Papers and Case Studies
Below is a collection of papers and case studies by Tenzing staff and associates.
Benchmarking Estimation Methods for Coal Resource Estimation
Z Casley, O Bertoli, C Mawdesley, G Davies and D Dunn
The coal industry in Australia has been actively working in recent years towards the(re)integration of geostatistical techniques to the process of coal resource estimation. The benefits of using geostatistical techniques, over the current interpolation algorithms in use in coal modelling packages used to generate the grid estimates, need to be illustrated for the methodology to gain a broader acceptance in the coal industry.
This paper focuses on the benefits gained at BHP Billiton Mitsubishi Alliance’s Saraji mine for the estimation of the total product yield value at a 9.7per cent product ash cut-off of a particular seam of the Saraji deposit.
In order to perform this comparison, the results of the alternative estimation methodologies need to be benchmarked, which in most
Situations is achieved through the reconciliation of the estimates against production and / or process plant reconciliation data. Unfortunately, this benchmarking was not possible as no reconciliation data for the area of interest in the chosen seam was available, as it has not been mined at the time of the study.
Where no reconciliation data is available, an alternative method is to use conditional simulations as the benchmark for comparison. The simulated values can be regarded as ‘reality’, and the alternative estimation methodologies, based on a sampling of the underlying ‘reality’, can then be compared using the simulated ‘reality’ as the benchmark for comparison.
Geoststistical Tools for Evaluating Domains
The development of appropriate geological domains is perhaps the most critical step in a geostatistical study. This brief case study introduces the concept of domains as applied to coal deposits and some of the tools used to determine whether or not domains are appropriate.
Quantitative Kriging Neighbourhood Analysis for the Mining Geologist — A Description of the Method With Worked Case Examples
J Vann, S Jackson and O Bertoli
Ordinary kriging and non-linear geostatistical estimators are now well accepted methods in mining grade control and mine resource estimation. Kriging is also a necessary step in the most commonly used methods of conditional simulation used in the mining industry. In both kriging and conditional simulation, the search volume or ‘kriging neighbourhood’ is defined by the user. The definition of this search can have a very significant impact on the outcome of the kriging estimate or the quality of the conditioning of a simulation. In particular, a neighbourhood that is too restrictive can result in serious conditional biases. The methodology for quantitatively assessing the suitability of a kriging neighbourhood involves some simple tests (which we call ‘Quantified Kriging Neighbourhood Analysis’ or QKNA) that are well established in the geostatistical literature. The authors argue that QKNA is a mandatory step in setting up any kriging estimate, including one used for conditioning a simulation. Kriging is commonly described as a ‘minimum variance estimator’ but this is only true when the neighbourhood is properly defined. Arbitrary decisions about searches are highly risky, because the kriging weights are directly related to the variogram model, data geometry and block / sample support involved in the kriging. The criteria to look at when evaluating a particular kriging neighbourhood are the following:
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1.the slope of the regression of the ‘true’block grade on the ‘estimated’ block grade;
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2.the weight of the mean for a simple kriging;
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3.the distribution of kriging weights themselves (including the proportion of negative weights); and
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4.the kriging variance.
Outside of the technical geostatistical literature, there is little in the published domain to describe the nature of QKNA and no practical presentation of case examples. In this paper we attempt to redress this by setting out the calculations required for QKNA and defining some approaches to interpreting the results. Several practical worked mining case examples are also given. Finally some comments are made on using the results of QKNA to assist with block size selection, choice of discretisation and mineral resource classification decisions.
An Overview of Geostatistical Simulation for Quantifying Risk
John Vann, Olivier Bertoli and Scott Jackson
This paper presents an overview of geostatistical simulation with particular focus on aspects of importance to its application for quantification of risk in the mining industry. Geostatistical simulation is a spatial extension of the concept of Monte Carlo simulation. In addition to reproducing the data histogram, geostatistical simulations also honour the spatial variability of data, usually characterised by a variogram model. If the simulations also honour the data themselves, they are said to be ‘conditional simulations’. In a sense, simulations are an attempt at ‘sampling the unknown’ using constraints, e.g. statistical moments imposed by the data. Thus, in simulation, the requirements of stationarity are stricter than for linear geostatistics (for example, kriging). Geostatistical simulation is much more computationally demanding than geostatistical estimation. However, the exponential increases in computer processing speed, memory and data storage capacity have brought these tools into wide operational use in the mining industry over the past decade. We can generate many (in theory an infinite number) of simulated images. The question still remains: ‘how many simulated images are required to properly characterise a given domain?’ To answer this we must test the simulations to ensure they reasonably reproduce the input statistics. The validity of any subsequent use of the simulations for risk characterisation will be heavily dependent on how well our set of simulations characterises the intended ‘probability space’. There now exists a plethora of methods to generate simulations. The main methods in use in the mining industry today are discussed and we briefly introduce some less common approaches. Finally, the concepts of multivariate simulation (‘co-simulation’) are touched upon. In conclusion we summarise some of the uses of geostatistical simulations for application to risk quantification problems in the mining industry.
Geostatistical Investigation of Fractures within Crystalline Rocks, Stripa Mine, Sweden
Aaron Tomsett competed his MSc in Mining and Environmental Geostatistics at the University of Leeds in August 2004, graduating with distinction and presenting a dissertation entitled ‘A Geostatistical Investigation of Fractures within Crystalline Rocks, Stripa Mine, Sweden’.
Recoverable Resource Estimation Using Bivariate Uniform Conditioning at the Lihir Gold Mine
O Bertoli, A Tomsett, R Kidd and Z Casley
Bivariate recoverable resource estimation aims at predicting the recovered metal for a secondary variable when a cut-off is applied to a primary variable. The choice of a consistent geostatistical model is advisable to allow a robust estimation from exploration data of the primary and secondary metal recovery functions on a generic selection block (selective mining unit – SMU) within large panels.
Ore processing decisions at Lihir Gold Limited’s Lihir Gold Mine are based on the gold and sulfur estimates of SMUs from production (grade control)data. The predictive model from exploration data at Lihir is based on the estimation of a recoverable resource for gold by Uniform Conditioning(UC), with an estimate of the sulfur grade being provided by Ordinary Kriging of panels. While univariate UC is adapted to the diffusive nature of the gold mineralisation (Ladolam orebody) at Lihir, the
independent estimation of sulfur, through ordinary kriging, fails to capture the potential spatial correlation that exists between gold and sulfur mineralisation. This paper presents a practical implementation of bivariate UC, which better represents in the resource model the spatial correlation between gold and sulfur. Incremental economic gains through improved definition of material categories and scheduling are investigated, and the particular impact on the process of geological interpretation and domaining is emphasised.
