On the use of non-linear geostatistical techniquesfor recoverable reserves estimation:A practical case study

Consideration of the mining method is an essential component of ore reserves evaluation. This is particularly true where the profitability of a project is conditioned by the ability to mine selectively. Linear estimation methods such as Ordinary and Simple Kriging commonly fail to provide unbiased estimates of recovered ore tonnage and metal content which means that a mining project can be exposed to undue risk. This risk is significant when the selective mining are small with respect to the data spacing. Non linear estimation, such as the Gaussian Disjunctive Kriging technique provide a mean of calculating unbiased estimates of ore and meta content over any cut-off range and mining unit size combination. The disadvantage of this methods is the requirement of an assumption of strict stationarity. When such an assumption can not be reasonably made, alternative simpler non linear methods can be employed such as Uniform Conditioning and ore and metal Service Variables. The application of these estimation methods to a porphyry type deposit is described. A discussion of the results from a practical point of view is also given. Introduction The objective of this paper is to demonstrate how recoverable reserve estimates vary according to the selection of estimation method. The applicability of three non linear estimation methods as applied to a porphyry copper deposit is discussed with reference to both the theoretical assumptions and the geological characteristics of this particular deposit. The relative performance of each method is assessed by comparing grade-tonnage curves and metal content estimates above cut-off thresholds. Additionally, conditional simulations are generated to determine which method has the best absolute performance and what practical recommendations can be made for the application of these techniques. All of the statistical and geostatistical calculations and graphical output generated for this case study was made using the Isatis (trade mark of TRANSVALOR) geostatistical software system. Presentation of the data Copper mineralisation is located within a stockwork zone which is structurally controlled by major stepfaults. The intensity of mineralisation is generally related to the degree of stockworking; at the deposit core where the host rock is most extensively stockworked, copper grades are highest. A decline in the intensity of stockworking away from this central zone is accompanied with a gradual decline in copper grades. The deposit has been extensively explored from surface diamond drilling and underground exploration drives, cross-cuts and raises. The sample database consists of a combination of diamond drillhole and channel samples. Statistical analysis confirmed that the support of these different sample types is compatible. For the purposes of this case study, 5m composites over only one exploration level are considered which gives a total of 1256 composite values. The map given in Figure 1 shows that the location of composites is dictated by the spacing and orientation of the underground development. Figure 1 The data density is such that linear kriging into small blocks which approximate the selective mining unit (SMU) size may be appropriate. This approach would negate the need to use more sophisticated methods because no further support correction would be required. However, the copper grade distribution is highly skewed (Figure 2) with a coefficient of variation of greater than 2. This characteristic suggests that the use of linear kriging methods for the estimation of recoverable reserves is inadvisable because estimates are unlikely to be conditionally unbiased. The use of non linear methods is therefore a more suitable option.