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By Leach B. G

A geostatistical study was made of diamond drill hole intersections within 18CC stope block at the C.S.A. Mine, Cobar, N.S.W. The stope block is located in 18CC orebody which is a massive sulphide - multiple vein, Copper-Zinc type, lacking clear definition on gangue mineralogy, base-metal assays and total sulphide considerations. Of the variograms constructed for inter- section width and copper, lead and zinc grades and accumulations, only zinc displayed behaviour amenable to model fitting and kriging procedures. Zinc grades were calcu- lated for sub-blocks comprising the total stope block and comparison with equivalent grades determined by traditional methods showed them to be generally less extreme in the highest and lowest grade sub-blocks. The total-block grades derived by the two methods were almost the same. It is suggested that the failure of copper to show variogram continuity might reflect the difficulty in defining the actual 18CC orebody, a proposition which is supported by the poor continuity in the variogram of horizontal width. In the case of lead the poor continuity may be due to the frequent manner of occurrence of galena as coarse grained patches of limited extent. The results of the study, did not provide a convincing reason to depart from the traditi- onal methods of grade estimation at the C.S.A. Mine.

Jan 1, 1979

By D. Rucker

Flow models are used to predict the extraction efficiency of metals in rock piles. These models typically use hydraulic parameters obtained through column studies, which assume that the material in the column wholly represents the entire pile and the parameters can be upscaled several orders of magnitude for model evaluation. This assumption fails for parameters that are spatially variable or scale dependent. To overcome these issues, measurements made directly on the heap at the appropriate model scale can be made with the electrical resistivity method. The method aims to map the variations in the electrical resistivity, which can be associated with moisture content, degree of fines, metal content, and leachate concentration. We present an example of calibrating the resistivity with borehole measurements of moisture using geostatistics to show how the resistivity method can be used to obtain a spatial moisture distribution. It was shown that cokriging the resistivity and moisture together gives a more reliable distribution.

Jan 1, 2010

By Michael J. Friedel

As part of a study aimed at understanding the hydrology of in situ leach mining (ISLM), the Bureau of Mines, in cooperation with the Cyprus Casa Grande Corporation and the University of Arizona, is investigating dynamic transmissivity conditions during ISLM of a copper oxide ore deposit. Spatial and temporal variations in ore zone transmissivity during two years of ISLM operations at the Cyprus Casa Grande mine are evaluated during sixteen intervals of steady-state injection and recovery well operation. Direct inversion of an analytical hydrologic model is used to obtain estimates of transmissivity at 58 well locations during these intervals. Univariate statistical and geostatistical methods are used to describe the temporal and/or spatial relationships that exist between transmissivity and other ISLM parameters, including average well injection pressure, average sulfuric acid concentration in leach solution, and the relative configuration of injection and recovery wells. Average transmissivity during the sixteen steady-state time intervals varies between 6.00 x 10-6 m2/min. (6.46 x 10-5 ft2/min.) and 3.61 x 10-8 m2/ min. (3.89 x 10-7 ft2/min.). A trend toward decreas¬ing transmissivity is evident during two year of ISLM operations. This decreasing trend is found to correlate with a decreasing sulfuric acid concentration in injected leach solution, and suggests increasing geochemical precipitation within the deposit. Geostatistical analyses reveal a dynamic and anisotropic transmissivity structure within the target ore zone, that is dependent upon spatial and temporal changes in injection pressure and well configuration.

Jan 1, 1992

By Robert M. Owen

Geochemical exploration for marine placers involves the acquisition, processing, and interpretation of geochemical data. Recent technological advances such as in-situ analysis systems and microcomputers have greatly improved our ability to acquire and process data, but their full benefits cannot be realized until we also develop improved methods for reducing and interpreting large amounts of raw geochemical data. Toward this end, our research has sought to identify existing and/or develop new geostatistical techniques for use in marine placer exploration. Each technique has been tested by evaluating its performance in the analysis of existing data sets. The data sets typically include the results of chemical analyses of suites of sediment samples collected from areas of known or suspected platinum and gold placers along the Bering Sea coast of Alaska. Results to date indicate that three geostatistical methods (subpopulation partitioning analysis, comparative factor analysis, and end-member compositional factor analysis) are useful in identifying elemental groups which can serve as "pathfinders" in the search for marine placers, and are also helpful in discerning the generic geochemical basis under lying observed statistical correlations between pathfinder elements and placer minerals. Existing methods of modelling sediment dispersal patterns have been examined with a view toward adapting them to the specific problem of understanding placer formation in

Jan 1, 1986

By R. Cao

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.

Jan 1, 2014

By Royle A. G

The paper describes a geostatistical structural analysis of an 80 square mile lease of the Athabasca tar sands. Each step of the analysis is presented with the ultimate objective of condensing the principal structural characteristics of the chosen regionalised variables into the opera- tional form of the variogram model. The variogram model is then used to form kriged local and global estimates, with the corresponding estimation errors.

Jan 1, 1977

By J. C. Danza Errico

The bauxite deposits on the Pocos de Caldas Plateau in the state of Minas Gerais, Brazil, were formed by the differential weathering and leaching of alcaline rocks in a ring structure. Their action on steep topography formed heterogeneous ore posture and chemical grades. Variographic analysis of several of these deposits show nested structures that are probably related to ore genesis. Kriged ore reserves estimation are presented with emphasis on the data pro cessing method that was employed. Programs were written in APL. Its intrinsic use of matrices contributed to faster programming and less computer time. In many cases looping was eliminated. The high resolution graphic resourses of APL. workspace facilitated programming of variogram analysis, fitting, and regularization. APL sub-routines are presented for variogram calculation and kriging.

Jan 1, 1986

By R. C. Bryan, D. B. Jamison

This paper describes a procedure for minimizing the operational costs associated with blending sodium in coal at a surface mine in the Powder River Basin. Mine site blending is performed by adjusting daily production rates for high- and low-sodium pits. These adjustments are designed to produce a consistent sodium value called the blending target. The mine's contractual limit for sodium is sufficiently close to the field average value that any decrease in the sodium blending target may result in an opportunity cost, if the number of potentially minable tons is reduced. Conversely, any increase in the blending target may result in a higher sampling cost if more information is required to keep the blend within contractual limits. Blending parameters were defined using a geostatistical block model of sodium content that was based on analyses of hundreds of in-pit sample holes. Variograms for these data were used to compute the marginal costs of opportunity and sampling for a series of hypothetical in-pit drilling patterns. These marginal costs provided a basis for selecting optimum values for key parameters such as the blending target, production variance and in-pit sampling density. The benefit of implementing these optimized parameter values is that operational costs of sodium blending will be minimized over the long-term. At the mine where this procedure was developed, each dollar spent to increase the sampling density to the optimum value was shown to generate a $10 savings in opportunity cost.

Jan 1, 1991

By C. Özgen Karacan

The formation of the gas emission zone in longwall mining and the potential amount of gas in this zone are factors of local geology and spatial variability within this geology. Therefore, geostatistical methods can be used for modeling and prediction of gas amounts and for assessing its uncertainty in the gas emission zone of longwall mines. This study used core data obtained from 64 exploration boreholes drilled from the surface to the bottom of the Pittsburgh coal seam in a mining district in the Northern Appalachian basin. After identifying important coal layers for the gas emission zone, semivariogram modeling was conducted for different coal seams to define the distribution and continuity of various attributes. Sequential simulations were performed for stochastic assessment of these attributes to calculate gas-in-place (GIP) in each coal seam. GIP calculations for coals of various gas emissions zones were combined and ranked for their cumulative distribution function to find GIP in the caved zone and in the fractured zone at the 5%, 50%, and 95% quantiles. Fifty percent quantile results were later used to isolate a panel from the whole area and create a mosaic representation corresponding to the daily advance rate of the longwall face. This approach helped to estimate the daily emissions of this panel from the caved zone and from the fractured zone. Results showed that gas-in-place in the Pittsburgh coal seam, in the caved zone, and in the fractured zone showed spatial correlations that could be modeled and estimated using geostatistical methods. This study showed that gas-in- place volumes in the study area may be as high as 12.3 Bscf and as much as 3.5 MMscf per acre of mining.

Jan 1, 2012

Knowledge of true block grades is obtained from a mathematical model of an orebody, simulated with sample grades normally distributed and spatially correlated according io a spherical semi-variogram model.The superiority of kriging to the polygonal method of estimation is demonstrated on this modelled deposit by comparing the true values with the kriged and polygonal estimates obtained from sampling the deposit. Finally, selection of blocks of the deposit on the basis of the estimated values, shows that if kriging is used, what is predicted is largely mined, whilst if the polygonal method is used large biases can occur depending on the position of the cut-off grade.

Jan 1, 1978

During a programme to determine the suitability of the UK site for deep disposal of radioactive wastes, geostatistical methods were used to characterise rock heterogeneity on the basis of seismic and wireline acoustic-impedance data. The data were analysed to yield semi-variogram models that quantified the three-dimensional spatial heterogeneity of acoustic impedance. These models were reconciled with geological interpretations of the area and used to generate simulations of acoustic impedance, with wireline acoustic impedance as conditioning data. The three-dimensional simulated images were compared with actual seismic acoustic impedance. The variography confirmed a vertical zoning effect in the Borrowdale Volcanics, showing that it is caused by preferential clusters of high acoustic impedance values corresponding to regions of relatively low porosity. The method provided realistic three-dimensional models from sparse, one-dimensional wireline data

Jun 19, 1905

By A. Unal

Coal resource characterization usually calls for estimating more than one variable over a block or node simultaneously. Within the realm of geostatistics, each variable has been evaluated independently from the others assuming a lack of significant correlation. Research conducted with coal seams, however, has shown that the variables of immediate interest, such as seam thickness, ash, sulfur content, and density depict some correlation schemes in distinct zones, if not throughout the entire area. The above findings have two immediate consequences : (1) correlation analyses provide guidelines to determine the geologically distinct zones, and (2) where possible, cokriging should be used instead of kriging. This will maximize data utilization decreasing the frequently criticized high estimation errors. The cokriging formulation will also provide more accurate estimates for under sampled variables using better-sampled ones. This is a common case with coal with regard to the non-cored reconnaissance drill holes for which only very few variables were recorded. A case study illustrates the improvements that may be obtained by taking advantage of the intervariable correlations.

Jan 1, 1986

By P. Diehl

The increasing public interest in a useful framework for an assessment and classification of mineral resources (1) is documented by the recently published international classification scheme of the United Nations (1979) and the revision of the classification system of USBM/USGS (2) (1980). Moreover, various classification systems are currently discussed by the mining industry. In spite of major improvements in respect of the concepts, definitions, and taxonomy of ore classification, it has been recognized that the recent practice to classify mineral resources does not create truly reproductible results, i.e. an assessment to the various categories which is free from personal bias or corporate interests. Following are geostatistical methods proposed for a standardization and quantification of various terms in ore classification. After critical review of present practices, we will establish a precise link between the classical terms such as "measured", "indicated", and "inferred" reserves and the geostatistical concept of estimation errors. Moreover, we will demonstrate, how the basic criteria of economic feasibility, geologic assurance and recovery can be taken into account by geostatistics. A specific algorithm will be proposed to block out and to classify reserves according to the degree of geologic assurance. . We will also show computerized methods which perform complete classification procedures, and will also exemplify them with typical case studies.

Jan 1, 1982

By G. Pan

A geostatistical approach is proposed for the design of infill drilling programs. The method consists of the following four major steps: developing geological favorability models, delineating mineralization and ore envelopes, classifying resource potentials, and designing infill drilling patterns. Geological modeling develops the permissible geological zones in which infill drilling is designed. Modeling mineralization and ore envelopes establishes criteria on the potential blocks to be drilled. The blocks that are included within the ore envelopes are considered in the infill drilling. The following four types of resource potentials are used in this analysis: measured, indicated, possible and barren. Blocks in the indicated category are the top targets to be confirmed in infill drilling. Blocks of possible resources may be considered exploration targets. The algorithms involved in the analysis include indicator favorability analysis, indicator kriging and ordinary kriging. A case study on a gold deposit of the Carlin type is presented to demonstrate the methodology. The deposit was originally delineated by a sparse drilling program with about 230ft of average spacing. The infill drilling design, based on the new method, suggests a significant reduction on the number of holes from a regular-grid infill drilling pattern.

Jan 1, 1996

By G. Pan

A geostatistical approach is proposed for the design of infill drilling programs. The method is consisted of three major steps: developing geological favorability models, delineating mineralization and ore envelopes, and classifying reserves or resources. Geological modeling aims at developing favorable geological zones in which drilling is designed. Modeling mineralization and ore envelopes establishes criteria on potential blocks to be drilled. Top target blocks should be those included within ore envelopes. The framework of resource categories includes five types: probable reserves, indicated reserves, indicated resources, possible resources, and barren. Indicated reserves or resources are the top priority to be drilled for the definition of minable reserves. Possible resources may be considered as targets for further exploration. The algorithms involved in the analysis include indicator favorablity analysis, ordinary kriging, and indicator kriging. A case study presented here involves a gold deposit of Carlin type. The deposit was delineated by a sparse drilling program with 230 feet of average spacing. The infill drilling program designed by the new method suggests a significant reduction on the number of holes from a regular-grid infill drilling pattern.

Jan 1, 1995

By J. A. McLennan

Geological uncertainty is an unavoidable characteristic of all mining projects since only limited information is available from sampling. Mine planning and development decisions with significant economic consequences are made when the geological heterogeneity is inherently uncertain. Geostatistical simulation is preferred over kriging because the methodology provides alternative property realizations that can be combined into a model of geological uncertainty. Geological uncertainty can be transferred into production uncertainty, which can help characterize the economic risk of the project. This paper presents a case study for the Pogo property, being prepared for development near Fairbanks, Alaska. The exact dimensions, grades and production predictions have been modified; however, the methodology is illustrative. The geostatistical methodology consists of (1) assembling the relevant drillhole data and establishing a suitable coordinate system, (2) calculating the target distribution, (3) creating a model of spatial correlation, (4) generating multiple realizations at a small scale and (5) linearly averaging all the realizations to the chosen selective mining unit (SMU) support size. The geostatistical model is then used to calculate production uncertainty.

May 1, 2004

The theory and practice of sampling of particulate material have been the focus of a continued attention on the part of the mining industry worldwide for almost a century now, because of its critical importance at all phases of a mining project, from exploration (bulk sampling, assaying) to production (grade control) and marketing (quality control). A powerful, complete theory was put together by P. Oy (1968 to i982), but its applications to gold ores have met with limited success to date, due to the inadequacy of its sampling variance and minimum sample mass determination formulae to the challenging case of gold ores. This paper presents a research project completed at Inco Exploration and Technical Services Inc., using a geostatistical approach, to shed light on the results of P.Gy's theory, and adapt them to the case of particulate gold ores. After a reminder of Gy's formulae and a simplified demonstration of the generic form of Gy's and more traditional formulae, an empirical approach, based on sampling experiments from four gold deposits, shows how Gy's formulae must be corrected to adjust to the case of gold ores. The generality of the results formula is then substantiated with a geostatistical analysis of the problem. A parameterized formula results, and indications are given on how to fit its parameters to experimental data. Application guidelines and charts to fit any case and budget are presented, along with a detailed practical example.

Jan 1, 1991

By Armstrong M

The highest grades of the Porgera gold deposit, Papua New Guinea, are contained in Zone 7 due to the presence of the Roamane fault, which acted as channelway of the gold-bearing fluids. Prior to the development and underground mining of this fault-controlled high-grade zone it was critical to provide grade estimates of relatively small mining units, and of the proportion of mining units above cutoff. To be applicable to Zone 7 of Porgera a grade estimation method should account for the following:1. the highly skewed and apparently lognormal distribution of the grades,2. the rapid drop off of the local mean grade and the variance as the distance to the Roamane fault increases,3. the presence of high grade pockets in the footwall, away from that fault, and4. the existence of variograms for the logs with sills parallel to the fault and without sills perpendicular to it.

Jan 1, 1990

By Dominigue Francois-Bongarcon

This paper presents a step by step vulgarized review of the applications of geostatistics to the estimation of the mineable, recoverable reserves of the Cinola gold deposit in British Columbia.

Jan 1, 1988

By J. M. Ortiz

Mineral resource evaluation requires defining geological domains that differentiate the types of mineralogy, alteration and lithology. Usual practice is to consider the domain boundaries as hard, i.e. data from across the boundaries are disregarded when estimating the grades within a given domain. This practice may hinder the quality of the estimates when a significant spatial correlation of the grades exists across the domain boundaries. In this paper, several geostatistical methodologies to handle soft geological boundaries are compared through a case study on a copper mine in Chile. The estimation methods considered are: ordinary kriging using hard boundaries between geological domains; ordinary kriging omitting the geological boundaries; traditional and standardized ordinary cokriging of the grades assayed in different domains; ordinary kriging within dilated geological domains, that is, incorporating samples from adjacent domains up to a given radius from the boundary of the domain being considered. The estimations are performed using a set of exploration data (drill hole samples) and are validated using a set of production data (blast hole samples collected for grade control). Results indicate that kriging with dilated domains performs better than ordinary kriging using hard boundaries or no boundaries and better than the ordinary cokriging approaches. It therefore appears as a simple alternative to global kriging (without considering the geological domains) and allows accounting for changes in the grade average, dispersion and spatial continuity with the geological characteristics of the deposit, via the use of grade variograms proper to each geological domain. The maximal distance for searching samples from adjacent domains should be chosen according to the spatial correlation of the grades across the domain boundaries, or via a cross-validation at an early stage of the mine or a jack-knife if production data are available. Keywords: Kriging; cokriging; soft boundaries; hard boundaries; geological control; geological domains.

Jan 1, 2006