Scielo RSS <![CDATA[Journal of the Southern African Institute of Mining and Metallurgy]]> vol. 114 num. 3 lang. es <![CDATA[SciELO Logo]]> <![CDATA[<b>Danie Krige</b>]]> <![CDATA[<b>President's Corner</b>]]> <![CDATA[<b>In Memory of Danie Krige a SA Legend of International Acclaim for His Distinguished Contributions to the Mining Industry 1919 - 2013</b>]]> <![CDATA[<b>Professor D.G. Krige FRSSAf</b>]]> <![CDATA[<b>Criteria for the Annual Danie Krige Medal Award</b>]]> <![CDATA[<b>Memories of Danie Krige</b>: <b>Geostatistician Extraordinaire</b>]]> <![CDATA[<b>List of papers published by Danie Krige from 1951-2001</b>]]> <![CDATA[<b>Cokriging for optimal mineral resource estimates in mining operations</b>]]> Cokriging uses a sparsely sampled, but accurate and precise primary data-set, together with a more abundant secondary data-set, for example grades in a polymetallic orebody, containing both error and bias, to provide improved results compared to estimation with the primary data alone, as well as filtering the error and mitigating the effects of conditional bias. The method described here may also be applied in polymetallic orebodies and in other cases where the primary and secondary data could be collocated, and one of the data-sets need not be biased, unreliable, etc. An artificially created reference data-set of 512 lognormally distributed precious metal grades sampled at 25x25 m intervals constitutes the primary data-set. A secondary data-set on a 10x10 m grid comprising 3200 samples drawn from the reference data-set includes 30 per cent error and 1.5 multiplicative bias on each measurement. The primary and secondary non-collocated data-sets are statistically described and compared to the reference data-set. Variograms based on the primary data-set are modelled and used in the kriging of 10x10 m blocks using the 25x25 m and 50x50 m data grids for comparison against the results of the cokriged estimation. A linear model of coregionalization (LMC) is established using the primary and secondary data-sets and cokriging using both data-sets is shown to be a significant improvement over kriging with the primary data-set alone. The effects of the error and bias are filtered and removed during the cokriging estimation procedure. Thus cokriging using the more abundant secondary data, even though it contains error and bias, significantly improves the estimation of recoverable reserves. <![CDATA[<b>Localized uniform conditioning (LUC): method and application case studies</b>]]> A new method, localized uniform conditioning (LUC), was proposed in 2006 for modelling grades of small blocks of ore when data spacing is too broad for their accurate modelling by the linear regression based techniques, such as kriging (Abzalov, 2006). It represents a modified uniform conditioning (UC) technique that calculates the grade distribution functions for the large panels. LUC uses partitioning of the panels onto the small blocks and then ranks them in increasing order of grade. Based on the block ranks, a single grade value can be deduced for each block from the UC model of the grade-tonnage relationships of the corresponding panel. After being first presented in 2006, the LUC method has been implemented in ISATISĀ© (commercial software) and became one of the common approaches for grade estimation when data spacing is broad in comparison with the estimated block size. Several years of study on the LUC method and its application to different geological environments, have allowed identification of the strengths and weaknesses of the method, which are as follows: ► The method produces accurate grade-tonnage functions, which are in a good accordance with a volume-variance relationship principles ► An initial ranking of the selective mining unit (SMU) blocks can be made by direct kriging from the sparse data grid. Therefore, the LUC method can be particularly useful at the early stages of exploration and mining project evaluations when sparsely distributed data is often the only available information ► Accuracy of the local estimation depends on the SMU ranking techniques. When ranking performed by direct kriging of the SMU blocks their spatial distribution is approximate. When the variogram of the studied variable is characterized by a large nugget effect, the block ranks produced by kriging can significantly differ from their 'true' distribution ► Block ranking can be improved using auxiliary data, either geophysical or geochemical. This allows use of the LUC method for integrating different data sets. In particular, LUC can be used for grade control in open pits by integrating resource definition data (e.g. drill-hole assays) and blast-hole assays. The latter are used for the block ranking. <![CDATA[<b>Communicating confidence in Mineral Resources and Mineral Reserves</b>]]> SYNOPSIS Mining is an inherently risky business; from the technical, environmental, social, and economic uncertainties associated with advancing an exploration prospect to a viable project to the operating, market, and safety risks and uncertainties attached to a developed mine. Since we cannot totally escape the risk and uncertainty related to resource projects, as an industry we should improve our presentation of the upside and downside risks in the context of the project's development path and maturity. More transparent, consistent, and balanced views of technical confidence will better inform both internal and external stakeholders about the expected risk in the project. International reporting codes set out the minimum standards, recommendations, and guidelines for public reporting of Exploration Results, Mineral Resources, and Mineral Reserves. However, the reporting code principles of transparency and materiality are largely subject to the interpretation of the competent person(s), which may introduce a degree of subjectivity in reporting, particularly the level of disclosure regarding supporting information. It is fundamental that Mineral Resources, Mineral Reserves, and study outcomes are reported so as to unambiguously present the level of inherent technical uncertainty (or confidence) in a project, while conveying a balanced view of the opportunities a project presents. Reporting needs to consider various stakeholders who may rely on this information, and present the data in the context of the changing risk profile associated with project development paths and project maturity. This paper discusses the interdependence of resource-to-reserve conversion, the consideration of various technical-economic study types, and the level of confidence conveyed to stakeholders relying on these technical reports and other company public announcements. <![CDATA[<b>Checks and measures of performance for kriging estimates</b>]]> Block model estimates are commonly calculated by the well-established technique of kriging. The mathematics are well established, but implementation details require site-specific considerations. Checking and measuring the performance of the estimates is important to ensure the block model is suitable for its intended purpose. There are different criteria for long-term planning and short-term planning. The implementation of kriging should be checked with cross-validation and assessed for conditional bias and departure from theoretical optimality with the calculation of kriging efficiency. A new expression of kriging efficiency, which compares the kriging variance with the theoretically optimal kriging variance, is developed to aid in this assessment. The assessment tools presented here can be applied in a number of situations; however, ordinary kriging with a reasonably large search performs well in most cases. <![CDATA[<b>Validity range of the discrete Gaussian change-of-support model and its variant</b>]]> The discrete Gaussian model is a very popular change-of-support model for estimating block grade distributions. It is designed for a stationary random function Z(x) that is regarded as the transform of a stationary random function Y(x) with Gaussian marginal. It is based on an assumption that is not fully true and thus constitutes an approximation to the exact solution. We examine the effect of this approximation on the modelling of the marginal distribution of block values of a lognormal random function. The initial discrete Gaussian model and a variant of that model are considered <![CDATA[<b>Genetic algorithms and scenario reduction</b>]]> Scenario reduction is designed for selecting a representative subset of geostatistical simulations out of a much larger set. Three steps are involved: measuring the dissimilarity between two simulations; finding a metric to measure the distance between any subset of k simulations and the full set of N simulations; and finding an efficient algorithm for selecting the subset that minimizes the metric. This paper focuses on the third question. We show that genetic algorithms are an efficient way of approaching the minimum when the population of subsets to be sampled is large. Two case studies based on the Walker Lake data-set are presented: firstly choosing k=4 simulations out of a total of 100, and secondly choosing 20 out of the same 100 simulations. In the first case it was possible to compute all possible combinations exhaustively and hence to demonstrate that the algorithm converges to the true minimum. This was not possible in the second case. Instead we demonstrate that it outperforms the random draw algorithm used in earlier work. A procedure for tracking individual selections during the iterative procedure was developed. This allows us to measure the evolution in the percentage of progeny resulting from crossing-over and from mutation that survived in the next generation. It gives valuable insight into how to choose the parameter values in the algorithm. Another key finding is that there is a trade-off between the number of individuals per generation and the number of generations required for the algorithm to converge. <![CDATA[<b>Kriging, indicators, and nonlinear geostatistics</b>]]> Historically, linear and lognormal krigings were first created to estimate the in situ mineral resources of blocks. Nonlinear geostatistics and indicator kriging were subsequently developed to evaluate also the portion recovered when applying a cut-off on selective mining units (SMUs) within blocks. In practice these methods are generally based either on the Gaussian model with a transformation generalizing the lognormal case or on the indicators above cut-offs. Very often the indicator approach is simplified by kriging separately each indicator, and when starting from a continuous variable, a practical advantage of the discretization into classes lies in the easy treatment of a zero effect and of the high values. However, a number of so-called isofactorial models have also been developed for a discrete or continuous variable, where the full cokriging of indicators (i.e. disjunctive kriging) simplifies to the separate kriging of factors. Moreover, these models are equipped with a change of support, allowing a consistent estimation of recoverable resources on SMUs. Min-Max Autocorrelation Factors (MAF) analysis of the indicators offers a new approach for indicator modelling. In particular the first factor, the one with the highest spatial continuity, can help in choosing the type of model. For example a monotonic experimental first factor can be used directly as the basis of a discrete diffusion model, unless a continuous diffusion model such as the Gaussian model can be used on the original variable. This approach is illustrated on a uranium deposit mined selectively: estimates of recoverable resources by discrete disjunctive kriging and uniform conditioning in a Gaussian model are compared locally to short-term estimates based on two areas densely drilled. <![CDATA[<b>Improved varicography using simulated annealing to adjust sample locations to align with diamondiferous linear beach structures</b>]]> At Namdeb, submerged beaches are earmarked for sampling and future mining and various sampling configurations are tested for optimality through the use of spatial simulations. For the creation of these virtual orebodies, basic statistics and variograms are needed, but in this specific instance no data exists from which the necessary parameters can be determined. The best that can be done is to use proxy data from onshore beaches, with adaptations where needed. The reworking of raised beaches during periods of rising and falling sea levels in some cases destroyed the internal beach structures, and it is very difficult to determine the variograms. A method is proposed whereby simulated annealing is used to adjust the sample locations to align the data pertaining to beach crests or cliff lines, thus improving the variogram structure along the shoreline in the direction of the highest geological continuity. <![CDATA[<b>Capping and kriging grades with long-tailed distributions</b>]]> Variogram analysis and kriging lack robustness in the presence of outliers and data with long-tailed distributions, which often arises when estimating grades in precious metal deposits. The capping technique, consisting of truncating the data to some top-cut grade, is widely used in order to mitigate the influence of the values in the upper tail of the distribution. However, this procedure omits part of the grade variability and is likely to provoke a bias in the estimates. To avoid these issues, a recently proposed approach is to decompose the grade of interest into three components (the truncated grade, a weighted indicator above the top-cut grade, and a zero-mean residual) and jointly estimate the truncated grade and the indicator by cokriging. This approach is attractive as it provides unbiased grade estimates, allows choosing the 'optimal' top-cut value, and essentially works with truncated and indicator data, thus avoiding the use of outlying values for calculating sample variograms and performing spatial interpolation. This work presents an application of this approach to a disseminated gold deposit that has been identified through exploration drilling. The effect of using an indicator covariate is assessed through leave-one-out cross-validation, by comparing the grade estimates with the true grades and with the grade estimates obtained with the conventional capping approach, which considers only the truncated grade as the variable of interest. As a result, cokriging the truncated grade and the indicator above top-cut grade outperforms the conventional capping approach, yielding significantly more accurate estimates. A few complementary guidelines are provided for validating the model hypotheses and for the implementation of cokriging <![CDATA[<b>Mineral resource classification: a comparison of new and existing techniques</b>]]> A survey of 120 recent NI 43-101 technical reports was conducted to evaluate the current state of practice regarding resource classification techniques. The most common classification techniques are based on search neighbourhoods (50% of recent reports), drill-hole spacing (30% of recent reports), and/or kriging variance (6% of recent reports). Two new techniques are proposed. The first is based on kriging variance and involves removing one or more drill-holes with the highest weights while performing kriging and using the resultant kriging variance for classification. This technique has the advantages of variance-based techniques and reduces artifacts. The second technique is based on conditional simulation and uses a moving window approach for classification at the desired selective mining unit resolution based on larger production volume criteria. This technique has the advantage of accounting for heteroscedas-ticity, which is a common characteristic in mineral deposits, and also reduces artifacts since a production volume scale is considered for the actual classification. The drill-hole spacing, search neighborhood, kriging variance, and simulation-based techniques are described and compared for 2D and 3D examples with regular and irregular drilling patterns to highlight the advantages and disadvantages of each method. <![CDATA[<b>Enhanced geological modelling of the Upper Elsburg reefs and VCR to optimize mechanized mine planning at South Deep Gold Mine</b>]]> South Deep Gold Mine, owned by Gold Fields Ltd., is situated near Westonaria in the Gauteng Province of South Africa and mines the conglomerate bands of the Upper Elsburg reefs (Mondeor Conglomerate Formation) of the Witwatersrand Supergroup and the Ventersdorp Contact Reef (VCR) of the Ventersdorp Supergroup. The stoping and underground developments are mechanized. The Upper Elsburg reefs are mined by a variety of mining methods, including mechanized drift and fill, modified drift and bench, longhole stoping, and low-profile mining. Optimal mine design and scheduling for deep-level mechanized mining are complex, and success is highly dependent on detailed, robust, and accurate geological and geostatistical models. Geological structures significantly influence the sedimentological characteristics, distribution, and preservation of the Upper Elsburg reefs and VCR. Accordingly, particular emphasis is placed on the generation of a mine-scale structural model that accommodates the relationships between the older north-trending fault systems (West Rand and Panvlakte faults) and younger east-trending dextral wrench faults. Results from underground mapping, borehole intersections, and high-resolution three-dimensional seismic data have been integrated to produce coherent three-dimensional geological models. The Upper Elsburg reefs suboutcrop against the VCR and comprise an easterly diverging clastic wedge, thickening from the suboutcrop position, to approximately 130 m at the mine's eastern boundary. The Upper Elsburg reefs are characterized by conglomerate and quartzite bands forming multiple, stacked, upward-fining unconformity-bounded couplets. Palaeocurrent directions are dominantly from west-northwest to east-southeast, indicating that the more proximal deposits are preserved close to the suboutcrop, with distal facies to the east. Sedimentological modelling is applied to individual stratigraphic units and caters for facies definition. This is achieved through channel width (CW) kriging and fitting of type sections to borehole and mapping data. Homogenous geological geozones for each stratigraphic unit are thus defined within individual structural blocks on the basis of those sedimentological parameters that have been found to have a positive spatial correlation to gold concentration. These geozones then serve as constraints to the evaluation of the orebody. This contribution presents a summary of the modelling processes that are currently applied in the development of high-confidence, timeously produced geological models that are essential input for mineral resource estimation and mechanized mine planning and scheduling <![CDATA[<b>Production reconciliation of a multivariate uniform conditioning technique for mineral resource modelling of a porphyry copper gold deposit</b>]]> The paper provides a brief review of a multivariate uniform conditioning and a localized multivariate uniform conditioning (LMUC) technique, and presents a production reconciliation case study based on a porphyry copper-gold deposit in Peru. The reconciliation study compares the long-term LMUC mineral resources model (typical of new mining projects, which are invariably based on drilling data on a relatively large grid) to the corresponding production blast-hole grade control model, as well as the final plant production.