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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

This study begins with the semivario- gram modelling of variables rutile grade and clay content from a beach sand rutile deposit. This is followed by two dimensional block kriging. The deposit was divided into blocks of 30 x 30 x 1.5 m dimensions and the kriged estimate together with the associated kriging variances for each variable within each block were determined. Finally, using the results of the krig- ing program and considering the acceptable limit of clay content together with the cutoff grade for rutile, a method for optimization of mineable thickness and hence the tonnage of ore was applied and the results were dis- Cussed.

Jan 1, 1986

By F. A. G. M. Camisani-Calzolari

Approximately 850 groundwater samples were collected over a 29 300 km2 region of the semi-arid Northwestern Cape during the site selection phase of the South African radioactive waste disposal project. The purpose of the geostatistical investigation was primarily to delineate metallogenic occurrences and provinces which might exist below the thin veneer of surficial material and could thus interfere with the suitability of the site, and to quantify the distribution patterns of groundwater parameters in order to establish a relationship to local and regional geology. Up to 34 variables were analysed for each sample. Structural analysis revealed that the study area is statistically uniform. The variables have low correlation coefficients, with the exception of major ions, indicating a general poor degree of interrelationship between the spatial distribution patterns of the different variables. On the other hand, the long semivariogram range of the majority of variables, which reaches 70 km in cases, demonstrates their continuity on a regional scale. Kriging, which was repeated for each parameter, reveals that most variables, particularly trace metals, have distribution trends which are not influenced by local geomorphology or surface lithology. A 50 km wide, 220 km long metallogenic province, defined by kriging, could possibly reflect a broad metallogenic imprint on the basement and could represent a target area for prospecting. Kriging also reveals the possible existence of a wrench faulting system which may well have influenced the Namaqualand coastal graben and the western boundary of the Karoo.

Jan 1, 1987

By A. A. Abdul-Latif, A. Sahin

"The phosphate deposit, located in the Abu Tartur plateau between the Kharga and the Dakhla Oases in the southern part of the Western Desert of Egypt, is the largest of its kind in the country. The phosphates are found in two horizons referred to as the Lower and Upper Phosphate Horizons within the Late Campanian Sibaiya Formation which belongs to the Nubia Group.This paper presents the results of a geostatistical study on the main phosphorite bed at the base of the Lower Phosphate Horizon which contains almost all the commercial reserves in the area. After semivariogram modeling for the phosphate thickness and accumulation, ordinary block kriging was employed to estimate the values of these variables in blocks of400 m by 400 m dimensions. The kriging results, which are presented in the form of contour maps, can be of considerable use in both future exploration and exploitation of the deposit. The grade-tonnage relationship based on the grade estimates derived from the corresponding thickness and accumulation estimates indicates the existence of 453.9 x 105 tonnes of phosphate above a cut-off grade of 18% P2O5. The mean grade of this tonnage has been estimated to be 25.77% P205"

Jan 1, 1990

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 G. H. Blackwell, A. J. Sinclair

"The main components of a ""PC” -based mineral inventory system are described in a sequence common to many real reserve/ resource estimation projects and in the practical context of problems and decision-making typically encountered in such studies. Some components are designed particuarly to improve the geostatistical instructional capability of the package. An important part of this approach involves the use of widely available software for data manipulation and evaluation in the design of a mineral inventory study progressing to mine design and feasibility. A variety of more or- less fixed routines written in high level languages provide acceptable computational speeds on a personal computer. These critical segments are linked by simple, short, compiled Basic programs easily adjustable to various data configurations and needs. IntroductionGeostatistical mineral inventory estimation has progressed greatly since its slow dissemination during the 1960s. The mining industry generally has accepted the benefits of the technique, notably the quantification of grade and geology, an indication of error in grade estimation, and of the mined volume / grade variance relationship (Clark, 1979, Isaacs and Srivastava, 1989).Acceptance has been slowed, first by complexities of geostatistical theory and second by a bewildering variety of computer systems and applications programs. Continuing improvements in education will facilitate a better understanding of the underlying theory.The purpose of this paper is to describe, in a practical context, the development of a geostatistical-based approach to reserve/resource estimation. The approach integrates various existing commercial software packages with a wide selection of programs developed by the authors for personal computers which estimate mineral inventories and educate users in the techniques applied; that is, the QMIN system.It is hoped that the approach presented here will convince mining and geological engineers concerned with resource estimation, of the soundness of geostatistical methods and its broad potential to their problems."

Jan 1, 1992

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 John S. F. Dunlop

One of the more difficult problems frequently facing geologists and mining engineers is that of estimating the ore reserves of mineral deposits. Cost conscious mining operations invariably require an accurate knowledge of tonnage and grade for both short and long term planning. A case study is presented, showing how a classical frequency distribution was fitted to a population of drillhole assays. Using these results, a grade- tonnage curve is derived using the Lasky expressions, and the results discussed. A geostatistical analysis is then presented. First, variograms are drawn, models fitted to them and analyses made of drift and anisotropy. Second, simple block kriging is carried out and the results plotted on large 1000 scale plans, suitable for overlay with routine .mine plans. Kriging results are verified using two independent techniques: random kriging on a regular grid and inverse distance weighting. Finally an attempt is made to optimize the drilling grid, and to fully tabulate the total computer running costs for the work described.

Jan 1, 1979

By Isobel Clark

The increasing complexity of modern mining technology makes it ever more difficult to decide on the 'best* way to solve problems in mine planning. Yet with escalating costs it becomes increasingly more important for the mining engineer to be able to evaluate quantitatively the implications of the 'what happens if' postulation on the efficiency and economics of exploitation. The use of a model of the orebody can yield an estimate, not just of overall expected results, but also of the sensitivity of these results to possible variations in the orebody. Estimation techniques, such as Kriging, will produce the expected value for the grade of ore at any given point, or over any given volume within a deposit. However, the actual grades mined during production will - of necessity - differ from the predicted values. These possible variations, and the sensitivity of the management decisions to them, can be investigated in detail by the use of simulation. An orebody can be simulated which follows the known characteristics of the deposit at any given stage in development. These properties might be the histogram of grade values, the semivariogram from the samples, the actual borehole assays, geological constraints and/or interpretation, topography, lease boundaries etc. This would be one possible 'realisation' of the deposit as dictated by the currently known data. If several of these simulations are carried out, each conditioned to the current knowledge of the orebody, then it is possible to gain an idea of the range of possible outcomes of any mining procedure or decision taken - all of which are equally likely. Not only can the best decision then be taken, but its sensitivity to the inherent variation within the orebody, and to the ever present estimation errors may be thoroughly studied.

Jan 1, 1977

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