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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 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 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 Y. C. Kim

The results from a retrospective study are described in this gaper in which she past development drilling activities were investigated using geostatistics. The purpose of the study was to determine the amount of savings in drilling cost that could have been realized through the optimal placement of sequential drill holes using geostatistics. Out of 144 DDH's that were in place within the study area, the results showed a possible elimination of 34 DDH's without any reduction on the confidence interval of the global reserve estimates. If the incremental savings from one drilling campaign to the next were considered, however, the amount of percentage savings were even greater. Other interesting results from this study were; 1) tangible demonstration of the importance of a proper geologic delineation within the study zone, and 2) the robustness of the obtained experimental variograms from the rather early stage in development drilling.

Jan 1, 1981

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 D. E. Ranta, M. G. Hester

The ore reserve modelling of stratiform uranium deposits to be mined by selective underground mining methods must be done with consideration of the erratic nature of the ore-forming processes that produced the mineralization. Estimation methods that model the uranium grade as a smooth transition between high-grade and low-grade drill hole intercepts tend to greatly overestimate the ore tonnage. Care must be taken to first establish realtistic ore pod geometries and then estimate the grade of the reserve units within the pods.

Jan 1, 1992

By M. G. Hester

The ore reserve modeling of stratiform uranium deposits to be mined by selective underground mining methods must be done with consideration of the erratic nature of the ore forming processes that produced the mineralization. Estimation methods that model the uranium grade as a smooth transition between high grade and low grade drillhole intercepts tend to greatly overestimate the ore tonnage. Care must be taken to first establish realistic ore pod geometries and then estimate the grade of the reserve units within the pods.

Jan 1, 1985

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 O. Babak, J. G. Manchuk

ABSTRACT A significant factor in evaluating bitumen recovery from an oil sands mine is the particle size distribution (PSD). Increased understanding of mined ore quality and improvement in predictions of recovery can be achieved through PSD modeling. This paper addresses PSD modeling using geostatistics. PSDs may be described using many discrete particle sizes, making this a challenge. The approach parameterizes PSDs with a few statistics. A lookup table is used to reconstruct the PSDs based on models of the statistics. The workflow is applied to Total E&P Canada’s Joslyn Lease and yields good results that reproduce input statistics without introducing artifacts.

Jan 1, 2013

By W Patton, I Minniakhmetov, H Talebi, U Mueller

The sustainability of mining projects is linked to informed investment decisions based on public reporting of exploration and mineral resource estimation results. In Australia, public reporting guidelines are established by the Joint Ore Reserves Committee reporting code through the JORC Code (2012). Although the assessment of uncertainty in the results reported is a requirement, this is often communicated qualitatively and evaluated subjectively. This can become a liability particularly in the early stages of mining projects when spatial domains of geological interpretation and mineralisation envelopes inform resource estimations’ reliability. A recent review of JORC reports found no reports used quantitative assessments of the geological interpretation or mineral resource estimation envelopes, and 27 per cent of reports did not address the question of quality of geological interpretation. Reports that did address the quality used 19 different terms to communicate quality. This work presents methodologies for quantitative uncertainty assessment and communication and explores how they could be applied in public reporting practice. Quantitative uncertainty reporting would benefit mine planning and financial modelling as they normally assume the geology is 100 per cent right (since no error is reported or only a single deterministic model is provided). The complexity, cost, and additional work of doing a quantitative assessment could hinder a straightforward implementation. This could be overcome if mining companies budget for quantitative uncertainty assessment and associated professional development. A compulsory requirement for the inclusion of uncertainty assessments in public reporting or adopting standardised subjective language would improve industry practice.

Mar 22, 2022

By C V. Deutsch

"Geometallurgical variables often cause problems to conventional geostatistical workflows. There are many variables; some are compositional and some are non-additive. They often show: complex multivariate relationships undersampling relative to conventional grade variables unequal sampling; that is, all variables are not available at all data locations.A variety of approaches have been developed over the years, but geostatisticians remain mostly focused on modelling rock types and a few grade variables with an abundance of data. The problems are reviewed and a chained workflow is presented where appropriate techniques are employed in sequence to permit reliable spatial prediction of geometallurgical variables. The spatial models may be used to assess the value of additional data, for prediction of process performance, for improved mine planning and other optimisation tasks. The chained workflow will include data transformations such as ratios and normal scores that make the variables amenable to geostatistical modelling. Data imputation techniques to account for missing values are considered with special consideration to spatial correlation with the available data. Decorrelation techniques such as the principal components, min/max autocorrelation factors and projection pursuit multivariate transformation are employed to manage massively multivariate modelling. Full distribution modelling must be considered to avoid biases in the prediction of non-additive variables. The post-processing of geometallurgical models must be streamlined for robustness and efficiency. The precise workflow varies according to the specific purpose of the study. Guidelines and thoughts on best practice are presented.CITATION:Deutsch, C V, 2013. Geostatistical modelling of geometallurgical variables - problems and solutions, in Proceedings The Second AusIMM International Geometallurgy Conference (GeoMet) 2013, pp 7-16 (The Australasian Institute of Mining and Metallurgy: Melbourne)."

Sep 29, 2013

By Kalyan Saikia

An integrated statistical-geostatistical modelling of gold exploration data of Gurahar Pahar prospect of Mahakoshal greenstone belt in Central India has been attempted. Statistical modelling of gold accumulation and width reveal a positively skewed 2-parameter lognormal distribution fit with an estimate of mean gold as 0.84 gram/tonne. Geostatistical modelling provided a spherical semi-variogram function fit with mean kriged estimate and mean kriging variance of gold as 0.76 gram/tonne and 0.23 (gram/tonne)2 -respectively. Ore inventory and grade-tonnage relationships for a selected part provided an estimate of 3,36,000 tomes of ore with an average gold of 0.76 gram/tonne at 0.5 gram/tonne cutoff grade.

Jan 1, 2002

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 O. Leuangthong, E. Schnetzler

"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 modelling of the McMurray formation using modern geostatistical techniques.Geostatistical modelling 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 optimization of the correlation structure; 2) determining representative distributions with declustering and debiasing techniques; 3) modelling 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."

Jan 1, 2006

Plurigaussian simulation allows constructing lithofacies or rock type models that reproduce the contacts between facies in accordance with the geologist?s interpretation. Its implementation requires inferring the local facies proportions, but the uncertainty in the true proportions is not accounted for. The simpler model with constant facies proportions may not yield realistic results, due to the possibility of obtaining facies at locations where it is geologically unlikely to find them. This article presents a variation of the plurigaussian model, in which the facies proportions are represented by random fields. The realizations can be made conditional to soft geological informati onto account for local changes in the facies proportions. The model is illustrated via a case study of a porphyry copper deposit where four Gaussian random fields are simulated conditionally to drill hole data and to constraints on the probability of finding a given facies at specific locations (control points) in the deposit. Then the first two fields are truncated using the random thresholds defined by the last two, generating a three-facies model. The proposed random proportion model proves to be simple to use and to account for spatial variations of the geological characteristics and for the uncertainty in the facies proportions. Keywords: categorical variable; lithofacies; truncated plurigaussian simulation; regionalized proportions

Jan 1, 2008