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For practical reasons all basic input data for the gold mines of the Anglovaal Group conform to a regular grid of averages of sample values within 25-ft squares in the plane of the ore body; individual sample values with their metric co-ordinates are input and converted by a computer program to the basic 25-ft square averages. At the Prieska copper mine the bore- hole data are forced on to a regular grid of 15-m squares corresponding to the coordinates of the grid points nearest to the actual borehole intersections. As for the gold mines the Prieska ore body, although some 3 to 30 m thick, is also dealt with on a two-dimensional basis (Krige, 1973). On the gold mines the data subjected to geostatistical analysis cover: gold values (in cm g/t), uranium values (cm kg/t), and channel widths (cm). The gold and uranium values are normalised on the basis of log (value plus constant) and all the geostatistical analyses are performed on these transformed values. The channel widths usually conform reasonably well to the normal distribution and are, therefore, not transformed. At Prieska the metal grades analysed cover the two main products, copper and zinc, as well as the impurities lead and bismuth; in addition the specific gravity values and the hanging- and foot-wall deviations from a projection plane are also handled. These were all previously used on an untransformed basis but because of problems associated with the proportional effect the lognormal-de Wijsian model is now used for some of the grade variables. The key computer pro- grams can be summarised briefly as follows:

Jan 1, 1981

By Roger A. Blais, Michel David

"Matheron's geoslalislical method for the estimation of ore reserves has been developed to the point at which real-life problem may be handled effectively. The steps involved in the method are:(i) obtalning the variogram,(ii) fitting a model, and(iii) producing block estimates.All three steps may cause difficulty, and would-be users need a deep understanding of the theory if failure is to be avoided.To illustrate these points, specific cause are considered:(i) two almost equidimensional porpbyry deposits, one drilled randomly and the other regularly; and(ii) two iron formation, one drilled extensively and being mined, while the other is still at the stage of early estimation."

Jan 1, 2014

By Marc Lavigne

"The Lac Knife graphite deposit was estimated, as part of a feasibility study, using a geostatistical ore reserve estimation method: ordinary kriging. Based on the geology and its interpretation, the results of a variogram study, and the statistical parameters of the grade distribution of the core samples and the composites through the mineralization, the deposit was divided into three separate zones (west, centre and east), and each of these zones was then analyzed and kriged independently.The geological ore reserve estimation results of ordinary kriging are compared to the results of a conventional method (sections) used previously. The two methods gave almost similar reserve figures. The conventional method provided a +2% estimation for tonnage and + 10% for grade because it ignored the spatial relation between sections and samples, and ordinary kriging gave a more accurate longitudinal definition of the deposit.Finally, the paper concludes with the advantages of proceeding with ordinary kriging, namely: higher flexibility (change of cut-off grade), better deposit resolution and enhanced selectivity for the design of the open pit.IntroductionWithin the context of a complete feasibility study for the Société d' Exploration Minière Mazarin Inc., specialists of the Mines and Geology Division of Roche Ltd., Consulting Group, defined a modelling method appropriate to the graphite deposit of the Lac Knife property near Fennont. Many patterns were considered. Based on the geology of this deposit, the planned mining method, the statistical parameters of grade distribution and the variogram study, the process of reserve estimation retained was to use the ordinary kriging in a selective way. It was required because the geometry of the deposit is such that it was unthinkable to apply ordinary kriging without restrictions.This paper gives a detailed explanation of the observations and interrogations which led to the choice of this ore reserve estimation method, and the calculation procedure itself."

Jan 1, 1991

By Leahey T. A

The variability of gold mineralization in the Warrego Gold Pod is described by classical statistical techniques using sample distrib- utions and analysis of variance; and by the use of geostatistical variogram analysis to define the spatial variability and anisotropy of the mineralization. Comparison is made between declared mine production from the Nineteen Stope and a series of ore reserve estimates derived by manual, numerical and disjunctive kriging methods.

Jan 1, 1979

By Indranil Roy

Gua supergene enriched iron ore deposit from Jharkhand, India has been geostatistically modeled. Population modeling shows a negatively skewed 3-parameter log-normal fit for Fe and positively skewed 3-parameter log-normal fit for Al2O3 and SO2. Semi-variographic studies for Fe indicate spherical function fit using point kriging cross-validation technique with Co=4.06(%)2, C5.11 (%)2, Co+C=9.1 7(%)2 and 'a'=348m. Kriging with 50mx50mx 10m block size at 740mRL led to a global mean kriged estimate of 61.98% and kriging variance of 4.04(%)2 for Fe with central 90% geostatistical confidence limits at 61.39% and 62.24% for that level. This led to an ore inventory at 740mRL as 7.29 million tonnes of ore.

Jan 1, 2002

By Sarkar B. C, Sen A. K

India is well endowed with vast reserves of banded hematite ore, about 12 billion tonnes, estimated by some conventional methods. Various authors have assessed this huge reserve using some advanced geostatistical methods. A Banded Iron Formation (BIF) belt named the `Singhbhum-Keonjhar-Bonai' belt in India has been chosen as a case study. In this paper, the experiences of Chiria iron ore, in particular, have been described. This study will finally create a dynamic mineral inventory after standardising the geostatistical parameters which will help to cater for the needs of the stringent quality requirements of the Indian steel industries.

Jan 1, 1995

By Sirayanone S, Rashad MZ

An important problem occurring in the iron and steel industry of Egypt is the presence of manganese oxide and chlorine with different percentages in the Bahariya Iron Ore Deposit, Western Desert, Egypt. In this work we used a geostatistical method known as the Volume- Variance Relationship to predict grade fluctua- tions of Fe% , Mn% and Cl% in the ore after blasting a certain volume from the ore deposit, on the other hand, if we have a certain limit for each of these chemical components, we can select the bench blasting dimension to give these limits.

Jan 1, 1986

By Mehmet Guney

[The Atlantis-II-Deep is a hydrothermal mineralization located along the median valley of the Red Sea at a water depth of about 2200 m. Extensive exploration of the metal-rich brine deep revealed a potentially mineable deposit on economic interest consisting of oxides, silicates and sulphides with considerable concentrations of zinc, copper, cadmium and silver. Geostatistics was applied to assess the most likely in-situ vague of the metal potential for economical exploitation. Semi-variograms were constructed to characterize the structure of the regionalized distribution of the geological parameters. Volume grades and thicknesses were determined by the kriging technique, avoiding systematically biased high or low grades, and then block .tonnages were computed. The estimation variances, distribution of errors and histograms of observed and kriged values in each grid Mock were also produced.]

Jan 1, 1983

A case study for the application of a novel geostatistical technique for resource estimation of a narrow steeply dipping, gold-silver mineralized quartz vein deposit is presented. The technique is novel in two respects. First, mineral grades are kriged directly rather via the accumulation method more often applied to vein deposits and, second, a modified 2D ordinary kriging algorithm is used that allows the calculation of a single grade and variance for irregular shaped blocks of varying sizes. The objective of this investigation was to evaluate the suitability of this novel geostatistical technique for resource estimation of the Poura mine deposit and, if appropriate, to lay a firm foundation for future geostatistical work at the mine. The reserve estimation concentrated on the remnant ore blocks and pillars in both underground and surface workings. The data, which was collected in 2D coordinates with grade and vein thickness values, was first analyzed statistically and used to compute experimental semi-variograms. Appropriate semi- variogram models were fitted and various aspects of the estimation technique were evaluated using cross-validation error analysis, with acceptable results. A block kriging computer program called Krige2D was developed to implement the modified 2D kriging algorithm and calculations. Production data were not available to evaluate the computed block resources, but they were compared with a previous resource data determined using an arithmetic approach. The geostatistical technique estimated slightly higher grades but lower overall tonnages as compared to the earlier arithmetic estimates.

Feb 1, 2004

By P. K. Frempong, S. D. Butt

"A case study for the application of a novel geostatistical technique for resource estimation of a narrow steeply dipping, gold-silver mineralized quartz vein deposit is presented. The technique is novel in two respects. First, mineral grades are kriged directly rather via the accumulation method more often applied to vein deposits and, second, a modified 2D ordinary kriging algorithm is used that allows the calculation of a single grade and variance for irregular shaped blocks of varying sizes. The objective of this investigation was to evaluate the suitability of this novel geostatistical technique for resource estimation of the Poura mine deposit and, if appropriate, to lay a firm foundation for future geostatistical work at the mine.The reserve estimation concentrated on the remnant ore blocks and pillars in both underground and surface workings. The data, which was collected in 2D coordinates with grade and vein thickness values, was first analyzed statistically and used to compute experimental semi-variograms. Appropriate semivariogram models were fitted and various aspects of the estimation technique were evaluated using cross-validation error analysis, with acceptable results. A block kriging computer program called Krige2D was developed to implement the modified 2D kriging algorithm and calculations. Production data were not available to evaluate the computed block resources, but they were compared with a previous resource data determined using an arithmetic approach. The geostatistical technique estimated slightly higher grades but lower overall tonnages as compared to the earlier arithmetic estimates."

Jan 1, 2004

By J. -M. Chautru

A geostatistical simulation of a typical mining site for polymetallic nodules in the North Pacific Ocean is presented. This is the first stage in the design of an industrial mining system. Two variables which have a major effect on the orebody's economic potential are considered, namely: the maximum slope of the ground inside a mining block of 50 x 100 m; and the average quantity of nodules on the same support. Two geostatistical problems have emerged in this study. The first is due to the lack of a change of support model for the maximum of a variable. A provisional solution, considering an experimentally accessible 'equivalent' support, is proposed. The second is due to a non-linear link between the two variables. To be able to take this into account in the simulation, we propose a new method based on the decomposition: X = E(X/Y) + Residue (X). Satisfactory results were obtained with this approach.

Jan 1, 1987

By J. A. McLennan

Nickel laterite deposits are typically formed from tropically weathered mafic-ultramafic complexes. The resulting nickel concentration is found within soil horizons and is mineable with regular dozer units. At the time of mining, digging elevations are needed at selective mining units (SMUs). Moreover, for mine planning, the costs due to dilution and lost ore require mining elevations to be specified. A conditional simulation approach is used to calculate ?optimum? SMU mining elevations. Multiple realizations of the ore base surface are simulated. For a single bottom surface realization, dilution and lost ore costs are calculated over the entire vertical extent of each SMU. The optimum mining elevation is the elevation where the lowest summed cost of ?accepting dilution? and ?wasting ore? occurs. The reported SMU dilution is the cost of mining the volume of waste located below the bottom surface and above the optimum mining elevation and the reported SMU lost ore is the cost of not mining the volume of ore above the bottom surface and below the optimum mining elevation. For all ore bottom surface realizations, optimum SMU mining elevations and their associated dilution and lost ore costs are calculated and compiled to represent production uncertainty.

Apr 1, 2005

By J. A. McLennan, J. M. Ortiz

Nickel laterite deposits are typically formed from tropically weathered mafic-to-ultramafic complexes. The resulting nickel concentration is found within soil horizons and is mineable with regular dozer units. At the time of mining, digging elevations are needed at selective mining units (SMUs) or representative dozer regions (RDRs). Moreover, for mine planning, the costs due to dilution and lost ore require mining elevations to be specified. A conditional simulation approach is used to calculate “optimum” RDR mining elevations. Multiple realizations of the ore base surface are simulated. For a single bottom surface realization, dilution and lost ore costs are calculated over the entire vertical extent of each RDR. The optimum mining elevation is the elevation where the lowest summed cost of “accepting dilution” and “wasting ore” occurs. The reported RDR dilution is the cost of mining the volume of waste located below the bottom surface and above the optimum mining elevation. The reported RDR lost ore is the cost of not mining the volume of ore above the bottom surface and below the optimum mining elevation. For all ore bottom surface realizations, optimum RDR mining elevations and their associated dilution and lost ore costs are calculated and compiled to represent production uncertainty.

Jan 1, 2006

By M Field

Kimberlite pipes, as opposed to dykes, sill and secondary deposits, are the primary target for diamond exploration companies because they have simple geometries and can contain large volumes of potentially diamond-bearing ore. Once discovered, important decisions have to be made regarding the sampling of these geological entities to establish the total volume of ore present, and to define the internal geology, which can be complex in nature and controls the distribution of diamond grade. It is essential that as part of this process the uncertainty in constructed geological models are assessed. In this paper the Orapa AK1 kimberlite pipe in Botswana is used as a case study to explore a potential methodology for defining this uncertainty. The uncertainty of the rock volumes of different types can be characterised by a geostatistical approach. Geostatistical simulations, based upon a plausible representation of the geological bodies, provide different possible images of the orebody that can be considered as different realities. By testing different borehole layouts and drilling the orebody virtually on the computer, many different, but equi-probable realisations of the pipes can be produced. It is then possible to estimate the rocksÆ volumes and compare them with the actual ones. A statistical analysis of the relationship between estimation error and the number of boreholes can then be used to optimise the next sampling campaign. The rock volumes are obtained from a two-step simulation process. Firstly, the pipe geometry is simulated by means of introducing variations around the geological block model, by an original method called centre point simulation (CPS), which has been developed for this purpose. Secondly, the internal geology is then simulated within the pipe. The methodology for simulating the internal geological zones has to be adapted to the level of information and to the geological structure itself. The upper portion at Orapa AK1 is filled with sedimentary crater facies. Here plurigaussian simulation techniques can be applied that are adapted to the simulation of sedimentary facies. The central zones of the pipe are typically subvertically-oriented massive volcaniclastic deposits and breccias and the lower regions comprise a complex root zone. CPS is appropriate for these zones.

Jan 1, 2006

By Shrivastava P

The iron orebodies of the Pilbara region are formed by supergene enrichment of banded iron formation and rarely do such processes produce orebodies with uniform grade distrib- utions. The orebodies being mined or developed have to be worked to grade/quality constraints imposed by contractual agreement rather than natural characteristics. Hence it is imperative to use a non-biased ore reserve calculation method. The geostatistical study of a typical iron orebody is presented. Emphasised are the geological characteristics of the orebody manifested as a variable grade distribution of iron and impurities; the determination of variogram model; subsequent uses of the model for computation of ore reserves and kriged lock estimates; computation of dispersion variance and conditional simulation of orebody.

Jan 1, 1977

By Th. Petropulos

The Zn-Ag-Pb mineralization zone near Molai (Greece) was explored by more, than 60 drillholes. Promising results led to the decision of additional drillholes in order to confirm the expected spatial extension of the deposit. A multiobjective approach is described which optimizes the location of a set of 5 additional drillholes. The decision is based on estimation errors for grade, thickness and depth of the main ore bearing layer, with respect to cut-off values for grade and thickness. The linear combination of these variables defines a favorability index which is used for mapping optimal drillhole locations. The map shows several clusters of favorable cells. A declustrering algorithm is used to select a representative cell for drilling in each cluster.

Jan 1, 1989

By M. H. M. von Wielligh

"Brick manufacturers supply a variety of uniquely coloured facebricks to the building industry, which requires a high level of colour consistency in the products. Colour variation in bricks is influenced by the composition and consistency of the white clay raw material. By blending varieties of naturally occurring white clay the manufacturers produce a unique range of facebrick products. Homogeneity of the white clay raw materials mined at Lenasia is crucial for producing bricks of consistent colour. Geostatistical investigations of the major element distributions (SiO2, Al2O3, Fe2O3, and K2O) and loss on ignition (LoI) were conducted. An analysis of the spatial continuity of these variables followed by ordinary kriging indicated that the upper white clay layer at Lenasia is richer in K2O and Fe2O3 than the lower layer. Consistency in the colour of facebricks depends critically on careful management of the variability in the K2O and Fe2O3 content of the clays. The geostatistical approach to understanding the distribution of elements in the clay allows miners to construct clay stockpiles of consistent quality for feeding the brick-making process. Geostatistical investigation of the chemical contents in other clay domains within the deposit is recommended, and could be extended to all facebrick manufacturers to assist in improving the colour consistency of their products. IntroductionMost clay in South Africa is used in the manufacturing of tiles, pipes, bricks, whiteware, refractories, and pottery. Bricks are manufactured from a wide variety of clay types, the behaviour of which during firing depends critically on the the clay mineralogy and chemical composition, but this relationship not well understood (Stein, 1982). The variety among clay deposits is related to the different processes of formation (Deer, Howie, and Zussman, 1992). The geochemical composition of the clay can vary between layers and within the same layer in an individual deposit (Lurie, 1984). The properties of clay minerals are determined by their structures and the different combinations of silicate layers, cations, and hydroxyl ions (Kingery, Bowen, and Uhlmann, 1976). South African clays can be classified as either kaolinite or montmorillonite and are seldom found in a pure form (Lurie, 1984). Different clay minerals affect the drying, forming, firing behaviour, colour, and quality of the brick product in different ways. Laboratory tests (full physical analysis) can indicate the suitability of a clay for the manufacture of ceramic products. The minerals most essential for the manufacturing of clay brick products are kaolinite, illite, and quartz (Stein, 1982)."

Jan 1, 2017

By Dimitrakopoulos R

Ore textures in base metal deposits are an important factor in the liberation of the economic components of the ore, metal recovery and reagent consumption during beneficiation. Optimising the mine profit requires knowing the relationship between ore texture and mineral processing behaviour, and the ability to predict the metal grade and the ore texture at a suitable scale. A new method that generates distributions of mesotextures for any mining block size or shape is proposed and includes: I . establishing a protocol for acquiring mesotexture data: 2. measuring the mesotexture spatial correlations using a multi-texture variogram; 3. generating multiple simulations of mesotextures; and 4. upscaling the simulations to generate the expected mining block/stope mesotexture distributions. Models of the ore textures built using the proposed methodology can be used to assess resources and reserves, enhance ore/waste discrimination and predict the metallurgical behaviour of parcels of ore.

Jan 1, 1997

By Ramani R. V

In this paper, a comparative performance evaluation of geostatistical, spectral, and fractal methods is made for short-scale variability prediction. The algorithms compared are: sequential Gaussian simulation method; a random fractal algorithm based on the generalised stochastic subdivision method; and a spectral simulation approach adopted for direct multi-dimensional simulation. The data for this study have been obtained from a mined out coal property. As this property was being mined, a 7315 m by 7315 m (24000 ft by 24000 ft) coal block was extensively sampled at an approximate spacing of 107 m (350 ft) and the 60-ton samples were analysed for sulphur in the 1.50 float gravity fraction. This data set is used here with the three methods to generate the simulated realisations, which are analysed for semivariogram reproduction and for simulation errors. Although all three methods converge to the true semivariogram in an average sense, the coefficient of variation of the average semivariogram for the Fourier integral method is minimum. The realisations generated by the sequential Gaussian method have minimum mean simulation error. The choice of a simulation method based on variability reproduction and simulation errors remains difficult.

Jan 1, 1995

By M Humphreys

Multi-episodic mineralisation is often characterised by different spatial trends exhibited by different generations of the mineralisation. The structural complexity of mineralisation together with the heterogeneous nature of the mineralised zones prevents unambiguous application of the conventional deterministic methodology for 3D constraining of the mineralised domains (ie conventional wireframing is ambiguous).A different approach, discussed in the present paper, includes a probabilistic definition of the domains encompassing one statistical population of the data. The domains are defined geostatistically using the indicator probability model. An indicator threshold is chosen for the definition of the high and low-grade domains. The spatial distribution of this indicator is then modelled by a variogram. The probability of exceeding the given grade threshold is than estimated by ordinary kriging for each modelled block. Blocks are then grouped according to their probability of exceeding the threshold and a continuous closed volume (domain) created from this likely patchy grouping using an appropriate structural model to fill the gaps). Methodology for the geostatistically assisted domaining is discussed in the paper. It is suggested that this technique represents an additional tool facilitating a structural interpretation of the mineralised zones.After the geostatistical domaining of the lode has been completed the grade within each of the domains is modelled using Uniform Conditioning method. Application of Uniform Conditioning for modeling the grade distribution has a significant advantage over linear methods (such as inverse distance or kriging) because Uniform conditioning enables estimation of local recoverable resources at different selective mining unit sizes that can be substantially smaller than the drilling density and are unable to be estimated directly.

Jan 1, 2002