Journal of the Southern African Institute of Mining and Metallurgy
On-line version ISSN 2411-9717
Geostatistical modelling aims at providing unbiased estimates of the grades of elements of economic interest in mining operations, and assessing the associated uncertainty in these resources and reserves. Conventional practice consists of using the data as error-free values and performing the typical steps of data analysis -domaining, semivariogram analysis, and estimation/simulation. However, in many mature deposits, information comes from different drilling campaigns that were sometimes completed decades ago, when little or no quality assurance and quality control (QA/QC) procedures were available. Although this legacy data may have significant sampling errors, it provides valuable information and should be combined with more recent data that has been subject to strict QA/QC procedures. In this paper we show that ignoring the errors associated with sample data considerably underestimates the uncertainty (and consequently the economic risk) associated with a mining project. We also provide a methodology to combine data with different sampling errors, thus preserving the relevant global and local statistics. The method consists of constructing consistent simulated sets of values at the sample locations, in order to reproduce the error of each drilling campaign and the spatial correlation of the grades. It is based on a Gibbs sampler, where at every sample location, the actual sample value (with error) is removed and a conditional distribution is calculated from simulated values at nearby sample locations. A value is drawn from that distribution and kept only if it satisfies some statistical requirements-specif-ically, the global relative error and local means and variances must be reproduced. All sample locations are visited and simulated sample values are generated iteratively, until the required statistics are satisfactorily attained over all sample locations. This generates one realization of possible sample values, respecting the fact that the actual samples are known to carry an error given by the global relative error. Multiple realizations of simulated sample values can be obtained by repeating the procedure. At the end of this procedure, at every sample location a set of simulated sample values is available that accounts for the imprecision of the information. Furthermore, within each realization, the simulated sample values are consistent with each other, reproducing the spatial continuity and local statistics. These simulated sets of sample values can then be used as input to conventional simulation on a full grid to assess the uncertainty in the final resources over large volumes. The methodology is presented and demonstrated using a synthetic data-set for clarity.
Keywords : sampling error; realizations of simulated sample values; uncertainty in final resources..