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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

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 Roger A. Blais, Michel David

"Matheron's geoslalislical method for the estimation of ore reserves has been developed to the point at which real-life problem may be handled effectively. The steps involved in the method are:(i) obtalning the variogram,(ii) fitting a model, and(iii) producing block estimates.All three steps may cause difficulty, and would-be users need a deep understanding of the theory if failure is to be avoided.To illustrate these points, specific cause are considered:(i) two almost equidimensional porpbyry deposits, one drilled randomly and the other regularly; and(ii) two iron formation, one drilled extensively and being mined, while the other is still at the stage of early estimation."

Jan 1, 2014

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

By Sarkar B. C, Sen A. K

India is well endowed with vast reserves of banded hematite ore, about 12 billion tonnes, estimated by some conventional methods. Various authors have assessed this huge reserve using some advanced geostatistical methods. A Banded Iron Formation (BIF) belt named the `Singhbhum-Keonjhar-Bonai' belt in India has been chosen as a case study. In this paper, the experiences of Chiria iron ore, in particular, have been described. This study will finally create a dynamic mineral inventory after standardising the geostatistical parameters which will help to cater for the needs of the stringent quality requirements of the Indian steel industries.

Jan 1, 1995

By Sirayanone S, Rashad MZ

An important problem occurring in the iron and steel industry of Egypt is the presence of manganese oxide and chlorine with different percentages in the Bahariya Iron Ore Deposit, Western Desert, Egypt. In this work we used a geostatistical method known as the Volume- Variance Relationship to predict grade fluctua- tions of Fe% , Mn% and Cl% in the ore after blasting a certain volume from the ore deposit, on the other hand, if we have a certain limit for each of these chemical components, we can select the bench blasting dimension to give these limits.

Jan 1, 1986

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

Jan 1, 1977

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 M Field

Kimberlite pipes, as opposed to dykes, sill and secondary deposits, are the primary target for diamond exploration companies because they have simple geometries and can contain large volumes of potentially diamond-bearing ore. Once discovered, important decisions have to be made regarding the sampling of these geological entities to establish the total volume of ore present, and to define the internal geology, which can be complex in nature and controls the distribution of diamond grade. It is essential that as part of this process the uncertainty in constructed geological models are assessed. In this paper the Orapa AK1 kimberlite pipe in Botswana is used as a case study to explore a potential methodology for defining this uncertainty. The uncertainty of the rock volumes of different types can be characterised by a geostatistical approach. Geostatistical simulations, based upon a plausible representation of the geological bodies, provide different possible images of the orebody that can be considered as different realities. By testing different borehole layouts and drilling the orebody virtually on the computer, many different, but equi-probable realisations of the pipes can be produced. It is then possible to estimate the rocksÆ volumes and compare them with the actual ones. A statistical analysis of the relationship between estimation error and the number of boreholes can then be used to optimise the next sampling campaign. The rock volumes are obtained from a two-step simulation process. Firstly, the pipe geometry is simulated by means of introducing variations around the geological block model, by an original method called centre point simulation (CPS), which has been developed for this purpose. Secondly, the internal geology is then simulated within the pipe. The methodology for simulating the internal geological zones has to be adapted to the level of information and to the geological structure itself. The upper portion at Orapa AK1 is filled with sedimentary crater facies. Here plurigaussian simulation techniques can be applied that are adapted to the simulation of sedimentary facies. The central zones of the pipe are typically subvertically-oriented massive volcaniclastic deposits and breccias and the lower regions comprise a complex root zone. CPS is appropriate for these zones.

Jan 1, 2006

By Shrivastava P

The iron orebodies of the Pilbara region are formed by supergene enrichment of banded iron formation and rarely do such processes produce orebodies with uniform grade distrib- utions. The orebodies being mined or developed have to be worked to grade/quality constraints imposed by contractual agreement rather than natural characteristics. Hence it is imperative to use a non-biased ore reserve calculation method. The geostatistical study of a typical iron orebody is presented. Emphasised are the geological characteristics of the orebody manifested as a variable grade distribution of iron and impurities; the determination of variogram model; subsequent uses of the model for computation of ore reserves and kriged lock estimates; computation of dispersion variance and conditional simulation of orebody.

Jan 1, 1977

By Dimitrakopoulos R

Ore textures in base metal deposits are an important factor in the liberation of the economic components of the ore, metal recovery and reagent consumption during beneficiation. Optimising the mine profit requires knowing the relationship between ore texture and mineral processing behaviour, and the ability to predict the metal grade and the ore texture at a suitable scale. A new method that generates distributions of mesotextures for any mining block size or shape is proposed and includes: I . establishing a protocol for acquiring mesotexture data: 2. measuring the mesotexture spatial correlations using a multi-texture variogram; 3. generating multiple simulations of mesotextures; and 4. upscaling the simulations to generate the expected mining block/stope mesotexture distributions. Models of the ore textures built using the proposed methodology can be used to assess resources and reserves, enhance ore/waste discrimination and predict the metallurgical behaviour of parcels of ore.

Jan 1, 1997

By Ramani R. V

In this paper, a comparative performance evaluation of geostatistical, spectral, and fractal methods is made for short-scale variability prediction. The algorithms compared are: sequential Gaussian simulation method; a random fractal algorithm based on the generalised stochastic subdivision method; and a spectral simulation approach adopted for direct multi-dimensional simulation. The data for this study have been obtained from a mined out coal property. As this property was being mined, a 7315 m by 7315 m (24000 ft by 24000 ft) coal block was extensively sampled at an approximate spacing of 107 m (350 ft) and the 60-ton samples were analysed for sulphur in the 1.50 float gravity fraction. This data set is used here with the three methods to generate the simulated realisations, which are analysed for semivariogram reproduction and for simulation errors. Although all three methods converge to the true semivariogram in an average sense, the coefficient of variation of the average semivariogram for the Fourier integral method is minimum. The realisations generated by the sequential Gaussian method have minimum mean simulation error. The choice of a simulation method based on variability reproduction and simulation errors remains difficult.

Jan 1, 1995

By M Humphreys

Multi-episodic mineralisation is often characterised by different spatial trends exhibited by different generations of the mineralisation. The structural complexity of mineralisation together with the heterogeneous nature of the mineralised zones prevents unambiguous application of the conventional deterministic methodology for 3D constraining of the mineralised domains (ie conventional wireframing is ambiguous).A different approach, discussed in the present paper, includes a probabilistic definition of the domains encompassing one statistical population of the data. The domains are defined geostatistically using the indicator probability model. An indicator threshold is chosen for the definition of the high and low-grade domains. The spatial distribution of this indicator is then modelled by a variogram. The probability of exceeding the given grade threshold is than estimated by ordinary kriging for each modelled block. Blocks are then grouped according to their probability of exceeding the threshold and a continuous closed volume (domain) created from this likely patchy grouping using an appropriate structural model to fill the gaps). Methodology for the geostatistically assisted domaining is discussed in the paper. It is suggested that this technique represents an additional tool facilitating a structural interpretation of the mineralised zones.After the geostatistical domaining of the lode has been completed the grade within each of the domains is modelled using Uniform Conditioning method. Application of Uniform Conditioning for modeling the grade distribution has a significant advantage over linear methods (such as inverse distance or kriging) because Uniform conditioning enables estimation of local recoverable resources at different selective mining unit sizes that can be substantially smaller than the drilling density and are unable to be estimated directly.

Jan 1, 2002

By Jaime Guzman

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

Jan 1, 1986

By M. G. Hester

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

Jan 1, 1990