By Principal Geology Consultants Cecilia Artica and Andrew Fowler
Drillhole Spacing Studies:
Drillhole spacing studies attempt to quantify the increased confidence gained from increased drilling. This can be measured in terms of improved theoretical estimation quality, or improved predictability in mine production. Typically, they are used to support Mineral Resource Classification, however, they may also be used to inform infill drilling programs for resource definition or for grade control drillhole design. All of the studies rely on well-defined domains and a reliable variogram model.
The types of studies fall into one of three main groups.
Estimation quality studies
Single block kriging studies
Conditional simulation studies
Estimation Quality Studies:
A drillhole spacing study based on theoretical estimation quality is undertaken by producing grids of artificial drillholes with increasing grid dimensions, running a theoretical estimate based on each drilling grid, and comparing the results. The statistic used to compare the quality of estimates is typically the slope of the regression (SR), which is the correlation coefficient between estimated and theoretical “true” block grades; or kriging efficiency (KE), which is the kriging variance normalized by the variance of the “true” blocks. The estimation uses the 3D variability modelled from the variograms. Hence, the results of the method are strongly influenced by the quality of the variogram model.
By way of example, a mean SR >0.85 would generally be considered in the mining industry to be well-estimated, and could support classification as a Measured Mineral Resource. A mean SR 0.6-0.85 would generally be considered to be adequately estimated, and could support classification as an Indicated Mineral Resource. A mean SR <0.6 would generally be considered to be poorly-estimated, but might be classified as an Inferred Mineral Resource if continuity could be reasonably surmised.
A typical DHSS methodology based on estimation quality is summarised below:
Variography is undertaken on declustered and capped composites from the most economically significant domain or combination of domains,
Artificial drillholes are produced on various grids (no grade variable is necessary to produce statistics),
A block model estimate is generated within the study area
The SR and/or KE is calculated for each drilling grid and the results compared.
This process has been streamlined in Supervisor geostatistical software and is widely practiced in Australia, although published examples are hard to find. An example from a lithium deposit is provided in Figure 1.
Figure 1. Mean slope of the regression and number of drillholes with increasing drillhole spacing.
Single Block Kriging Studies:
The single block kriging method considers the production rate, the variogram model and sample co-efficient of variation to assess the variability of grade estimation over various production periods for various drillhole grids. It is referred to as a single block kriging method because the production volume is represented as a single large block, which may be equivalent to a month or quarter of production. The authors apply the method described by Verly et al., (2014), which the reader is referred to for further details.
A kriging estimate is performed in the large block for each drilling grid, and the estimation error stored. The error is assumed to be normally distributed due to the large block size and many samples, which then allows the practitioner to deduce confidence intervals. An example from an open pit gold mine is provided in Figure 2.
Figure 2. Increasing drillhole spacing overlain on a single block representing one month of production.
While international reporting codes (e.g. JORC, NI43-101) do not prescribe the methodology that should be applied in the classification of Mineral Resources; one recognised industry practice is that for a Measured Resource, the drillhole spacing should be sufficient to predict tonnage, grade and metal on quarterly production with ±15% relative precision at the 90% confidence interval. In the case of an Indicated Resource, the ±15% relative precision should be achieved on an annual production volume. For the Inferred Category, the data are inadequate for assessing confidence intervals.
A typical DHSS methodology based on a single block kriging estimate is summarised below:
Model a variogram for the element and area of interest using declustered and capped composites,
Define dimensions of a large single block equivalent to one month of production,
Set up artificial drilling grids at various spacings (no grade variable is necessary to produce errors),
Run a kriging estimate in the large single block for each artificial drilling grid,
Calculate relative standard error at 90% confidence interval for the various artificial drilling grids,
Scale up results to represent quarterly and yearly volumes,
Plot results and use risk-based Mineral Resource category definitions.
The authors are not aware of any commercially available software that has streamlined this process, however, due to its simplicity, it is able to be undertaken in most mining software packages. It is widely practiced in the Americas and referenced in the Estimation of Mineral Resources and Mineral Reserves Best Practice Guidelines produced by the Canadian Institute of Mining, Metallurgy and Petroleum (CIM, 2019). An example of the method applied to the predictions of tonnes above cut-off grade from an open pit gold mine is provided in Figure 3.
Figure 3. Relative error at 90% confidence interval of tonnes above cut-off grade on quarterly and yearly production volumes with increasing drillhole spacing.
Conditional Simulation Studies:
Conditional simulation based DHS studies take many forms but they are all aimed at quantifying the reduced risk resulting from increased drilling. This may be quantified using the production rate and “15% error at 90% confidence interval” rule, or may be related to specific value drivers such as net smelter return, thickness of the transitional zone, or presence of deleterious elements, to name a few.
Examples of DHSS based on conditional simulation include Boucher et al., (2004) and Abzalov and Bower, (2009).
While no standardized method exists in the literature, an example approach to DHSS using conditional simulation is summarised below:
Model a normal-score variogram for the element and area of interest,
Complete sequential Gaussian simulation (SGS) from the exploration drillholes and produce 10 realizations,
Select one realisation that best represents the input data statistics and variogram – this then becomes the “target” realisation.
Set up artificial drilling grids at various spacings and populate the artificial drillholes with the simulated grades from the target realisation,
Complete SGS from the artificial drillholes with target realisation grades and produce 50-100 realisations,
Reblock each of the resulting 50-100 realisations into production volumes representing one quarter and one year.
Calculate the error relative to the target realisation at 90% confidence interval for the various artificial drilling grids and for each production volume.
Plot results and use risk-based Mineral Resource category definitions.
The advantages of the conditional simulation approach over the other two approaches is that it is more statistically robust as it relies less on theoretical assumptions, and it can take into account the proportional effect (higher grades have higher variance), which is important for precious metal deposits with skewed grade distributions. Additionally, the simulation can be used to investigate many different issues related to mining such as dilution, ore loss, grade variability etc.
The disadvantage is the considerable time to set-up, run and validate a conditional simulation. This all depends on the complexity of the mineralisation, however, for example, A DHSS using the estimation quality approach might take 1-2 days, a single block kriging study might take twice as long as that, while in the authors’ experience, a conditional simulation study could be an order of magnitude longer, depending on the software and processing power of the computer used.
Abzalov, M Z and Bower, J, 2009. Optimisation of the drill grid at the Weipa bauxite deposit using conditional simulation, in Proceedings Seventh International Mining Geology Conference 2009, pp 247-252. The Australasian Institute of Mining and Metallurgy: Melbourne.
Boucher, A., Dimitrakopoulos, R., Vargas-Guzmán, J. A., 2004. Joint Simulations, Optimal Drillhole Spacing and the Role of the Stockpile. Geostatistics Banff 2004 pp 35-44.
CIM, 2019. CIM Estimation of Mineral Resources and Mineral Reserves Best Practice Guidelines. Prepared by the CIM Mineral Resource and Mineral Reserve Committee. Adopted by the CIM Council on November 29, 2019. https://mrmr.cim.org/media/1129/cim-mrmr-bp-guidelines_2019.pdf
Verly, G., Postolski, T., Parker, H.M., 2014. Assessing Uncertainty with Drill hole Spacing Studies – Applications to Mineral Resources. Orebody Modelling and Strategic Mine Planning Symposium 2014, pp109-118. The Australasian Institute of Mining and Metallurgy: Melbourne.