Mining Goes Digital – Mueller et al. (Eds)
© 2019 Taylor & Francis Group, London, ISBN 978-0-367-33604-2
134
Application of localized multivariate uniform conditioning and
conditional simulation for a stockwork niobium deposit
L. Bertossi
CMOC US, Phoenix, USA
Sr. Geologist Modeler, MAusIMM, Brazil
D. Raposo, J. Watanabe & S. Silva
CMOC Brasil, Ouvidor, Brazil
G. Usero
Regional Director, Geovariances, Belo Horizonte, Brazil
ABSTRACT: Linear estimation approaches as Ordinary Kriging and Simple Kriging are
widely used and successfully applied to estimate mineral resources in the mining industry,
although it may generate a biased estimate of metal tonnage and ore recovery after a cutoff
application. The bias is more evident in narrow veins or deposits with tight mineralization
that are modeled with small blocks when the data spacing is much larger than the SMU
size.
Uniform Conditioning (UC) can be used as an alternative to generate unbiased estimates
for the evaluation of the potential of selective mining. The Localized Uniform Conditioning
(LUC) technique has been applied to enrich the UC distribution by localizing the results at
the SMUs scale. A complementary workflow using Conditional Simulations is also applied
in this study to access the grade fluctuations at the SMU scale.
1 INTRODUCTION
In some kinds of deposits well covered by sample with normal distribution grades, all linear
estimation, including ordinary kriging, can correctly predict the grade and the tonnage, with
a low conditioning bias. However, in deposits poorly sampled with a lognormal underlying grade distribution, liner estimation will provide a biased estimate of metal tonnage and
it can produce smoothed assessment of the recoverable resources when applied to a small
block model which is not supported by dense data spacing (Armstrong and Champigny,
1989; Ravenscroft and Armstrong, 1990; Pan, 1998).
Uniform conditioning (Rivoirard, 1994) is one of the methodologies widely used in the
mining industry for modelling the recoverable resources above cut-off grades, the advantage
of UC is that it can be used in a widely spaced data, across domains that are not strictly
stationary, provided that there is a sufficient data for conditionally unbiased estimate of the
panel mean grade (Rivoirard, 1994; Hansmann, 2016).
The drawback of the conventional Uniform Conditioning (UC) method is its inability to
predict a spatial location of the economically extractable mineralization (Abazlov, 2014), in
other words, UC does not estimate grades directly, it calculates the tonnage and the mean
of recoverable resources distributed in a large panel. Abzalov (2006), proposed a method for
modelling grades of selective mineable units (SMU) called Localized Uniform Conditioning
(LUC), it enhances the UC approach by localizing the model panel results, representing a
partitioning of this panel.
According to Hansmann 2016, UC and the add-on LUC has been successfully applied
in several different types of deposits, indicating that the method is applicable on a normal
© 2019 Taylor & Francis Group, London, ISBN 978-0-367-33604-2
134
Application of localized multivariate uniform conditioning and
conditional simulation for a stockwork niobium deposit
L. Bertossi
CMOC US, Phoenix, USA
Sr. Geologist Modeler, MAusIMM, Brazil
D. Raposo, J. Watanabe & S. Silva
CMOC Brasil, Ouvidor, Brazil
G. Usero
Regional Director, Geovariances, Belo Horizonte, Brazil
ABSTRACT: Linear estimation approaches as Ordinary Kriging and Simple Kriging are
widely used and successfully applied to estimate mineral resources in the mining industry,
although it may generate a biased estimate of metal tonnage and ore recovery after a cutoff
application. The bias is more evident in narrow veins or deposits with tight mineralization
that are modeled with small blocks when the data spacing is much larger than the SMU
size.
Uniform Conditioning (UC) can be used as an alternative to generate unbiased estimates
for the evaluation of the potential of selective mining. The Localized Uniform Conditioning
(LUC) technique has been applied to enrich the UC distribution by localizing the results at
the SMUs scale. A complementary workflow using Conditional Simulations is also applied
in this study to access the grade fluctuations at the SMU scale.
1 INTRODUCTION
In some kinds of deposits well covered by sample with normal distribution grades, all linear
estimation, including ordinary kriging, can correctly predict the grade and the tonnage, with
a low conditioning bias. However, in deposits poorly sampled with a lognormal underlying grade distribution, liner estimation will provide a biased estimate of metal tonnage and
it can produce smoothed assessment of the recoverable resources when applied to a small
block model which is not supported by dense data spacing (Armstrong and Champigny,
1989; Ravenscroft and Armstrong, 1990; Pan, 1998).
Uniform conditioning (Rivoirard, 1994) is one of the methodologies widely used in the
mining industry for modelling the recoverable resources above cut-off grades, the advantage
of UC is that it can be used in a widely spaced data, across domains that are not strictly
stationary, provided that there is a sufficient data for conditionally unbiased estimate of the
panel mean grade (Rivoirard, 1994; Hansmann, 2016).
The drawback of the conventional Uniform Conditioning (UC) method is its inability to
predict a spatial location of the economically extractable mineralization (Abazlov, 2014), in
other words, UC does not estimate grades directly, it calculates the tonnage and the mean
of recoverable resources distributed in a large panel. Abzalov (2006), proposed a method for
modelling grades of selective mineable units (SMU) called Localized Uniform Conditioning
(LUC), it enhances the UC approach by localizing the model panel results, representing a
partitioning of this panel.
According to Hansmann 2016, UC and the add-on LUC has been successfully applied
in several different types of deposits, indicating that the method is applicable on a normal