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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

Types of structure found in 'Jest Australian beach sands are described. Their recognition by geostatistical methods follows nth a discussion of the effectiveness of sampling patterns. Examples of structures are given, and an account of their effect on valuation procedures.

Jan 1, 1977

By Hassan Madani, A. Malek Mohammadi

Dorreh barite mine located in the central part of Iran is one of the largest barite mines, in the country. The mine is subdivided into three blocks, which are called block 1,2,3 according the barite quality. In the central part of each block, a heavily concentrated grid of exploratory drill holes have been drilled and the reserves of area was calculated based on these holes, some years ago. It was decided to compute the reserve of the area by geostatistical methods, in the form of an M.Sc. project. In order to study the area, three regionalized variables including density, thickness and density-thickness (accumulation) was studied and the spherical variograms were fitted to these variables. These models were evaluated by cross-validation method. The optimized block size was chosen in order to compute the reserves by kriging method. The reserves of explored parts of each block of mine was calculated and the results were extended to the whole area of the blocks. The reserve of the explored parts and the total reserve of the area were calculated to be 96,000t and 1,670,000t respectively.

Jan 1, 1996

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 W. D. Grundy, Frances Wahl Pierce, Jean-Paul Marbeau, Carol Waite Conner

Resource and coal quality estimates of three coal deposits in the Western United States were estimated by kriging, a geostatistical method that yields unbiased estimates with maximum achievable precision. Derived geostatistical models were used in kriging to estimate the tonnages of the deposits and to derive contour maps of thickness, structure, and sulfur content. Where data were available on quarter-mile spacing, kriging was used to obtain detailed information applicable to mine planning and design. Where data were sparse, kriging was used to do a preliminary evaluation of total resources. Geologic studies were required to correlate the individual coal beds and to identify complicating conditions such as the presence of faults, burnt zones, channels, and regional changes in thickness and elevation. Where these conditions were identified, they were explicitly integrated into the estimation procedure.

Jan 1, 1983

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

By Barton G. Stone

The mining and exploration industries have been using Geostatistics (Matheron, 1963) for the past forty years. It has been extensively incorporated into three dimensional block modeling software whose usage has reflected the growth in the use of personal computers since 1980. Because of the utility of geostatistical models in mining and production planning, much of the modern reserve and resource modeling is done by mining engineers, geostatisticians and geological engineers. Explorationists are initially less concerned with three dimensional models until such time as a deposit has been roughly delineated. However, the concept of regionalized variables in ore deposits deals with the effect of spatial correlations between data points in a three dimensional sample space and should be useful for optimizing the spacing of drill holes to allow maximum bang-for-the-buck in drilling programs. This paper examines three common deposit types (porphyry copper, VMS and intrusive gold) to examine whether geostatistical methods have been used to minimize drilling costs because of better understanding of spatial correlations. The three model types were chosen from publicly available corporate websites of Canadian based Junior Mining Companies. They include the Wolverine polymetallic zinc deposit of Yukon Zinc in Yukon, Canada; the El Morro Deposit in Chile (30 percent ownership by New Gold Mining Company, and the Fort Knox Gold deposit in Alaska and 50 percent ownership by Nova Gold Resources). Typically, individual mining corporations post their technical reports as CNI 43-101 reports on their corporate website as indications of the favorability or progress on their more exciting properties. Data considered for this paper was not collected or generated by the author, but the information was extracted from these publicly available sites and had a variety of authorship.

Oct 1, 2009

By Jaime Guzman

Mineral exploration decision problems involve the economic evaluation of upgraded geological information and the costs of obtaining it. This paper presents a valuation theory of risky projects applicable to the analysis of exploration investments. The valuation model is predicated on the Capital Asset Pricing Model (CAPM) from financial economics; its parameters can be objectively measured from publicly available information. Geostatistics is used to derive simplified random cash flow models which incorporate the impact of improved deposit knowledge in terms of reduced estimation variance. The application of the theory is illustrated by means of hypothetical exploration optimization examples.

Jan 1, 1986

By M. G. Hester

The inadequacy of traditional geostatistical methods for estimating some precious metals deposits has become apparent in the last few years. New methods or estimation such as Indicator, Probability and Multigaussian Kriging are difficult to understand and apply. Case studies using a new method of variogram calculation proposed by Srivastava show the method valuable for variogram estimation in precious metal deposits. Some simple, sometimes unorthodox. estimation methods that have proved useful in Some situations are presented.

Jan 1, 1990