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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 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

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

In the estimation of reserves the known values of the variables of interest from surrounding drill holes are used to compute or estimate the unknown value of the orebody over a given region or at a given point of interest. The classical means of doing this are: 1. The Polygonal Method û where the region is divided into polygons centred on bore holes, each variable is then assumed to have constant value over each polygon. 2. Inverse distance methods, where the variable is assumed to vary linearly with the distance between the known values of the drill holes. 3. Inverse distance squared method û a quadratic variation is assumed for the variables between the bore holes.

Jan 1, 1983

By A. H. Onur, S. Ural

"The Afsin-Elbistan coal deposit with its 3.4 billion metric tons of reserve is the biggest coal basin and one of the most important resources for electrical energy production in Turkey. The coal deposit is located north of Elbistan, Kahramanmaras Province, in southeast Turkey (Fig. 1).The Kislakoy sub-basin of the Afsin-Elbistan basin was selected as the first open cast mine to feed four power station blocks of 340 MW each. The mine is equipped with six identical bucket wheel excavators of the type Sch Rs (2300/5) 32. The annual coal demand of the power station is 18.5 million metric tons. The Elbistan basin encompasses an area of 900 km2, and its centre lies about 1150 m above mean sea level. The sedimentation took place mainly in the upper Pliocene period. The thickness of the coal bed varies from 20 m to 60 m, respectively. The basal part of the coal beds consists of clay, marl and sandy clay. These formations are overlain by gyttja, which may also occur in the form of calcareous ooze, enveloping coal beds. The thickness of the gyttja is up to 35 m (Otto-Gold, 1969). The coal of Afsin-Elbistan is soft coal and the quality has been found to vary considerably throughout the deposit. The thicknesses of the sterile intercalations vary from 0.50 m to 2.2 m and average 1 m in thickness. From the quality control point of view, the coal seam is regarded as upper seam where the gyttja formation occurs as sterile intercalations, and lower seam where the clay formation occurs instead of the gyttja (Fig. 2). The CaO content of upper Kislakoy coal is very high, grinding resistance is low and base to acid ratio of ash, that is, the ratio of acid oxides of metals to base, is greater than one (Ural and Onur, 2001). Contrary to upper Kislakoy coal, CaO content of lower Kislakoy coal is very low, grinding resistance is high and base:acid ratio of ash is smaller than one. Modified Impact Strength Index (MISI) tests are used to determine the grindability of the Elbistan coals (Ural, 1999)."

Jan 1, 2003

By Jennifer Riefenberg

Ground control hazards, coal quality, ore reserve estimation, and pollution modeling seem unrelated topics from most mining perspectives. However, geostatistical methods can be used to characterize each of these, and more topics. Exploratory drill core data, and continued drilling and field measurements, can provide a wealth of information related to each of the above areas and are often severely underutilized. Recent studies have led to the development of the Multiple Parameter Mapping (MPM) technology, which utilizes geostatistics and other numerical modeling methods, to generate a "hazard index" map, often from exploratory drill core data. This mapping has been presented for ground control hazards relating roof quality, floor quality, numerically modelled stresses due to mining geometry, and geologic features. A review of the MPM method, future directions with the MPM, and a discussion of using these and other geostatistical methods to quantify coal quality, ore reserve estimation, and pollutant modeling are presented in this paper.

Jan 1, 1996

By Oy Leuangthong

The McMurray formation in the Athabasca oil sands deposits of Northern Alberta is part of the world?s second largest proven crude oil reserves. The formation is characterized by stratigraphic layers that correspond to three different depositional environments: Marine, Estuarine and Fluvial facies. Resource estimation for oil sands has traditionally relied on polygonal and inverse distance schemes. These techniques are simple and straightforward in practice, but they do not permit reliable uncertainty assessment. This paper describes the modeling of the McMurray formation using modern geostatistical techniques. Geostatistical modeling should be performed within homogeneous geological facies. The methodology for geostatistical simulation within each of the identified facies involves: (1) assessing the most appropriate stratigraphic transformation for optimisation of the correlation structure, (2) determining representative distributions with declustering and debiasing techniques, (3) modeling spatial continuity of the bitumen grade, fines grade, water saturation and other petrophysical variables, (4) performing estimation and cross validation as checks against simulation results, (5) performing simulation for uncertainty quantification of bitumen and fines grade, and (6) model checking of simulation results against the input data and comparisons against the kriged models. These steps are described in detail. The application of these models for uncertainty quantification in support of resource classification is also discussed.

May 1, 2004

By P Landeros, D Benado, J Cornejo, A Pinochet, C Caviedes

In 2005, El Teniente mine began preconditioning the primary rock mass by hydraulic fracturing (HF). The major perceived benefits of this process are a decrease in the magnitude of the expected maximum seismic event and improved cave propagation. In addition, HF has resulted in new information on the propagation pressures of each fracture. Previous studies have attempted to relate propagation pressure to minor principal stress or confining stress.Considering the spatial continuity of propagation pressure and the significant quantity of collected data since the incorporation of the HF technique, minimum requirements for geostatistical modelling have been reached, permitting robust estimates inside the representative volume with acceptable errors (Cornejo, Muñoz and Rojas, 2012; Cornejo and Landeros, 2013). These results are then used to identify zones with higher magnitudes, which are mostly related to more complex geotechnical zones (intrusive and major faults) and caving singularities, making it possible to estimate the spatial extension of these zones.Finally, these results are integrated with other geomechanics aspects to support risk analysis of the mining plan.CITATION:Cornejo, J, Landeros, P, Benado, D, Caviedes, C and Pinochet, A, 2016. Geostatistical modelling of hydraulic fracturing pressures at El Teniente Mine, in Proceedings Seventh International Conference and Exhibition on Mass Mining (MassMin 2016), pp 183–190 (The Australasian Institute of Mining and Metallurgy: Melbourne).

May 9, 2016

By Raymond G. F

Geostatistics - a tool used by geologists and mine planning engineers to estimate grades and rapidly evaluate alternative mining strategies has reached an advanced stage of development for the silver-lead-zinc orebodies at Isa and Hilton Mines. Geostatistics has been used for over a decade in the massive copper orebodies but the stratiform lead-zinc orebodies are much more complex and provided a completely different set of challenges. Recent increases in computer processing speed and power provided by the Integrated Mine Planning System (IMPS) has aided the development of the geostatistics package. Also the formation of a project team and the subsequent in-house development which has drawn together the expertise of geologists, engineers and system analysts has contributed significantly to the success of the project.The most important feature of any approach to modelling the lead-zinc orebodies is that the kriging search must consider estimate and sample points according to their positions relative to bedding surfaces. By transforming co-ordinates as perpendicular offsets from a plane representing the local strike and dip, it is possible to elongate the ellipsoidal influence to parallel bedding. By interactively modelling surfaces using CAD facilities and then specifying these surfaces as 'hard' or 'soft' boundaries, the geologist has complete control over the kriging process.

Jan 1, 1993

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

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

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. 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 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 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 Dominique Francois-Bongarcon

The world mining industry is facing a severe recession. Thus, it is time to recall the value of geostatistical methods which were formerly developed as a money-saving and productivity-increasing tool. The situation has worsened, but the techniques of geostatistics have dramatically changed. Up to millions of dollars can be saved during exploration with simple use of variograms; then, during reserves estimation with kriging methods; and finally, with the parameterization of reserves, when evaluating a project and optimizing its global mining parameters.

Jan 1, 1983