Evaluation of gold deposits—Part 1: review of mineral resource estimation methodology applied to fault- and fracture-related systems S. C. Dominy and A. E. Annels
Synopsis Mineral resource estimation is a highly skilled activity that is critical to the successful development and exploitation of any gold deposit. The methods available to the estimator for the determination of local and global grades and tonnages fall into two categories: conventional and geostatistical. Conventional techniques are generally based on weighting, averaging or projection of grade, thickness, etc., to produce a global or local resource. Geostatistical methods are mathematically more complex, less biased and permit global and local estimation through the use of interpolation procedures, which reflect the nature and continuity of the mineralization. The choice of what method to apply must be made in consideration of the deposit geology, grade distribution and sample density. In fault- and fracture-related gold deposits major considerations in resource estimation comprise the deposit geology (including continuity and ore controls) and grade distribution (skewness, nugget effect, continuity, mixed populations, etc.). Selected conventional and geostatistical methods are subjected to a critical review, and deposit characteristics that must be taken into account during estimation are discussed. Mineral resource estimation requires a high level of skill and experience.33,34 The role of properly experienced geoscientists and engineers has been heightened following the Bre-X and other recent scandals. Modern mining projects require substantial investment for exploration, evaluation and subsequent exploitation and it is important, therefore, that investors, shareholders, etc., are protected through highquality work. A critical review of selected estimation methods as applied to fault- and fracture-related gold deposits and of important deposit characteristics is presented here. The discussions have wider applications and relevance to all types of gold mineralization. In the authors’ experience of both teaching and professional practice it is still common to find ‘estimators’ who are not fully aware of the relative advantages and disadvantages of the various techniques. Further details of the estimation methods have been given in publications of previous workers.1,3,10,11,12,22,23,36,37,38
General background: geology and grade characteristics Deposit geology The types of gold mineralization considered for the purposes Manuscript first received by the Institution of Mining and Metallurgy on 23 January, 2001; revised manuscript received on 7 February, 2002. Paper published in T rans. Instn Min. Metall. (Se ct. B: Appl. earth sc i.), 110, September–December 2001. © The Institution of Mining and Metallurgy 2002.
of this work include shear-zone (Archaean), other mesothermal-type systems (e.g. intrusive and black-shale hosted) and epithermal systems as fault- and fracture-related deposits. These systems can comprise discrete veins, reefs or lodes, sheeted veins/stockworks, en-échelon veins, net veins, saddle reefs, etc. Individual structures may display forms ranging from breccia through to laminated vein. In some instances gold may also be distributed in the wallrocks through disseminations and/or micro-veining. Some of these deposits will be characterized by fine, sulphide-locked gold and others by coarse, free gold. Those containing coarse gold will be particularly challenging to evaluate because of their inherent sampling and grade estimation problems.16,17
Fig. 1 Schematic representation of geological and grade variability for range of deposit types
The main point to consider when undertaking a resource estimation is that it must be appropriate to the geology of the deposit in question.12,25,33 Fig. 1 is a schematic representation of geological and grade variability for a range of deposit types, which depicts the degree of difficulty in resource estimation. Deposits with reasonably simple geometrical shapes and regular grade distributions can be evaluated by a variety of techniques with little inherent risk. In contrast, deposits with high geological variability and complex grade distributions can only be evaluated properly by fewer techniques and substantial experience and knowledge are required. For example, there is little point in applying a block-modelling technique to a poorly drilled gold reef characterized by an extreme nugget effect—generally, such deposits can be estimated only globally.17 Most fault- and fracture-related gold deposits plot in a zone that extends from the centre to the top right-hand corner of Fig. 1. Table 1 indicates the general geological and resource-estimation characteristics of these deposits. B145
Table 1 General geological and grade characteristics of fracture-hosted gold deposits Criteria
Features
Geological characteristics
Dip between 0 and 90°. Width variable; potentially pinch and swell. Structural variability; potentially splitting and branching. Variable mineralogy. Free and/or sulphide-locked gold
Data characteristics
Drill-holes typically 50% is expected for an estimate based on ‘exploration’ drilling (e.g. during a feasibility study) and a value of >90% for a production ‘grade control’ estimate.
Geostatistical interpolation methods Linear methods Simple (SK) and ordinary (OK) kriging SK and OK are reasonably robust estimators, though ideally they should be used on normally distributed variables. When the sampling distribution is skewed the evaluation of some blocks is not well done when the local samples around the block contain one or more high values. In these conditions SK and OK assign a value to the block that is much more than its true value. This is because the weights do not depend on the sample grades. In general, if SK and OK are used where the sampling distribution is skewed towards logB160
normality but is not lognormal, they are more satisfactory estimators than lognormal kriging in that fewer nonsensical block estimates are made. A characteristic of OK is known as ‘the weight independence of data’ value (WID), which reflects the fact that the OK weights do not depend on the sample grades. This is commonly considered one of the major causes of the oversmoothing of estimates when OK is used. For most configurations of samples the variance of the kriged estimates is lower than the dispersion variance of the blocks being estimated. Contributors to WID are highly skewed distributions, extreme values and mixed grade populations (e.g. related to several stages of mineralization). Such features of grade distribution may be interrelated—for example, a highly skewed distribution is usually related to the mixture of two or more grade models. In any of these instances OK will probably fail to quantify the spatial variabilities of grades accurately. A major reason for this is that OK uses only information on average continuities of grade. In other words, it does not distinguish continuities of high grades from those of low grades. SK and OK should theoretically be applied in stationary conditions, i.e. where drift or trends are absent.29 Applied rigorously, the no-drift requirement would exclude their use from virtually all orebodies. However, as they are robust estimators and where the drift is a large-scale feature it is often possible to assume local stationarity over a restricted field— for example, over the size of the search area. The main feature of the OK method is that the sum of the kriging coefficients equals 1. With SK the condition that the sum of the weighting coefficients equals 1 is not applied, but the unity condition is achieved by calculating an ‘external weight’ by subtracting the sum of the kriging coefficients from 1. This external weight is then applied to the mean value of the whole deposit, or of a locally defined area within the deposit, on the basis of geological criteria. If the external weight is small, this implies that there are adequate data points in the search area and the results of OK and SK are similar. Conversely, a large external weight indicates that the available data are inadequate and the block value is close to that of the deposit or sub-area as a whole. Blocks that have low confidence can thus be detected by a comparison of the results of the two methods. One problem in the application of both OK and SK is their inability to produce a semi-variogram with a recognizable structure. This is generally due to a combination of extreme skewness, erratic data distributions, lack of data, extreme values, very high nugget effect and/or short range or the incorrect estimation of semi-variogram parameters. SK is rarely used in the mining industry, OK being more popular. Lognormal kriging (LK) Where the data distribution is highly skewed log-transformation of the data may result in a lognormal population. It must first be established whether the population is two- or threeparameter lognormal, requiring either ln(value) or ln(value + a) to be modelled. If the modelled lognormal semi-variograms are robust and without significant zonal anisotropy, LK is likely to be an appropriate method. The log-transformed values are then kriged by OK and the results are back-transformed. The method requires that the log-transformed data have a normal distribution to avoid the production of nonsensical results and negative kriging variances. High kriging variances resulting from this may cause problems in the back-transformation of the log values and give excessively high grades. When LK is used it is often found that in the majority of cases the mean of the block values estimated by LK differs
from the mean of the data values. This is because although the variable is lognormally distributed, it does not necessarily follow that its multivariate distribution is lognormal. This bias (of the order of 5–7%) is a negative feature of the method, but LK has the advantage that it gives smaller kriging variances than SK.31 LK gives similar results to OK at low grades, but at higher grades OK gives higher results and is biased; LK is more resistant to extreme values than OK. A critical aspect of LK is the back-transformation of log values to return to the original units. Simply antilogging the value does not produce unbiased estimators. The correct back-transformation for LK contains the kriging estimate for the average log, g; half of the kriging variance for this estimate, s2/2; and the Lagrangian multiplier, µ. The backtransformation to obtain the absolute estimate, Z*, is æ ö s2 - m÷ Z* = expç g + 2 è ø
(14)
A similar back-transformation is required to covert the log variance into an absolute kriging variance:
( ){
(
)[
s K = m exp s v 1 + exp m - sKE exp( m) - 2 2
2
2
2
]}
(15)
where sK2 is the absolute kriging variance; m is the average of block values in the orebody; sv2 is the variance of the logs of the block values; and s2KE is the log kriging variance. Another important aspect of applying LK is accurate deter-
(a)
(b)
Nonlinear methods Indicator kriging Indicator kriging (IK) and its variants do not rely on the assumption of a particular statistical distribution model for their results24 and, despite the relative difficulty of their application, they have grown to be one of the most widely used kriging systems. IK is the prime nonlinear geostatistical technique used in the minerals industry today and has found application to different styles of gold mineralization. There are, however, well-documented pitfalls in the use of this method.40 For IK a threshold is selected for a specific variable that may reflect, for example, a cutoff grade or an acceptable level of core recovery, and the data are split at this level. All values above this level are set to 1 and those below to 0. These are referred to as indicator variables. An indicator semi-variogram is produced and then each ore block is kriged, using OK, to produce a kriged indicator value. This lies between 0 and 1 and represents the proportion of the block whose grade lies above the cutoff or the proportion of the grade values used to evaluate the block that lie above this cutoff. Indicator semi-variograms are generally superior to ordinary semivariograms in having well-defined structures from which the parameters can be determined with ease (Fig. 16). The technique offers practical solutions to some of the common estimation problems, such as the issue of mixed or poorly domained populations and their theoretical ability to generate ‘recoverable’ resources.
(c)
Fig. 16 (a) Directional ‘indicator’ experimental semi-variogram for grade from Australian shear-zone hosted deposit with (b) fitted spherical model and (c) special case ‘Paddington mix’ model9
mination of the relevant grade distribution. It is vital to recognize the mineralization indicator grade above which the data are lognormally distributed during semi-variogram calculation. This is effectively the removal of the spike of near-zero values that do not represent the orebody as such, but are merely due to drilling through barren ground. If these are not removed, the variance of the population predicted by the semi-variogram will be inflated. LK is sensitive to the total variance and caution should be exercised in defining the variance correctly.
‘Three-stage’ indicator kriging A variant of IK is referred to as ‘three-stage kriging’ (TSK). This is used for data populations that are clearly bimodal in that a low-grade population (e.g. disseminated in host rock) is combined with a high-grade population (e.g. quartz veining), as in some epithermal gold deposits. This method breaks the problem of grade estimation down into three more manageable problems: (1) what is the proportion of material in the high-grade class? (2) What is the grade of the highgrade material? And (3) what is the grade of the low-grade B161
material? An indicator threshold is selected to separate the two populations, which are then modelled (by variography and OK) totally separately before recombination using the indicator variable assigned to each block by IK as the weighting factor. The data are thus split, following statistical analysis, into a high-grade and a low-grade population. Indicator kriging is then undertaken to assess the proportion of each block, IK, that lies in the high-grade category, ZH, and, hence, the portion in the low-grade category, ZL. The two data-sets are then separately kriged by either OK or LK following variography of the two populations. The three values thus obtained for each block can be combined to produce a final block grade: ZB = (IK ´ ZH) + (1 – IK) ´ ZL
(16)
Multiple indicator kriging (MIK) MIK is a variant of IK that estimates the proportion of each block that lies above each of a series of thresholds across the entire data population. The application of MIK has been the subject of much recent debate. 40,41 It requires indicator vari ography for each threshold followed by block kriging— usually OK. The proportion of the block that lies in each grade range can then be obtained by subtracting the indicator variable for the upper limit for each range from that for the lower limit (Fig. 17). This value is then used as a weighting
Fig. 17 MIK thresholds showing means by which grade weighting factors are calculated
factor for the mean grade that lies in each range to produce the final block grade according to the equation n ZB = éë å i =1( I i -1 - I i ) ´ Gi ùû + I n -1 ´ Z B
(17)
where n is the number of indicator thresholds, Ii is the indicator value at each threshold I and Gi is the mean grade for that threshold. I0 (=1) is the lowest threshold above which all the data population lies; In–1 is the indicator value for the upper threshold above, in which the majority of the extreme values Table 3
Example of application
Threshold
Grade
IK
Ii–1 – I i
Mean
Product
I0 I1 I2 I3 I4
0 1 2 3 4
1.00 0.60 0.45 0.15 0.00
0.40 0.15 0.30 0.15 –
0.5 1.5 2.5 3.5 –
0.20 0.22 0.75 0.52 –
1.00
–
1.70
Totals
B162
lie. To reduce the impact of these high grades the median grade value, ZM, is used. The application of this method can be illustrated by the worked example shown in Table 3, where the deposit grades lie between 0 and 4 g/t Au. The weighted grade assigned to this block is thus the sum of the ‘product’ column, whose values are calculated by multiplying the åni=1(Ii–1–Ii) values by the mean values. The sum of the weighting factors is 1. In MIK the histogram is discretized into n classes each bounded by an upper- and a lower-cutoff threshold value (Fig. 17). The estimator defines the number of classes and their bounding value, which poses a number of practical problems—in particular, the choice of cutoffs is often evenly distributed. In gold deposits the geological domain may be divided into decile classes on the basis of grade. The disadvantage of grade-based deciles is that many of the indicator grades will be concentrated at the lower end of the positively skewed grade distribution. Fewer indicator thresholds will represent the higher grades, which contain most of the metal. Potential alternatives include additional discretization of these critical parts (e.g. the tail, in particular) or discretization such that equal metal content is assigned to each class.38 Metal content indicators also provide the advantage of revealing the amount of metal that is associated with the higher grades. Metal indicators for gold projects often reveal that 40% of the metal is derived from grades above the nintieth grade percentile. In rarer cases up to 75% of the metal may be above the nintieth grade percentile. The disadvantage of metal-based indicators is that it is often difficult to define the continuity of grades for indicators set at or above the nintieth grade percentile owing to the low numbers of high-grade samples and their sparse distribution. This often results in the most significant part of the distribution being estimated under conditions of poorly defined or assumed grade continuity. This is not necessarily a fatal flaw in the method, but careful consideration and judgement are needed. If indicator grades have been selected carefully with regard to the grade distribution, the distribution within many classes will be nearly linear. The distribution of sample grades in the upper and lower grade classes will not normally be linear and will require special treatment. In the case of a positively skewed grade distribution the greatest estimation sensitivities are associated with the grade assigned to the upper class. Distribution skew and extreme grade values both influence the grade distribution in this class, which requires a more sophisticated method of mean grade selection if grade overestimation or underestimation is to be avoided. The tail of the population generally has few samples, which means that a model must be defined to give the ‘shape’ of the histogram to the tail. Choices between different models may have a material effect on the estimates at higher cutoffs, but there is little objectivity in such choices. When evaluating grade it is necessary to have estimates of the average grades of each class. It is common practice to take the average value of the samples belonging to that class. A different choice is often made for the final class (e.g. the tail): potentially the median or trimmed mean. This choice is often arbitrary, yet it can have a strong impact on the estimation of the richest zones of the orebody. In MIK the search volumes defined during kriging at the various cutoffs are the same. This situation is valid only when the semi-variograms for all the indicators have roughly the same shape (e.g. are proportional—showing the same ranges and nugget effect), which is not usually the case for mineral deposits. This results in serious order relation problems leading, for example, to the prediction of significantly higher grade or more metal above a higher cutoff than above a lower
one. Semi-variograms for the high-grade classes often tend towards pure nugget effect. With such semi-variograms large search ‘areas’ should be used to avoid conditional biases. Change of support is not inherent in MIK and is applied as a post-modelling step. Many practical applications of MIK involve use of the affine correction, which assumes that the shape of the selective mining unit’s distribution is identical to that of the samples.40 The sole change in the distribution is variance reduction, as predicted by Krige’s relationship. Warnings have been given in the literature about the inherent deskewing of the distribution when going from samples to blocks.42 The affine correction assumes no deskewing and thus is not suited to situations where there is a large decrease in variance, e.g. where the nugget effect is high and/or there is a pronounced small-scale structure in the grade semi-variogram. Other approaches that have been adopted include indirect lognormal corrections (very distribution-dependent), conditional simulation and assumptions that the block distribution is normal.40 In the last instance the underlying assumption is that block grades are totally deskewed. Whichever method is used, there can be no guarantee that the corrections applied at the local level are consistent with the same type of correction applied at a global level. In response to these problems in the application of MIK such techniques as residual indicator kriging (RIK) and uniform conditioning (UC) have been reported as being more robust and effective.40,41,42 Median indicator kriging (MedIK) In MedIK the median indicator semi-variogram is used to define the continuity conditions for all indicators. The method is a simplified form of MIK that may be considered in the early stages of a resource project when sample data are sparse and it is difficult to define grade continuity for a full range of indicators. The median indicator semi-variogram is typically the most robust of all indicators as it tends to have the greatest range of continuity. It is the easiest to define with some confidence from sparse data. The semi-variogram at the median is sometimes considered to be ‘representative’ of the indicator semi-variograms at other ‘cutoffs’.41 This may or may not be true and needs to be checked. Experience from full indicator variography shows that grade continuity almost always varies with indicator grade and invariably declines with increasing indicator grade. This will often result in an overestimation of the quantiles of the upper grade classes with MedIK, resulting in a higher than normal expected grade. In practice MedIK is not a recommended method where the data permit full estimation of a set of indicator semi-variograms. The clear advantage of MedIK over MIK is one of time. The critical risk is in the adequacy of the implied approximation. If there are noticeable differences in the shape of the indicator semi-variograms at various cutoffs, caution should be used in applying the method.41
Discussion Validation of kriged estimates Kriged block models must be validated to ensure that they reflect the truth. The validity of a block model is conditional on geological interpretation, grade domaining, continuity parameters (e.g. the semi-variogram), handling of extreme grades and the grade interpolation method. The mean grade of the block model should equal the mean grade of the input samples, indicating that there is no global bias. Similarly, comparison of input and output grade histograms should show the same distribution. At the local scale comparison between block grades and composite grades should show a close correspondence. Further checks can be undertaken by
comparison of different estimation methods—for example, an IK and an IDW block model. If a major difference is found in the results, there is likely to be a problem.
Problems in the kriging method Kriging has had its share of sceptics over the 40 years since its inception. Various criticisms have been levelled at the method, a few of which are noted here.21 Interpretation of an experimental semi-variogram to fit a model can be difficult and generally requires a high degree of experience. Various problems related to mixed populations and high grades and the need for effective domaining have already been highlighted. An orebody for which the semivariogram is not satisfactorily identified by the available data may be incorrectly evaluated. Semi-variogram model quality can be checked by cross-validation (or jack-knifing) methods, in which values at known points are estimated from those around them and the set of estimates is compared with the original data-set. The kriging or estimation variance, sK2, is derived from the semi-variogram and is based on the number of samples that were available within the defined search area and their spacing. It is not directly related to the actual data points (meaning it has no dependence on local data conditions), which may deviate from those represented in the semivariogram. For example, in a high-grade zone within a gold vein the kriging variance would be just the same as in a lowgrade zone. This is potentially unrealistic, as the predictability of grades will be poorer in the high-grade zones than in the low-grade zones. If the correct semi-variogram model is not fitted to the data, the resulting estimation variance may yield a value lower than if the correct model had been used, the result being undue confidence in the estimate. Conversely, the value could be higher, the result being undue caution. Geostatistical theory requires that the data population shows stationarity, i.e. it may be correctly assumed that the mean grade of a deposit is the same everywhere. This is often not true in mineralized systems, where there will be both lowand high-grade regions. Linear kriging methods do not work well where there is systematic variation over the region being modelled, but the global estimate will remain relatively unbiased. The development of the universal kriging technique was an attempt to resolve this problem, but its application is complex.32 Another problem encountered in the application of geostatistics is that of data distribution. A normal distribution is not generally expected for the data (e.g. OK is robust in the presence of some skewness), but a normal distribution is assumed for errors. In many cases of precious-metal deposits the data are far from normal and the error distribution cannot be assumed normal either. Even if the error distribution is normal, use of a linear kriging method will tend to underestimate the peaks and overestimate the troughs. For highly skewed distributions, as in gold deposits, this smoothing of the peaks will often result in the underestimation of high-grade zones. This problem has been addressed to some extent by the application of nonlinear methods. There is no doubt that there are imperfections in the kriging process. The important point is that it is a better, less biased technique than conventional estimation methods. It does, however, require a high level of skill to implement properly. Until such time as an alternative is developed kriging will continue to be the most important technique used to evaluate mineral resources.
Recent advances—conditional simulation Conditional simulation is a set of geostatistical tools that is becoming more popular for resource-evaluation purposes. B163
Like the other methods for spatial estimation (OK, IK, etc.), conditional simulation addresses the problem of characterizing the variability of a deposit between the known data locations by different means. Such models honour the real sampling data, but have no smoothing effect so that effects of decisions on grade variability can be modelled. Conditional simulation provides a number of equiprobable images of a deposit, at a finer resolution than would be economic or practical to sample, that can be constrained by various criteria (e.g. geological, statistical and geostatistical), to ensure that the images represent the deposit reasonably. These images can then be used to assess the risk involved in various practical mining decisions. Conditional simulation can be used for validating resource-estimate parameters, for optimizing grade-control sampling grids and for ore-block optimization for mining grade control.
Final comments on geostatistics Geostatistics is a powerful technique for grade estimation provided that it is applied in the light of geological understanding. Most importantly, the evaluator must examine the results of a kriged estimate and pay particular regard to: the location of very high- and very low-value blocks; estimates near the margins of the deposit; estimates in the context of geology (especially continuity); kriging variance in relation to sample spacing; and estimates for poorly sampled or unsampled regions. There are three advantages in the use of geostatistics. First, resource-estimate results are more easily duplicated by different persons and there is less requirement for subjective interpretation after the semi-variogram models are defined. Second, the technique effectively improves grade estimates even when using grade data of differing size and reliability. Third, the improved mineral resource (and, hence, reserve) permits better long- and short-term planning and allows the
operator flexibility when dealing with such problems as metal price changes, mining difficulties, etc. Many companies have faced considerable difficulties in their attempts to implement geostatistical techniques. Possible reasons for this includelack of ‘in-house’ geostatistical expertise as a consequence of time and training constraints; an erroneous attitude that geostatistics is not applicable to gold deposits; an erroneous attitude that geostatistics only works for open-pit operations; managerial resistance to change or lack of understanding of the benefits; inability to produce recognizable or reliable semi-variograms owing to inadequate geological understanding and control or to inappropriate data manipulation; sparse data and/or no financial commitment to improve the level of sampling; poor-quality data stemming from poor drill recoveries, sampling, sample splitting or mixing procedures or analysis; choice of inappropriate methodology; or a high degree of unpredictability of the mineralization and lack of grade continuity due to factors related to structural or lithological control or the mineralization process. Table 4 indicates types of deposit to which the geostatistical techniques discussed can sometimes be applied. The list is not exhaustive and should not be considered definitive. Use of the correct kriging method is vital as misuse can be as dangerous as non-use. It is important that the grade distribution within the mineralization and the relevant estimation technique for the style of mining be considered: for selective mining: normal distribution, OK; lognormal distribution, LK; highly skewed distribution, IK (e.g. TSK, MIK, MedIK and possibly UC or RIK); for bulk mining: normal distribution, OK; lognormal distribution, LK.
Conclusion Conventional methods are playing a less important role in the
Table 4 Summary of geostatistical resource-estimation techniques and their application to different gold deposit types (modified from Annels and Armitage2) Ordinary kriging
Lognormal kriging
Indicator/three-stage kriging
Multiple indicator kriging
Project status
Feasibility to gradecontrol estimates
Feasibility to grade-control estimates
Feasibility to grade-control estimates
Feasibility to grade-control estimates
Deposit geometry
Two- and threedimensional tabular and massive deposits
Two- and threedimensional tabular and massive deposits
Two- and three-dimensional Two- and threetabular and massive deposits dimensional tabular comprising different ore types and massive deposits
Grade distribution (method best suited to)
Normal statistical distributions with observable spatial distribution patterns
Strictly lognormal statistical distributions with observable spatial distribution patterns
Different ore types with different and largely separate statistical distributions each with observable spatial distribution patterns
Statistically skewed or complex distributions with observable spatial distribution patterns
Key factors
Nugget effect, topcuts, assay weighting, composite length, search parameters, degree of smoothing, unfilled blocks and orebody limits
Nugget effect, assay weighting, composite length, search parameters, degree of smoothing, unfilled blocks, orebody limits, back-transformations and classical statistical comparisons
Nugget effect, assay weighting, composite length, search parameters, indicator cutoff, mean grade selection, degree of smoothing, unfilled blocks, orebody limits and classical statistical comparisons
Nugget effect, assay weighting weighting, composite length, search parameters, indicator cutoff, grade estimators for upper bins, degree of smoothing unfilled blocks, orebody limits, order relational problems and classical statistical comparisons
Styles of gold mineralization where method has been applied
Various types, though not commonly applied due to nature of gold distributions
Shear-zone gold deposits
Shear-zone, epithermal and ‘other’ vein gold deposits
Shear-zone, epithermal and ‘other’ vein gold deposits
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evaluation of mineral deposits. Their application is generally only relevant during the exploration or perhaps pre-feasibility stages, although they are sometimes used to cross-check geostatistical estimates during feasibility studies etc. In instances of highly discontinuous and/or high nugget-effect mineralization the only practical estimation method available may well be conventional. If the only method deemed applicable to the particular situation is conventional, the evaluator should consider carefully whether sufficient sample/drilling data are available. Financial judgments cannot be based on flawed estimates founded on sparse data. If the data density does not permit geostatistical estimation, one is bound to ask whether it will allow the definition of proven and probable ore reserves anyway. Conventional techniques have many shortcomings that can affect the reliability of the estimate. Their limitations need to be assessed in the light of the geological and grade continuity of each particular deposit. One very important limitation is the fact that most can only be applied in two dimensions and are thus only suitable for deposits that are thin and tabular in form. Geostatistics is an extremely powerful method for grade estimation provided that it is applied correctly and in the light of geological understanding. Because kriging is not a ‘black box’ technique, its use requires a variety of interactive decisions, including variography, search strategy, number of samples, etc. One of the principal complaints voiced against the use of geostatistical methods is that they require larger amounts of data than conventional techniques. This is incorrect as the conventional methods give biased estimates for which estimation error cannot be calculated. Geostatistical methods reveal where data are inadequate.28 The excuse given by many engaged in the evaluation of gold orebodies is that they are characterized by complex geology and grade distribution—as expected, for instance, in shear zone-related mineralization.4,6,7,8 Such deposits require very careful geological interpretation, grade domaining and statistical study.4,14,15,26 If, however, the geology is discontinuous and/or an extreme nugget effect (in excess of 75%) is present, geostatistics may be inapplicable and reliance placed in conventional methods.17 Another problem encountered in applying geostatistics is the difficulty in obtaining reliable semi-variograms in the presence of high grades and inadequate samples. Many gold deposits have a coefficient of variation ³200%.6 A CV% of this magnitude may require 800 plus data-points according to the relationship of Royle.30,32 There are many instances in which the application of geostatistics to complex gold deposits is possible through the use of kriging variants such as LK, IK or MIK.2 On a final note, it is important to remember the critical role that geology plays in the resource-evaluation process. Such exhortations as ‘Let’s put the “geo” back into geostatistics’ and ‘Geology is king’ are important. Geology should guide resource estimation, not resource estimation guide the geology. Geological interpretations are continually evolving components of the resource-estimation process because new information becomes available continually as exploration, evaluation and exploitation proceed. The requirement for high-quality resource estimates demands upgrading of the geological database and related interpretations. The evaluation process is affected significantly by various aspects of geology, including sampling and sample quality, geological mapping, three-dimensional modelling, mineralogy and studies of continuity, etc. If the resource estimation is based on high-quality data whose interpretation is controlled by geology and statistics, it has a good chance of being close to the truth.
Acknowledgement The authors thank many individuals who have helped with this contribution. S.C.D. thanks Welsh Gold PLC, Cardiff University, the Royal Society, the Institution of Mining and Metallurgy and the North Queensland Branch of the Australasian Institute of Mining and Metallurgy for funding study leave periods to Australia during 1998–2001. A.E.A. acknowledges colleagues from SRK Consulting (UK), Ltd., including Dr. M. G. Armitage, Dr. J. Arthur, M. F. Pittuck and R. Clayton. Discussions with Dr. Isobel Clark (Geostokos, Ltd., Scotland), Dr. A. G. Royle (independent consultant, England), Dr. S. Henley (Resources Computing International, Ltd., England), Vivienne Snowden, I. Glacken and M. Noppe (Snowden Mining Industry Consultants, Ltd., Australia), P. R. Stephenson (Australian Mining Consultants Pty, Ltd., Australia) and Dr. Suzanne Hunt (University of Adelaide, Australia) are acknowledged. P. B. Bright (SRK Consulting UK, Ltd.) drafted Figs. 1, 4–11 and 17. R. Evans (Cardiff University) produced Figs. 3, 12 and 13 and Lucy Roberts (James Cook University) Fig. 14. Fig. 16 is reproduced with the kind permission of Dr. Isobel Clark. Three IMM referees are thanked for their critical review of this contribution, as is Dr. Simon Dunton for his expertise in making it publishable and, it is hoped, readable. References 1. Annels A. E. Mineral deposit evaluation—a practical approach (London: Chapman and Hall, 1991), 141 p. 2. Annels A. E. and Armitage M. G. An overview of resource evalua tion techniques, a short course for the Association of Mining Analysts, London (Cardiff: SRK Consulting UK, Ltd., November 1999), 32 p. 3. Armstrong M. Basic linear geostatistics (Berlin: Springer-Verlag, 1998), 153 p. 4. Baxter J. L. and Yates M. G. Estimation of reserves and resources in shear zone hosted gold deposits. In Mineral resource and ore reserve estimation—the AusIMM guide to good practice (Melbourne: Australasian Institute of Mining and Metallurgy, 2001), 125–34. Monograph 23 5. Camisani-Calzolari F. A. G. M. Pre-check for payability. Nuclear Active, 29, 1983, 33–6. 6. Carras S. N. Comparative ore reserve methodologies for gold mine evaluation. In Proc. gold mining, metallurgy and geology (Melbourne: Australasian Institute of Mining and Metallurgy, 1984), 59–70. Spec. Pub. 4/84 7. Carras S. N. Gold mine evaluation: some evaluation concepts. In Proc. Congress on the geology, structure, mineralization and econom ics of the Pacific Rim (PACRIM ’87) (Melbourne: Australasian Institute of Mining and Metallurgy, 1987), 845–50. Spec. Pub. 7/87 8. Carras S. N. Let the orebody speak. Reference 4, 199–205. 9. Clark I. Geology and statistics—striking the balance in the real world. In Dominy S. C. ed. Proc. mineral resource evaluation into the 21st century conference—‘Annels’ meeting, March 2000 (Cardiff: Department of Earth Sciences, Cardiff University, 2000), 5–9. 10. Clark I. and Harper W. V. Practical geostatistics (Columbus: Ecosse North America, 2000), 342 p. 11. David M. Geostatistcal ore reserve estimation (Amsterdam: Elsevier Scientific, 1977), 364 p. Developments in Geomathematics 2 12. David M. Handbook of applied advanced geostatistical ore reserve estimation (Amsterdam: Elsevier Scientific, 1988), 216 p. Develop ments in Geomathematics 6 13. Dominy S. C. et al. Geology in the resource and reserve estimation of narrow vein deposits. Explor. Min. Geol., 6, (4), 1997, 317–33. 14. Dominy S. C. et al. Resource evaluation of narrow gold bearing veins: problems and methods of grade estimation. Trans. Instn Min. Metall. (Sect. A: Min. industry), 108, 1999, A52–70. 15. Dominy S. C. et al. Gold grade distribution and estimation in narrow vein systems. In Proc. Int. Congress on earth science, explo ration and mining around the Pacific Rim, PACRIM ’99 (Melbourne: Australasian Institute of Mining and Metallurgy, 1999), 411–25. Spec. Pub. 4/99 16. Dominy S. C. et. al. General considerations of sampling and assaying in a coarse gold environment. Trans. Instn Min. Metall. (Sect. B: Appl. earth sci.), 109, 2000, B145–67. 17. Dominy S. C. et al. Estimation and reporting of mineral resources for coarse gold-bearing veins. Explor. Min. Geol., 9, (1), 2000, 13–42.
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18. Dominy S. C. et al. Evaluation of gold deposits—Part 2: results of a survey of estimation methodologies applied in the Eastern Goldfields of Western Australia. Trans. Instn Min. Metall. (Sect. B: Appl. earth sci.), 110, 2001, B167–75. 19. Dominy S. C. et al. Errors and uncertainty in ore reserve estimates: operator beware. In Proc. underground operators conference (Melbourne: Australasian Institute of Mining and Metallurgy, 2002), in press. 20. Gy P. M. Sampling of particulate materials (Amsterdam: Elsevier, 1982), 231 p. Developments in Geomathematics 4 21. Henley S. and Watson D. F. Possible alternatives to geostatistics. In Proc. 27th Int. Symp. Computer applications in the minerals industries (London: IMM, 1998), 337–53. 22. Houlding S. W. Practical geostatistics—modelling and spatial analysis (Berlin: Springer-Verlag, 2000), 160 p. 23. Journel A. G. and Huijbregts C. J. Mining geostatistics (London: Academic Press, 1978), 600 p. 24. Kwa B. L. and Mousset-Jones P. F. Indicator kriging applied to a gold deposit in Nevada, USA. In Proc. Symp. ore reserve estimation: methods, models and reality (Montreal: CIM, 1986), 185–94. 25. Long S. D. Practical quality procedures in mineral inventory estimation. Explor. Min. Geol., 7, (1,2), 1998, 117–28. 26. Pelham D. A. The evaluation of vein gold deposits—part II. Min. Quarry. Tech. Int., 1992, 31–4. 27. Platten I. M. and Dominy S. C. The occurrence of high-grade gold pockets in quartz reefs at the Gwynfynydd mine, Wales, UK: a geological explanation for the nugget effect. Accepted for publication in Explor. Min. Geol. 28. Royle A. G. and Newton M. J. Mathematical models, sample sets and ore reserve estimation. Trans. Instn Min. Metall. (Sect. A: Min. industry), 81, 1972, A121–8. 29. Royle A. G. Estimating global ore reserves in a single deposit. Minerals Sci. Engng, 12 (1), 1980, 37–50. 30. Royle A. G. The volume–semi-variogram relationship in gold mines. LUMA—J. Leeds University Mining Association, 1988, 55–60. 31. Royle A. G. A personal overview of geostatistics. In Annels A. E. ed. Case histories and methods in mineral resource evaluation (London: Geological Society, 1992), 233–41. Spec. Pub. geol. Soc. Lond. 63 32. Royle A. G. The sampling and evaluation of gold deposits. Ph.D. thesis, University of Leeds, 1995. 33. Sinclair A. J. Geological controls in resource/reserve estimation. Explor. Min. Geol., 7 (1,2), 1998, 29–44. 34. Stephenson P. R. The 1999 JORC code—what does it mean for today’s mining geologist? In Proc. 4th Int. mining geology conf. (Melbourne: Australasian Institute of Mining and Metallurgy, 2000), 157–68. Spec. Pub. 3/00 35. Stephenson P. R. and Vann J. Common sense and good communication in mineral resource and ore reserve estimation. Reference 15, 435–41. 36. Stone J. G. and Dunn P. G. Ore reserve estimates in the real world (Littleton: Society of Economic Geologists, 1996), 160 p. 37. Wellmer F. W. Statistical evaluations in exploration for mineral deposits (Berlin: Springer-Verlag, 1998) pp 380. 38. Vallée M. Guide to the evaluation of gold deposits (Montreal: CIM, 1992), 300 p. 39. Vallée M. Resource/reserve estimation and inventory: can reporting definitions substitute for standards? Explor. Min. Geol., 7 (1,2), 1998, 15–24. 40. Vann J. et al. Multiple indicator kriging—is it suited to my deposit? Reference 34, 187–94. 41. Vann J. and Guibal D. Beyond ordinary kriging—an overview of non-linear estimation. Reference 4, 249–56. 42. Vann J. and Sans H. Global resource estimation and change of support at the Enterprise gold mine, Pine Creek, Northern Territory—application of the geostatistical discrete gaussian model. In Proc. 25th APCOM Conference (Melbourne: Australasian Institute of Mining and Metallurgy, 1995), 171–9. Spec. Pub. 4/95 Authors S. C. Dominy Member is a graduate of the City of London Polytechnic and the Camborne School of Mines and was awarded a Ph.D. from Kingston University, England, in 1992. He has recently moved from Cardiff University, Wales, to take up the post of Minerals Council of Australia lecturer in mining geology and director of the M.App.Sc. mining and exploration geology course at James Cook University, Australia. He is principal mining geologist with GGI Consulting and has worked on a number of gold deposits in Eastern and Western Europe, Africa, Australia and North and South America. Address: Economic Geology Research Unit (EGRU), School of Earth
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Sciences, James Cook University, Townsville, Queensland 4811, Australia. email:
[email protected] A. E. Annels Fellow is a graduate of King’s College, London, and was awarded a Ph.D. from the Royal School of Mines (University of London). He is currently principal mining geologist with SRK Consulting (UK), Ltd., Wales. He was a mine geologist and assistant chief mine geologist on the Zambian Copperbelt before holding a lectureship then senior lectureship at Cardiff University, Wales, from 1975 to 1998. He specializes in mining geostatistics and mine feasibility studies.
