247
the cell size for declustering and the thresholds for differentiating the mineral resource categories.
The classification of mineral resources and reserves has long been a combination of science, past
experience and professional judgment of the estimator. All of the definitions are similar and deal
with “sample points sufficiently closely spaced to support confidence in the continuity of …”
(CIM Standing Committee 2014). There are two challenges to the classification; determining the
adequate sample spacing to meet the confidence criteria; and defining which blocks in a model
meet those criteria in such a way that the model is useful for reporting and planning.
“Sufficiently closely” has been interpreted in several manners. One method uses the distance between the block estimated and the nearest sample (or samples). Geostatistics gave us
the calculation of the estimation variance of the block, an implicit part of the calculation of
kriging weights, to account for the confidence in the estimate. A more refined method called
“kriging efficiency” has been has been developed to use more aspects of the kriging machinery (Krige 1997). However, kriging efficiency is also sensitive to the estimation variance, thus
it tends to generate confidence class patterns that are sensitive to the distance from the closest sample. These methods can result in a pattern called the “spotted dog” where individual
samples are surrounded by a higher classification near each sample decaying into pattern
of decreasing confidence halos. (Stephenson 2006) In addition to the visual image of the
spots, this raises the more practical problem of mine design when the classification changes
between measured, indicated and inferred.
These challenges have led to ad hoc methods to classify material within the mining block so
larger areas receive a given classification. A popular technique is a multiple search method,
where the estimator defines a minimum of number of samples from a minimum number of
holes within a nested set of search distance that are used to classify estimates. These specified
set of increasing distances are usually proportional to the variogram range. This technique
overcomes the spottiness of the closest sample or kriging error.
These manual methods even with the assistance of modern computer programs described
by (Seibel and Ligocki 2017) “can be both labor intensive and subjective”. Other authors
argue that a probability range and confidence interval of the produced grades over a certain
time can define the necessary spacing (Verly, et al. 2017), (Reid and Parker 2017). These
authors use a 15% relative precision at the 90% confidence interval for annual production to
achieve an Indicated Mineral Resource classification and a similar probability range for each
quarter to be deemed a Measured Mineral Resource. These methods are computationally
intensive and are best utilized by experienced practitioners.
The authors believe that the technique presented herein provides a useful method whereby
the needed spacing as determined by the qualified person can be mapped into a pragmatic
classification of estimation confidence that is useful for planning and reporting of mineral
resources and reserves.
2 DISCUSSION
As described by Stephenson “Block-by-block resource classifications should be smoothed
into geologically sensible and coherent zones that reflect a realistic level of geological and
grade estimation confidence, taking into account the amount, distribution and quality of
data.” There is a tool available in much geostatistical software call declustering. The method
used herein was made popular by the GSLib software published in 1992 (Deutsch and Journel 1992). Tools for declustering are included in a number of commercial mining software.
MicroMODEL (R.K.M. Software 2016), DataMine (Datamine n.d.), MineSight (Hexagon
Mining n.d.), and Vulcan (Maptek Inc. n.d.) provide declustering tools. The tool was developed to discount the statistical effect of closely spaced or “clustered” samples. It is often used
in the exploratory data analysis stage of a study.
Data clustering can be simply due to the available access where samples points can be collected. It is often due to continually “testing” the continuity of the highest-grade areas of a
deposit. The latter can produce biased average grade results from repeated drilling near other
high-grade samples. In both cases, closely spaced, interdependent samples can skew the sta-
the cell size for declustering and the thresholds for differentiating the mineral resource categories.
The classification of mineral resources and reserves has long been a combination of science, past
experience and professional judgment of the estimator. All of the definitions are similar and deal
with “sample points sufficiently closely spaced to support confidence in the continuity of …”
(CIM Standing Committee 2014). There are two challenges to the classification; determining the
adequate sample spacing to meet the confidence criteria; and defining which blocks in a model
meet those criteria in such a way that the model is useful for reporting and planning.
“Sufficiently closely” has been interpreted in several manners. One method uses the distance between the block estimated and the nearest sample (or samples). Geostatistics gave us
the calculation of the estimation variance of the block, an implicit part of the calculation of
kriging weights, to account for the confidence in the estimate. A more refined method called
“kriging efficiency” has been has been developed to use more aspects of the kriging machinery (Krige 1997). However, kriging efficiency is also sensitive to the estimation variance, thus
it tends to generate confidence class patterns that are sensitive to the distance from the closest sample. These methods can result in a pattern called the “spotted dog” where individual
samples are surrounded by a higher classification near each sample decaying into pattern
of decreasing confidence halos. (Stephenson 2006) In addition to the visual image of the
spots, this raises the more practical problem of mine design when the classification changes
between measured, indicated and inferred.
These challenges have led to ad hoc methods to classify material within the mining block so
larger areas receive a given classification. A popular technique is a multiple search method,
where the estimator defines a minimum of number of samples from a minimum number of
holes within a nested set of search distance that are used to classify estimates. These specified
set of increasing distances are usually proportional to the variogram range. This technique
overcomes the spottiness of the closest sample or kriging error.
These manual methods even with the assistance of modern computer programs described
by (Seibel and Ligocki 2017) “can be both labor intensive and subjective”. Other authors
argue that a probability range and confidence interval of the produced grades over a certain
time can define the necessary spacing (Verly, et al. 2017), (Reid and Parker 2017). These
authors use a 15% relative precision at the 90% confidence interval for annual production to
achieve an Indicated Mineral Resource classification and a similar probability range for each
quarter to be deemed a Measured Mineral Resource. These methods are computationally
intensive and are best utilized by experienced practitioners.
The authors believe that the technique presented herein provides a useful method whereby
the needed spacing as determined by the qualified person can be mapped into a pragmatic
classification of estimation confidence that is useful for planning and reporting of mineral
resources and reserves.
2 DISCUSSION
As described by Stephenson “Block-by-block resource classifications should be smoothed
into geologically sensible and coherent zones that reflect a realistic level of geological and
grade estimation confidence, taking into account the amount, distribution and quality of
data.” There is a tool available in much geostatistical software call declustering. The method
used herein was made popular by the GSLib software published in 1992 (Deutsch and Journel 1992). Tools for declustering are included in a number of commercial mining software.
MicroMODEL (R.K.M. Software 2016), DataMine (Datamine n.d.), MineSight (Hexagon
Mining n.d.), and Vulcan (Maptek Inc. n.d.) provide declustering tools. The tool was developed to discount the statistical effect of closely spaced or “clustered” samples. It is often used
in the exploratory data analysis stage of a study.
Data clustering can be simply due to the available access where samples points can be collected. It is often due to continually “testing” the continuity of the highest-grade areas of a
deposit. The latter can produce biased average grade results from repeated drilling near other
high-grade samples. In both cases, closely spaced, interdependent samples can skew the sta-