Search Results (3)

The efficiency of sampling is a critical concern in Monte Carlo analysis, which is frequently used to assess the effect of the uncertainty of the input variables on the uncertainty of the model outputs. The projection pursuit multivariate transform is proposed as an easily applicable tool for improving the efficiency and quality of a sampling design in Monte Carlo analysis. The superiority of the projection pursuit multivariate transform, as a sampling technique, is demonstrated in two synthetic case studies, where the random variables are considered to be uncorrelated and correlated in low (bivariate) and high (five-variate) dimensional sampling spaces. Five sampling techniques including Monte Carlo simulation, classic Latin hypercube sampling, maximin Latin hypercube sampling, Latin hypercube sampling with multidimensional uniformity, and projection pursuit multivariate transform are employed in the simulation studies, considering cases where the sample sizes $\left(n\right)$ are small (i.e., $10\le n\le 100$), medium (i.e., $100<n\le 1000$), and large (i.e., 1000 < n≤ 10,000). The results of the case studies show that the projection pursuit multivariate transform appears to yield the fewest sampling errors and the best sampling space coverage (or multidimensional uniformity), and that a significant amount of computer effort could be saved by using this technique. Full article

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 paper proposes a geostatistical approach for geological modelling and for validating an interpreted geological model, by identifying the areas of an ore deposit with a high probability of being misinterpreted, based on quantitative coregionalised covariates correlated with the geological categories. This proposal is presented through a case study of an iron ore deposit at a stage where the only available data are from exploration drill holes. This study consists of jointly simulating the quantitative covariates with no previous geological domaining. A change of variables is used to account for stoichiometric closure, followed by projection pursuit multivariate transformation, multivariate Gaussian simulation, and conditioning to the drill hole data. Subsequently, a decision tree classification algorithm is used to convert the simulated values into a geological category for each target block and realisation. The determination of the prior (ignoring drill hole data) and posterior (conditioned to drill hole data) probabilities of categories provides a means of identifying the blocks for which the interpreted category disagrees with the simulated quantitative covariates. Full article