Scielo RSS<![CDATA[Journal of the Southern African Institute of Mining and Metallurgy]]>
http://www.scielo.org.za/rss.php?pid=0038-223X20140008&lang=es
vol. 114 num. 8 lang. es<![CDATA[SciELO Logo]]>http://www.scielo.org.za/img/en/fbpelogp.gif
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<![CDATA[<b>Danie Krige</b>]]>
http://www.scielo.org.za/scielo.php?script=sci_arttext&pid=S0038-223X2014000800001&lng=es&nrm=iso&tlng=es
<![CDATA[<b>President's Corner</b>]]>
http://www.scielo.org.za/scielo.php?script=sci_arttext&pid=S0038-223X2014000800002&lng=es&nrm=iso&tlng=es
<![CDATA[<b>Professor D.G. Krige FRSSAf</b>]]>
http://www.scielo.org.za/scielo.php?script=sci_arttext&pid=S0038-223X2014000800003&lng=es&nrm=iso&tlng=es
<![CDATA[<b>Criteria for the Annual Danie Krige Medal Award</b>]]>
http://www.scielo.org.za/scielo.php?script=sci_arttext&pid=S0038-223X2014000800004&lng=es&nrm=iso&tlng=es
<![CDATA[<b>Memories of Danie Krige</b> - <b>Geostatistician Extraordinaire</b>]]>
http://www.scielo.org.za/scielo.php?script=sci_arttext&pid=S0038-223X2014000800005&lng=es&nrm=iso&tlng=es
<![CDATA[<b>Advancement in vertical tunnelling in mining</b>]]>
http://www.scielo.org.za/scielo.php?script=sci_arttext&pid=S0038-223X2014000800006&lng=es&nrm=iso&tlng=es
<![CDATA[<b>Use of geostatistical Bayesian updating to integrate airborne radiometrics and soil geochemistry to improve mapping for mineral exploration</b>]]>
http://www.scielo.org.za/scielo.php?script=sci_arttext&pid=S0038-223X2014000800007&lng=es&nrm=iso&tlng=es
SYNOPSIS Mineral exploration programmes around the world use data from remote sensing, geophysics, and direct sampling. On a regional scale, the combination of airborne geophysics and ground-based geochemical sampling can aid geological mapping and mineral exploration. Since airborne geophysical and traditional soil-sampling data are generated at different spatial resolutions, they are not immediately comparable due to their different sampling density. Several geostatistical techniques, including indicator cokriging and collocated cokriging, can be used to integrate different types of data into a geostatistical model. However, with increasing numbers of variables the inference of the cross-covariance model required for cokriging can be demanding in terms of effort and computational time. In this paper a Gaussian-based Bayesian updating approach is applied to integrate airborne radiometric data and ground-sampled geochemical soil data to maximize information generated from the soil survey, enabling more accurate geological interpretation for the exploration and development of natural resources. The Bayesian updating technique decomposes the collocated estimate into two models: prior and likelihood models. The prior model is built from primary information and the likelihood model is built from secondary information. The prior model is then updated with the likelihood model to build the final model. The approach allows multiple secondary variables to be simultaneously integrated into the mapping of the primary variable. The Bayesian updating approach is demonstrated using a case study from Northern Ireland. The geostatistical technique was used to improve the resolution of soil geochemistry, at a density of one sample per 2 km², by integrating more closely measured airborne geophysical data from the GSNI Tellus Survey, measured over a footprint of 65 x 200 m. The directly measured geochemistry data were considered as primary data and the airborne radiometric data were used as secondary data. The approach produced more detailed updated maps and in particular enhanced information on the mapped distributions of zinc, copper, and lead. The enhanced delineation of an elongated northwest/southeast trending zone in the updated maps strengthened the potential for discovering stratabound base metal deposits..<![CDATA[<b>Witwatersrand gold reef evaluation: the ‘variancegram’ tool</b>]]>
http://www.scielo.org.za/scielo.php?script=sci_arttext&pid=S0038-223X2014000800008&lng=es&nrm=iso&tlng=es
SYNOPSIS The resolution with which the different categories of resources are forecast for Witwatersrand gold reefs should ideally tie in with block sizes that are optimal in terms of the variability structures of the reefs. A tool, called the 'variancegram', is proposed as a basis for block size choice. A variancegram is intrinsic to the particular reef and mine concerned. A further requirement is the ability to attach global confidence limits to weighted average estimates built up from combinations of local kriged estimates. Approximations to derive global kriging variances based on variables derived from local kriging deliver hugely inflated results if ordinary kriging is used, and markedly better, but not accurate, values if simple kriging is used. These approximations improve as the number of samples used in kriging each block is increased. It is shown that the behaviour of the different components of the global kriging variance with increasing number of samples, all differs, but they all link to the variancegram for the particular reef. The variancegram can thus be used to correct the different components to the values they would have had if all samples were used in kriging each block, and so deliver the 'correct' global kriging variance, even though only a limited number of samples were used in kriging each block. The desirability of having very stable solutions implemented in production systems is taken into account in the proposals. It is anticipated that the same variancegram findings will also hold for other densely sampled deposits, but this remains to be investigated.<![CDATA[<b>Analysis of the dispersion variance using geostatistical simulation and blending piles</b>]]>
http://www.scielo.org.za/scielo.php?script=sci_arttext&pid=S0038-223X2014000800009&lng=es&nrm=iso&tlng=es
SYNOPSIS The additive property of dispersion variances was found experimentally by D.G. Krige using data from the gold deposits of the Witwatersrand. In this property, called 'Krige's relationship', the dispersion of a small unit, v, within the deposit is equal to the sum of the dispersion of v within a bigger unit, V, and the dispersion of these units, V, within the deposit, D. It is known that the variance of the grades decreases as the support increases, the so-called volume-variance relationship. To analyse volume-variance and Krige's relationship, the methodology herein proposed combines blending piles and geostatistical simulation to simulate the in situ and the pile grade variability. Variability reduction in large piles is based on the volume-variance relationship, i.e. the larger the support, the smaller the variability (assuming perfect mix). Based on a pre-defined mining sequence to select the blocks that will form each pile for each simulated block model, the statistical fluctuation of the grades derived from real piles can be simulated. Using this methodology, one can evaluate within a certain time period the expected grade variability for various pile sizes, and also calculate the Krige's relationship between the small blocks and the piles of different sizes. A real case study using a large Brazilian iron ore deposit illustrates the methodology and demonstrates the validity of the results.<![CDATA[<b>Geostatistics: a common link between medical geography, mathematical geology, and medical geology</b>]]>
http://www.scielo.org.za/scielo.php?script=sci_arttext&pid=S0038-223X2014000800010&lng=es&nrm=iso&tlng=es
SYNOPSIS Since its development in the mining industry, geostatistics has emerged as the primary tool for spatial data analysis in various fields, ranging from earth and atmospheric sciences to agriculture, soil science, remote sensing, and more recently environmental exposure assessment. In the last few years, these tools have been tailored to the field of medical geography or spatial epidemiology, which is concerned with the study of spatial patterns of disease incidence and mortality and the identification of potential 'causes' of disease, such as environmental exposure, diet and unhealthy behaviours, economic or socio-demographic factors. On the other hand, medical geology is an emerging interdisciplinary scientific field studying the relationship between natural geological factors and their effects on human and animal health. This paper provides an introduction to the field of medical geology with an overview of geostatistical methods available for the analysis of geological and health data. Key concepts are illustrated using the mapping of groundwater arsenic concentration across eleven Michigan counties and the exploration of its relationship to the incidence of prostate cancer at the township level.<![CDATA[<b>Investigating 'optimal' kriging variance estimation using an analytic and a bootstrap approach</b>]]>
http://www.scielo.org.za/scielo.php?script=sci_arttext&pid=S0038-223X2014000800011&lng=es&nrm=iso&tlng=es
SYNOPSIS Kriging is an interpolation technique for predicting unobserved responses at target locations from observed responses at specified locations. Kriging predictors are best linear unbiased predictors (BLUPs) and the precision of the BLUP is assessed by the mean square prediction error (MSPE), commonly known as the kriging variance. Both the BLUP and the MSPE depend on the covariance function describing the spatial correlation between locations and on specific parameters. The parameters are usually treated as known, whereas in practice they invariably have to be estimated and the empirical BLUP (that is, the EBLUP) so obtained. The empirical or estimated mean square prediction error (EMSPE), or the so called 'plug-in' kriging variance estimator, underestimates the true kriging variance of the EBLUP, at least in general. In this paper five estimators for the kriging variance of the EBLUP are considered and compared by means of a simulation study in which a Gaussian distribution for the responses, an exponential structure for the covariance function, and three levels of spatial correlation - weak, moderate, and strong - are adopted. The Prasad-Rao estimator obtained using restricted or residual maximum likelihood (REML) is recommended for moderate and strong spatial correlation and the Kacker-Harville estimator for weak correlation in the random fields.<![CDATA[<b>Limitations in accepting localized conditioning recoverable resource estimates for medium-term, long-term, and feasibility-stage mining projects, particularly for sections of an ore deposit</b>]]>
http://www.scielo.org.za/scielo.php?script=sci_arttext&pid=S0038-223X2014000800012&lng=es&nrm=iso&tlng=es
SYNOPSIS A localized nonlinear recoverable resource estimate technique has been applied using typical feasibility or new mining drilling data configurations drawn from a massive database from a mined-out area on a hydrothermal gold deposit. The results were then compared with the corresponding 8 m W 5 m grid grade-control data in order to determine the efficiency of the approach and the validity of the recoverable resource estimates for mine planning and financial forecasts.<![CDATA[<b>Geostatistical applications in petroleum reservoir modelling</b>]]>
http://www.scielo.org.za/scielo.php?script=sci_arttext&pid=S0038-223X2014000800013&lng=es&nrm=iso&tlng=es
SYNOPSIS Geostatistics was initially developed in the mining sector, but has been extended to other geoscience applications, including forestry, environmental science, soil science, and petroleum science and engineering. This paper presents methods, workflows, and pitfalls in using geostatistics for hydrocarbon resource modelling and evaluation. Examples are presented of indicator variogram analysis of categorical variables, lithofacies modelling by sequential indicator simulation and hierarchical workflow, porosity modelling by kriging and stochastic simulation, collocated cokriging for integrating seismic data, and collocated cosimulation for modelling porosity and permeability relationships. These methods together form a systematic approach that can be effectively used for modelling natural resources.<![CDATA[<b>Designing an advanced RC drilling grid for short-term planning in open pit mines: three case studies</b>]]>
http://www.scielo.org.za/scielo.php?script=sci_arttext&pid=S0038-223X2014000800014&lng=es&nrm=iso&tlng=es
SYNOPSIS This paper shows the usefulness of geostatistical conditional simulation combined with the quantification of sampling errors obtained from the analyses of fundamental errors - validated from duplicate data - to assess the relevance of the quality and quantity of the information, for short-term mine planning purposes. Traditional blast-hole drilling equipment has been designed for efficient drilling, but not for obtaining high-quality samples. Furthermore, blast-hole sampling interferes with production, and thus usually produces poor-quality results. These results are the basis of short-term plans, where the grades of selective mining units are estimated and used for distinguishing between ore and waste. Under these conditions, misclassification (ore blocks sent to the waste dump and waste blocks processed at the plant) is inevitable, leading to significant hidden losses that can amount to millions of dollars per annum. Reverse circulation drilling with the latest automated sampling technology improves significantly the quality of the information used for short-term planning, and thus reduces misclassification, improving the financial returns of the operation. In this paper, we present the general methodology for assessing the effect of poor blast-hole sampling, as compared to advanced reverse circulation drilling grids at several spacings, in order to arrive at the most appropriate grid for short-term planning. This plan can be prepared well in advance using several additional variables that are usually not available when the plan is based on blast-hole samples. Furthermore, blending options can be analysed in order to optimize plant recovery, minimize the use of sulphuric acid, etc. Three case studies are presented, namely a typical porphyry copper deposit, an exotic oxide copper deposit, and a complex gold deposit, where mineralization is controlled by structures and lithology. This paper shows that in all cases, advanced reverse circulation drilling grids provide good-quality information that, coupled with the use of geosta-tistics for short-term mine planning, significantly improve the financial returns of the operation.<![CDATA[<b>On localizing uniform conditioning estimates</b>]]>
http://www.scielo.org.za/scielo.php?script=sci_arttext&pid=S0038-223X2014000800015&lng=es&nrm=iso&tlng=es
SYNOPSIS Localized uniform conditioning is a technique developed to spatially locate selective mining unit grades that have been derived using uniform conditioning for the assessment of recoverable resources. The technique has the advantage of producing selective mining unit estimates conforming to the uniform conditioning panel-specific grade-tonnage curve while introducing spatial information at the scale of the selective mining units. This paper describes an alternative technique to localized uniform conditioning which does not explicitly require the uniform conditioning panel-specific grade-tonnage curve to localize the selective mining unit estimates. The technique can therefore be implemented in mining software where uniform conditioning is not available.<![CDATA[<b>Iron oxide Cu-Au (IOCG) mineralizing systems: an example from northeastern Russia</b>]]>
http://www.scielo.org.za/scielo.php?script=sci_arttext&pid=S0038-223X2014000800016&lng=es&nrm=iso&tlng=es
SYNOPSIS GIS and multivariate geometric distribution have been used to predict the association of high-level intrusives with hydrothermal alteration related to iron oxide Cu-Au (IOCG) mineralizing systems. Several examples in the Russian northeast are presented in this paper. IOCG ore deposits can have enormous geological resources containing significant reserves of base, precious, and strategic metals, and hence are economically attractive targets for mineral exploration. To date, examples of this type of mineralization have not been reported from the northeastern area of Russia. The Tarinskiy ore cluster, located in Eastern Yakutia, shows brecciated altered rocks with sulphide and iron oxide cement, which is typical for IOCG mineralization of the iron oxide Cu-Au±U type. This cluster was formed near surface and is linked with the Rep-Yuruinskiy pluton. It has potential to host new world-class precious metal deposits in northeastern Russia<![CDATA[<b>Factorial kriging for multiscale modelling</b>]]>
http://www.scielo.org.za/scielo.php?script=sci_arttext&pid=S0038-223X2014000800017&lng=es&nrm=iso&tlng=es
SYNOPSIS This paper presents a matrix formulation of factorial kriging, and its relationships with simple and ordinary kriging. Similar to other kriging methods, factorial kriging can be applied to both stationary and intrinsic stochastic processes, and is often used as a local operator. Therefore, the concepts of intrinsic random function and local stationarity are first briefly reviewed. Kriging is presented in a block matrix form in which the kriging solution is useful not only for understanding the relationships between simple and ordinary kriging methods, but also the relationships between interpolative kriging and factorial kriging. When used as a signal/noise-filtering method, factorial kriging is especially useful for multiscale modelling. Examples for general signal analysis and geophysical data signal filtering are given to illustrate the method.<![CDATA[<b>Application of a localized direct conditioning mineral resource modelling technique for medium- and long-term planning of underground mining operations</b>]]>
http://www.scielo.org.za/scielo.php?script=sci_arttext&pid=S0038-223X2014000800018&lng=es&nrm=iso&tlng=es
SYNOPSIS At the exploration stage for new mining projects or for medium- and long-term areas of existing mines (typical of South African gold mines), drilling data is on a relatively large grid. This grid is normally larger than the selective mining units (SMUs). Direct estimates for the SMUs and also of much larger block units will then be smoothed due to the information effect and the high error variance. Any capital-intensive project decisions made on the basis of any of the smoothed estimates will tend to misrepresent the economic value of the project or operation, i.e. the average grade of blocks above cut-off will be underestimated and the tonnage overestimated for cut-off grades below the mean grade of the orebody. This paper presents a direct approach technique for deriving recoverable resources, referred to as localized direct conditioning (LDC), designed to correct smoothing effects and also to provide support corrections.<![CDATA[<b>On the reduction of algorithmic smoothing of kriged estimates</b>]]>
http://www.scielo.org.za/scielo.php?script=sci_arttext&pid=S0038-223X2014000800019&lng=es&nrm=iso&tlng=es
SYNOPSIS Utilizing a very large database from a mined-out area on a South African gold mine, the relative efficacy of a method to mitigate the smoothing effect introduced by the algorithmic constraints imposed by kriging was investigated. Smoothing effects arising from limited data availability are differentiated from the smoothing arising from the application of estimation algorithms. Very little can be done to ameliorate smoothing of estimates because of too little data, barring additional drilling or sampling. However, the smoothing effects resulting from the kriging process are shown to be mitigated by use of an alternative algorithm. The primary criterion in the development of the new algorithm was to avoid re-introducing conditional bias. This paper examines firstly the smoothing effects introduced into estimates via the kriging covariance matrix, secondly the process for ameliorating the smoothing effect, and finally it uses a case study to demonstrate the effectiveness of the new algorithm on a very large database. The database was used to introduce a 60 m by 60 m drilling pattern which in turn was used to model the semi-variogram and produce 30 m by 30 m kriged block estimates. The follow-up database was then re-introduced (roughly 5 m by 5 m grid spacing) and averaged into 30 m by 30 m blocks to provide a direct comparison with the initial estimates. In this way the extent of smoothing and accuracy of the estimates before and after the corrections was tested.<![CDATA[<b>Multivariate block simulations of a lateritic nickel deposit and post-processing of a representative subset</b>]]>
http://www.scielo.org.za/scielo.php?script=sci_arttext&pid=S0038-223X2014000800020&lng=es&nrm=iso&tlng=es
SYNOPSIS Utilizing a very large database from a mined-out area on a South African gold mine, the relative efficacy of a method to mitigate the smoothing effect introduced by the algorithmic constraints imposed by kriging was investigated. Smoothing effects arising from limited data availability are differentiated from the smoothing arising from the application of estimation algorithms. Very little can be done to ameliorate smoothing of estimates because of too little data, barring additional drilling or sampling. However, the smoothing effects resulting from the kriging process are shown to be mitigated by use of an alternative algorithm. The primary criterion in the development of the new algorithm was to avoid re-introducing conditional bias. This paper examines firstly the smoothing effects introduced into estimates via the kriging covariance matrix, secondly the process for ameliorating the smoothing effect, and finally it uses a case study to demonstrate the effectiveness of the new algorithm on a very large database. The database was used to introduce a 60 m by 60 m drilling pattern which in turn was used to model the semi-variogram and produce 30 m by 30 m kriged block estimates. The follow-up database was then re-introduced (roughly 5 m by 5 m grid spacing) and averaged into 30 m by 30 m blocks to provide a direct comparison with the initial estimates. In this way the extent of smoothing and accuracy of the estimates before and after the corrections was tested.