IN MINERAL RESOURCE ESTIMATES

The estimation of mineral resources forms the basis for proving the viability of any mining project. While the exploration activities have many steps and extensive data collection to support the resource estimation, it is the geological and geostatistical interpretation of that data that forms the underpinning of the mineral resource estimate. Often the upper 10% of the assays represent as much as 90% or more of the metal content, and the upper 1% of the assays may contribute the majority of the metal to the upper 10%. These very high grade values are often referred to as outliers. Most low grade mineralized units, with skewed grade distributions (typically precious metals like gold, silver or P.G.M. but also base metals and uranium) exhibit sample grade distributions with extreme high grade values or outliers on the high tail of a histogram. An outlier is an observation that appears to be inconsistent or anomalous with the vast majority of data values. The proper interpretation and handling of outliers in a data set is crucial to estimating a mineral resource that is representative of the deposit. Without a firm understanding of the distribution of metal in a deposit, mine planning, scheduling, process planning and economic analysis will likely be flawed. Three of the most important issues in the mineral resource estimation process are the recognition of outlier values in a data set, the source of the outlier values, and the subsequent handling of these high values.

#131 February 2016

MANAGEMENT OF EXTREME HIGH GRADE ASSAYSRichard Kehmeier Chief Geologist

Brian Hartman Principal Geologist

Esteban Acuna Principal Geologist

John Zeise Senior Geologist

CONTENTS Introduction Page 02

RPMGlobal’s Position on Capping Page 02

Outlier Detection Page 02

Accepted & Best Industry Practices Page 03

Conclusion Page 04

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IntroductionTreatment of outliers in mineral resource estimations is a perplexing problem for which there is no generally accepted solution. Each deposit may have a unique distribution of outlier values which may require multiple methods of treatment to fully understand the issues and their effect on the mineral resource estimate. If good sampling and QA/QC protocols have been followed (i.e. good results in high grade duplicates) and the geological description of these intervals matches with the high grade values, and there is sufficient close spaced sampling to limit the influence of the high grade in the estimation, there is no theoretical or scientific ground to cap these outliers. “High grade capping is commonly considered to be more psychological than anything else. For example, if your sample data in a gold deposit is not capped, people will not trust the results” (Dagbert, 2008 ). Outlier issues are especially critical in the first stages of projects when data density is still low and projects are looking for funding.

Grade estimation is fundamentally a synonym for grade averaging in a spatial context. Averaging means that available sample data are weighted by a scheme. This, in itself, is not an issue nor is it normally a problem, except in the presence of outliers. On the scale of the deposit, using a large number of samples in the interpolation routine, outliers do not impact the mean grade; however, outliers may locally be over-represented in the blocks around the extreme high grades. The outliers generally represent less than 1% of the population (hence less than 1% of the tonnage) but because of their high grade, they may contribute significantly to the global metal content (typically > 10%).

Said another way, estimation of the grade of mining blocks around an outlier in which the outlier is included in the estimate of the grade of the mining blocks can contribute a disproportion amount of metal in relation to the block size or tonnage causing an over-estimation of the contained metal. Therefore, the treatment of high grade or outlier values plays a crucial role in evaluating the economic viability of a mining project.

Additionally, outliers introduce substantial variability in estimates of various statistical parameters including the mean, variance, and covariance. Hence, they impact variograms. As well, in a block estimation process such as Kriging, if an outlier value coincides with a negative weight, the resulting Kriged estimate can be seriously incorrect, and may even be negative in extreme cases (Sinclair 2002.)

For the above reasons, geostatisticians and geomodelers have proposed and used various methods to mitigate the impact of high grade data on mineral resource estimation. These various methods generally involve some form of capping and/or high grade influence restrictions to mitigate the disproportionate influence of true outlier values on the contained metal in a resource.

RPMGlobal’s Position on CappingTreatment of outliers in mineral resource estimations is a perplexing problem for which there is no generally accepted Given the impact that outliers can have on the economics of a project, RPMGlobal considers doing nothing to mitigate the disproportionally large influence of extreme high grades during the mineral resource estimation process is not consistent with industry practice and can potentially create a material issue. RPMGlobal recommends, no matter how one chooses to handle outliers, a “metal at risk” assessment should be performed to ensure that high grades are not locally over-estimating blocks.

The threshold for outliers may be arbitrarily chosen in the last percentiles of the data distribution, RPMGlobal accepts that applying capping is a common industry practice intended to limit the potential undue economic influence of high metal values; however, from the geostatistical point of view, RPMGlobal opines that truncated distributions (after capping) may provoke conditional bias in the estimates, and for this reason RPMGlobal considers as best practice estimation procedures to reduce the influence of extreme high values. Among these geostatistical techniques are: multiple Indicator Kriging (IK) or Outlier Restricted Kriging (ORK) (Arik, 1992 ), metal at risk simulations (Parker, 2004 ), and the top-cut model (Rivoirard, 2012 ).

For projects where production data is available, reconciliation of the block model against production should be used to guide decisions about the handling of outliers.

Outlier DetectionHigh values may arise because of sampling errors or may reflect distinct geological sub-environments or domains within a mineral deposit. Effort must be directed to examining these high values and their geological context as soon as is feasible after identification in order to distinguish errors from “real” high grades, investigate their characteristics, and how they relate to the mineral inventory estimates. A first step is to examine the relationship between sample size and grade because outliers are more likely to be found in small samples than in big ones. The sample lengths should theoretically be standardized by compositing and then capping the grade of composites. Compositing to the smallest consistent support size is a recognized industry practice (this compositing length can be modified later for resource estimation purposes). Furthermore, outliers should be defined on a de-clustered dataset. As the data density increases, the influence of each single sample is better constrained and therefore sample influences decrease (amount of metal at risk declines as well), leading to an increase in the value of the capping threshold (Marinho, 2009.)

Some commonly used techniques to identify possible outliers are:

• Histograms or Log probability Plots - It is easy to detect outliers from a sample grade distribution or histogram: they are separated from the rest of the distribution by gaps. Note, gaps on a histogram with a log scale are more significant than gaps on a histogram with an arithmetic scale. On a cumulative

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frequency plot, gaps appear like steps or sharp changes of the slope (inflection point or where blue dots fall below the line in Figure 1.)

Figure 1. Probability plot with outliers above percentile 90th and their lognormal corrections, after reducing the grade of the outliers the corrected mean drops to 1.61 from 2.15 (Babakhani, 2014 ). A more common correction is to cap down the outliers to the threshold, 4 in this case (P90th).

• Decile analysis (Parrish, 1997 )

• Assays in the highest 10% of the sample population (D10 ) contains between 40%to 50% of total metal

• D10 contains between 2.3 -3.0 times more metal than assays between the 80th and 90th percentiles of the assay population (D9 )

• P99 contains between 10% - 15% of metal

• P99 contains between 1.75 – 2.0 times more metal than in P98

Figure 1. Probability plot.

If any of the conditions below occur there is potential that outliers are present and may impact the resource estimate.

Contained metal in excess of these ranges might indicate that a separate domain exists.

• Actual versus smoothed grade profiles.

• Two or three standard deviations (SD) above the mean.

There are other less common methods of determining outliers which become quite technical and rely on a good understanding of geostatistics and sampling theory. As this Perspective is concerned with basic identification of outliers it will focus on more common techniques of the handling of outliers in the estimation process and will not go into these more complex methods. RPMGlobal can assist with the more complex methods, which are listed below along with the references.

• Semi-variogram clouds (Journel, 1987 )

• Indicator correlation plot (Srivastava, 1994 )

• Cutting curves (Roscoe, 1996 )

• Coefficient of variation plot (Parker 1991 ):

• Quantity of metal plot (metal at risk analysis) (Dagbert, 2008, Deutsch, 2010.)

• Metal risk analyses using simulations (Parker, 2005 ).

• Central variation error (CVE) from cross validation of ranked transformed data (Babakhani, 2014 ).

Accepted & Best Industry Practices RPMGlobal feels the first task in dealing with extreme values is to determine the validity of the data. The geologist’s role is to confirm that the assay values are free of errors related to sample preparation, handling, and measurement during the QA/QC of each drilling campaign. Part of the necessary analysis is checking control samples, especially the high grade duplicate(s), of the outlier’s batch and checking the geological description and the surrounding data of the high grade which has been identified as a potential outlier. If the sample is found to be erroneous, then the drill core interval should be re-sampled or the sample should be removed from the assay database.

If the sample is deemed to be free of errors (excluding fundamental sample error), then it should remain in the sample database and subsequent treatment of this data may be warranted. Too often, dealing with outliers is left to engineers who are disconnected from the geologist who mapped the deposit. Consequently, these engineers have to make decisions based upon arbitrary assumptions about outliers, instead of basing their treatment on geological knowledge (Sinclair 2002 ).

Once outliers have been identified and confirmed as true outliers, the geologist must make decision as how to handle the outliers in the mineral resource estimation process.

Although outliers may or may not be obvious, a metal risk analysis is recommended as a best industry practice to quantify the metal generated by the highest sample grades in the block model. Commonly, outlier values are geological singularities and have very limited geological continuity relative to lower-grade values. To assume high grades can be extended into neighboring rock the same distance as low-grade samples can lead to a significant overestimation of mineral resource/reserves.

Once the database is free of errors, there are three general non-exclusive procedures of the mineral resource workflow wherein the impact of high-grade samples can be explicitly addressed: (Leauangthong, 2015 ).

1. Domaining to constrain the spatial impact of outliers

The geological domains may be used directly to constrain grade estimation to only those geological units that may be mineralized. It is also quite common during this first stage of the modeling process to design grade domains to further control the distribution of grades during mineral resource estimation.

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One of the objectives of grade domaining is to prevent smearing of high grades into low-grade regions and vice versa. The definition of these domains should be based on an understanding of grade continuity and the recognition that the continuity of low-grade intervals may differ from that of higher grade intervals (Guibal, 2001; Stegman, 2001 ). If subdomains can be defined then the extreme value may be reasonable within the context of that subpopulation.

2. Capping or “cutting” means to reduce all the grades above a threshold to the threshold.

The threshold to cap can be chosen by any of the methods discussed previously. Given the prevalence of this approach in mining, it is no surprise that there are a multitude of tools available to help a modeler determine what grade value is an appropriate threshold to cap. Capping is also available in many commercial general mining packages. This method can generate conditional bias (under estimation of a high grade zone) because it cuts completely the presence of possible real high values (Maleki, 2014.)

3. Restricting the spatial influence of high-grade samples during the estimation.

If the result of the early estimation validation steps reveals that high-grade composites may be causing over-estimation of the resources, but there is some evidence of the presence in small quantities of real, very-rich ore, it would be inappropriate to cap or allow this composite to have a large influence. This large influence should be reduced or constrained to the nearest block. That influence is specified by the design of a search ellipsoid with dimensions smaller than that applied for grade estimation. Typically the choice of the high-grade search ellipsoid dimensions is based upon an educated guess which stems from the notion that the size of the high-grade search ellipsoid should not extend beyond the high-grade continuity. Although there currently are two acceptable approaches available to assess high-grade continuity, RPMGlobal recommends assessing the grade continuity via indicator variograms.

RPMGlobal can assist with more sophisticated geostatistical techniques, which are considered as best practices including:

• Indicator Kriging (IK)

IK is perhaps the most widely used method of dealing with outliers. This non-linear estimation method does not depend on grades since the original distribution is transformed to a binomial distribution, 0 ≤ threshold and 1 > threshold. Thus, the probabilities of a series of thresholds are determined based on the continuity model of each threshold. The high grades likely have much less continuity than the lower grade “average” parts of the mineralized unit (shorter range and higher nugget effect in this “outlier” population). There is abundant literature about IK, a good example of its method with outlier sample data is given in a paper by Journel and Arik, 1988. IK is not particularly effective if the outlier domain is an abnormally small percentage of the mineral deposit and outlier values occur as widely scattered individuals, apparently randomly positioned. This feature makes it imperative that the continuity relationships of the high grade

samples be assessed in cross sections or level maps.

• Top-cut model

Rivoirard ( 201 2 ) mathematical framework called the top-cut model, wherein the estimated grade is separated into three parts: a truncated grade estimated using samples below the top-cut grade, a weighted indicator above the top-cut grade and an independent residual component.

• Estimate of the mean for small lognormal distributions

Sichel ( 1952 ) formulated an estimate of the mean for small lognormal distributions that is more sensitive to outliers than the arithmetic mean of those data. Sichel’s method calculates the arithmetic mean of log-transformed grade (or log-transformed grade + constant if you have a third-parameter lognormal model) and also calculates the logarithmic variance of the same data. The final estimate is the exponential of the log-mean multiplied by a coefficient which is a function of the log-variance and the number of samples. In lognormal space the high tail influence is reduced. When the number of samples is high, Sichel’s factor becomes close to the usual correction factor of the mean of a lognormal model i.e. exp(v2/2 ), where v2 is the logarithmic variance. Lognormal kriging is a natural extension of the Sichel method that allows the use of dependent data (the dependence is expressed by the logarithmic variogram) and weighted average estimates.

ConclusionThe proper treatment of outliers during the estimation of a mineral resource has been demonstrated to be critical for the accurate economic evaluation of a mineral deposit because the tenor and quantity of the mineral resource forms the basis for all further studies. When the estimate is biased by the inappropriate treatment of outlier values in the database, the subsequent studies are flawed and may lead to decisions that are unsound.

Understanding the nature of the outliers, their influence on the mineral resource estimate, and making every effort to apply the proper handling to the outliers so the mineral resource estimate is the best representation of the mineralization within the deposit are the tasks of the resource geologist. RPM approaches each mineral resource estimate as unique and strives to choose the best method or combination of methods to arrive at a “best” estimate for each deposit that is representative of the mineralization defined by the raw data.

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ReferencesArik, A., 1992, Outlier restricted kriging: a new kriging algorithm for handling of outlier high grade data in ore reserve estimation. in Proceedings of the 23rd International Symposium on the Application of Computers and Operations Research in the Minerals Industry. Kim, Y.C. (ed.). Society of Mining Engineers, Littleton, CO. pp. 181–187.

Babakhani, M., 2014, Geostatistical modeling in presence of Extreme Values. Master of Science Thesis, Department of Civil and Environmental Engineering. University of Alberta. Canada

Dagbert, M., 2008, Geostatistical mineral resource/ore reserve estimation and meeting, JORC requirements: step by step from sampling to grade control. Seminar Notes. Perth, Australia.

Deutsch, J. L., 2010, Fitting probability plot to identify multiple population and outliers. CCG Annual Report 12.

Journel, A. G., 1987, Geostatistics for the environmental sciences, an introduction; Project No. CR 811893, Exposure Assessment Res. Div., Environmental Monitoring Systems Laboratory, Las Vegas, Nev., 89114, 135 pp.

Journel A.G. & Arik A., 1988, Dealing with outlier high grade data in precious metals deposits. in Proceedings of Computer Application in the Mineral Industry—Canada. Balkema, Rotterdam, 161-171.

Leuangthong, O. and M. Nowak, M., 2015, Dealing with high-grade data in resource estimation. The Journal of the Southern African Institute of Mining and Metallurgy. Vol.115.

Maleki, M., Madani, N., and Emery, X., 2014, Capping and Kriging grades with long-tailed distributions. The Journal of the Southern African Institute of Mining and Metallurgy. March 2014.

Marinho, R A. & Machuca M., 2009, Capping and outlier restriction: State-of-Art. in APCOM 2009 – Proceedings, Vancouver. B.C. Canada. pp 337-346.

Parker, H. M, 1991, Statistical treatment of outlier data in epithermal gold deposit reserve estimation. Mathematical Geology, vol 23, pp. 175-199.

Parker, H.M., 2005, Risk Hi 2a program documentation. AMEC Technical library.

Parrish, I.S., 1997, Geologist’s Gordian knot: to cut or not cut. Mining Engineering, vol. 49. pp. 967 - 982.

Rivoirard, J., Demange, C., Freulon, X., & Lécureuil, A. 2012, A top-cut model for deposits with heavy-tailed grade distribution. Mathematical Geosciences, vol. 45, pp. 967-982.

Roscoe, W.E. 1996, Cutting curves for grade estimation and grade control in gold mines. 98th Annual General Meeting, Canadian Institute of Mining, Metallurgy and Petroleum, Edmonton, Alberta, April 1996. 8 pp.

Sichel H.S., 1952, New methods in the statistical evaluation of mine sampling data. Trans. I.M.M., London, Vol. 61, pp. 261-288

Sinclair, A. J., & Blackwell, G. H., 2002, Applied mineral inventory estimation. Cambridge University Press.