Field parametric geostatistics - An alternative to tackle gold grade estimations

Rochana Da Silva Machado,João Felipe Coimbra Leite Costa

doi:10.1590/0370-44672018720085

Rochana Da Silva Machado, João Felipe Coimbra Leite Costa

Open Access

https://doi.org/10.1590/0370-44672018720085

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Abstract

Abstract High anomalous grades are very common in gold deposits, whose presence requires careful treatment to prevent overestimation of metal content. Mineral resource analysts have worked on the estimation of several gold deposits, and none of the classical methods were able to avoid manual interventions, such as cutting high grades for local estimation or using more information beyond the data for the variogram inference. The Field Parametric Geostatistics (FPG) is presented as an alternative for the application of linear kriging methods to estimate highly skewed distributions, proposing a mathematical model which incorporates the grades and its representativeness into a new variable, reducing the influence of high grades without empirical manual interventions. In this article, the mathematical formulation of the FPG theory is presented, as well as its application in datasets with outliers and high skewed distributions: the Walker Lake dataset and the Amapari gold deposit. The results are compared to results obtained by the application of standard techniques, demonstrating that FPG is a feasible alternative to estimate local grades and local reserves for highly skewed variables.

Highlights

High anomalous grades are very common in mineral deposits of precious metals, such as gold and platinum
The grade estimation was performed by Field Parametric Geostatistics (FPG) and its results are compared to other traditional techniques: ordinary kriging of the original values (OK), ordinary kriging after capping the extreme values, and median indicator kriging with hyperbolic upper tail extrapolations (E-type 1.5 and E-type 3.0) whose results were post processed with postik from GSLIB (Deutsch and Journel, 1998)
The results show that the global average of deposit was best approximated by FPG, especially for the U variable where other applications of kriging lead to overestimation

Summary

Introduction

High anomalous grades are very common in mineral deposits of precious metals, such as gold and platinum. A low number of outliers could be responsible for a metal content overestimation; in other words, a minimum alteration in the number of high grade samples can cause a huge difference between the estimated and mined reserves. Due to their effect on resource estimation, these values should be identified and carefully treated. The technique of capping applied to outliers as an attempt to reduce their importance during grade estimation is widespread over the mining industry, based on previous experiences or statistical parameters related to the cumulative distribution function These methods are subjective and sometime not common sense. Armony (2000; 2001; 2005) developed a theory based on mathematical methods to limit the influence of outliers, which explains and justifies the practice of resource analysts of lowering high grades: the Field Parametric Geostatistics (FPG)

The theory of field parametric geostatistics

Case studies

Walker lake dataset: variables U and V

Amapari Gold Deposit

Findings

Conclusions