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ArticleName Application of nonlinear methods in evaluation of mineral grades
DOI 10.17580/gzh.2021.09.08
ArticleAuthor Vyaltsev A. S.

Polymetal, Saint-Petersburg, Russia:

A. S. Vyaltsev, Head of the Analysis and Methodological Support Monitoring and Modeling Department,


The requirements for the reliable and accurate definition of mineral reserves escalate from year to year. Earlier it was sufficient to have a model with estimated contents of useful components and their bulk weight, while today the correct mine planning model is to contain supposed mining systems and predicted mining selectivity. It is possible to use the nonlinear methods to assess mineral grades based on nonlinear transformations of sampling data. The author gives general information about nonlinear estimation methods and describes the implemented research flowchart of quality assessment of interpolation procedures for mineral grades. The main part of the article describes the following modeling methods: ordinary kriging, implicit modeling, local uniform conditioning and conditional stochastic modeling. The results of the grade estimation using these techniques are comprehensively compared. The author concludes that in mineral grade control during production, with regular dense sampling grids and with the data spacing less than the range of the variograms, the results of the estimates are almost equal to each other. Therefore, it is no need to use more complex estimation methods which require more computing power and advanced professional skills gained in resource appraisal. Using ordinary kriging on the sparse grid of drillhole data leads to distortion of the grade–tonnage curve. When the distance between drillholes is substantially greater than the size of the minimum extraction unit, a highly smoothed estimate is obtained, clustered around the local mean grade. The alternative approaches which can provide a reliable estimate of recoverable tonnage and grade based on the sparse grid drillholes data are the local uniform conditioning and implicit modeling.

keywords Ordinary kriging, local unified conditioning, conditional stochastic modeling, implicit modeling, multiple indicator kriging, quality kriging analysis of neighbor points

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