can reproduce certain univariate properties, preserving multivariate dependency remains challenging within the TBSIM framework.
NDOU et al. (2026) studied this question.