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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 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

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

For practical reasons all basic input data for the gold mines of the Anglovaal Group conform to a regular grid of averages of sample values within 25-ft squares in the plane of the ore body; individual sample values with their metric co-ordinates are input and converted by a computer program to the basic 25-ft square averages. At the Prieska copper mine the bore- hole data are forced on to a regular grid of 15-m squares corresponding to the coordinates of the grid points nearest to the actual borehole intersections. As for the gold mines the Prieska ore body, although some 3 to 30 m thick, is also dealt with on a two-dimensional basis (Krige, 1973). On the gold mines the data subjected to geostatistical analysis cover: gold values (in cm g/t), uranium values (cm kg/t), and channel widths (cm). The gold and uranium values are normalised on the basis of log (value plus constant) and all the geostatistical analyses are performed on these transformed values. The channel widths usually conform reasonably well to the normal distribution and are, therefore, not transformed. At Prieska the metal grades analysed cover the two main products, copper and zinc, as well as the impurities lead and bismuth; in addition the specific gravity values and the hanging- and foot-wall deviations from a projection plane are also handled. These were all previously used on an untransformed basis but because of problems associated with the proportional effect the lognormal-de Wijsian model is now used for some of the grade variables. The key computer pro- grams can be summarised briefly as follows:

Jan 1, 1981

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 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

By Mehmet Guney

[The Atlantis-II-Deep is a hydrothermal mineralization located along the median valley of the Red Sea at a water depth of about 2200 m. Extensive exploration of the metal-rich brine deep revealed a potentially mineable deposit on economic interest consisting of oxides, silicates and sulphides with considerable concentrations of zinc, copper, cadmium and silver. Geostatistics was applied to assess the most likely in-situ vague of the metal potential for economical exploitation. Semi-variograms were constructed to characterize the structure of the regionalized distribution of the geological parameters. Volume grades and thicknesses were determined by the kriging technique, avoiding systematically biased high or low grades, and then block .tonnages were computed. The estimation variances, distribution of errors and histograms of observed and kriged values in each grid Mock were also produced.]

Jan 1, 1983

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