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 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.
Highlights
Accurate evaluation of viable mineral resources is fundamentally important in optimal sustainable development and mine planning procedures since it has an enormous impact on the value of produced metals and formation of technical plans, from extraction to closure of the mine [1,2,3]
The objectives of this paper are fourfold: (1) to briefly present the concept of-simulation and projection pursuit multivariate transform (PPMT) and the proposed algorithm; (2) to apply the proposed algorithm in a real case study of a limestone deposit in Kazakhstan; (3) to classify resources based on Joint Ore Reserves Committee (JORC) code over the results obtained for objective 2; and (4) to provide a discussion and conclusion
A way around this impediment is to co-simulate the PPMT factors even with small correlation that are left after forward transformation of the original variables to factors by inference of cross-dependency functions using the linear model of co-regionalization [25]
Summary
Accurate evaluation of viable mineral resources is fundamentally important in optimal sustainable development and mine planning procedures since it has an enormous impact on the value of produced metals and formation of technical plans, from extraction to closure of the mine [1,2,3]. The main problems in conventional methods affect the poor reproduction of original variability of grade (e.g., smoothing effect), and lead to other issues such as the inability to quantify the uncertainty within each block Ignoring this type of valuable information, such as risk and uncertainty, in mineral resource evaluation may result in unrealistic outcomes of planned production and cash flow of mine projects [10,12]. The application of stochastic models to the estimation of resources based on international standards is important in terms of both reproducing original variability of grade and quantifying uncertainty [14] In this regard, there are two commonly used simulation methods, turning bands (co)-simulation [15] and sequential Gaussian (co)-simulation [16,17]. The objectives of this paper are fourfold: (1) to briefly present the concept of (co)-simulation and PPMT and the proposed algorithm; (2) to apply the proposed algorithm in a real case study of a limestone deposit in Kazakhstan; (3) to classify resources based on Joint Ore Reserves Committee (JORC) code over the results obtained for objective 2; and (4) to provide a discussion and conclusion
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