Drill Hole Spacing Analysis is successfully used for coal resource uncertainty analysis
The study demonstrated the possibility of using the Kriging variances in drill-hole spacing analysis (DHSA) for SMU uncertainty. That paves the way for an easier integration of the characterization of uncertainty in the decision making process.
The main purpose of the project was for Geovariances to investigate possibilities for modeling the uncertainty of thickness and coal quality variables on selective mining units (SMU’s) in the deposits of the client mine site.
At the difference of metal mining, SMU’s in coal are usually not vastly different in size than the nominal drill spacing for thickness. However the sample spacing for quality variables is usually much greater than the SMU size. That makes the direct utilization of co-Kriging variances for characterizing local uncertainty more difficult particularly given that the uncertainties sought, apply to ratios of estimates (the estimate of a given coal quality variable is usually obtained as the ratio of the estimated accumulated coal quality variable over the estimated thickness).
To test the validity of using (co-)Kriging variances calculated on SMU’s to characterize local uncertainty, a suite of conditional simulations is generated for each coal quality variable, and subsequently used as a benchmark against which the Kriging results could be compared.
The main statistics used for comparison is the relative uncertainty defined as the width of the 90% confidence interval divided by the estimated value on the SMU. The 90% confidence interval is calculated as Q95-Q5 when using the simulation platform and as 3.29 x the kriging standard deviation when relying on the (co-)Kriged estimates.
The study demonstrates the possibility of using the Kriging variances in drill-hole spacing analysis (DHSA) for SMU uncertainty. That paves the way for an easier integration of the characterisation of uncertainty in the decision making process.
The agreement between the Kriging and simulation methods for thickness is excellent, with much closer correlations than for the quality variables. This is to be expected, both because there is much more thickness data than quality data, and because there are fewer steps involved in the calculation (ordinary Kriging as opposed to co-Kriging and un-accumulating).
In the main, the Kriging variances are shown to give very reasonable approximations to the simulation-based uncertainties, though there can be some systematic discrepancies which may become much more critical if a classification is to be based on a thresholding of the SMU’s relative uncertainties.
The results of the benchmarking process for a particular deposit (not mentioned here) and a series of quality variables (Ash, Sulphur, Phosphorous and Fluorine) are tabulated below:
Rel. uncertainty | Simulations | Co-Kriging Thickness | 5.0% | 5.2% Ash | 11.8% | 14.7% Fluorine | 45.6% | 40.8% Phos | 35.8% | 37.3% Sulphur | 35.8% | 37.3%