Resource and reserve evaluation in the presence of imprecise data
CIM Bulletin, Vol. 98, No. 1089, 2005
X. Emery, J.P. Bertini and J.M. Ortiz
Several sources of information often contribute to the comprehension of an ore deposit, for instance samples from diamond drill holes, reversed-circulation drill holes, or blast holes. Even if all the available information comes from the same drill hole type, it may have been collected through several campaigns, sampled with different protocols, or analyzed by different laboratories. In general, these sources of information do not have the same quality, therefore, they constitute different statistical populations for mineral resource/ore reserve estimation studies.This work examines the impact of data imprecision in resources and reserves evaluation through two case studies on simulated deposits. The first one is a porphyry copper deposit represented by blocks 15 m by 15 m by 12 m in size; the copper grades are conditioned to real exploration and production data (diamond drill holes and blast-holes) and show gradational transitions. The second case study consists of a bench of a gold deposit simulated without any conditioning data, with 5 m by 5 m blocks, for which there is a clear-cut discontinuity between the waste and the ore. In each deposit, a set of exploration samples is defined to estimate the block grades. These samples are divided into two subsets standing for two different sampling campaigns: a set of hard (error-free) data and a set of imprecise data obtained by altering the true grade values. Two types of imprecision are examined: measurements with multiplicative errors (each measured value is the true value times a random number lying between 0.75 and 1.25) and measurements defined as intervals. Additionally, two reference situations are considered: the block model obtained using the complete exploration dataset without data imprecision and the one obtained using the hard data subset exclusively. The results are compared to the simulated block grades from a statistical and an economic viewpoint, by assessing the true and expected profits associated with the block estimated models.Five geostatistical techniques are used to estimate the block grades: 1) ordinary kriging, for which all the data are pooled together as if they belonged to a single statistical population; 2) separate kriging, where each data subset originates its own block model (the models are then unified by a weighted average); 3) ordinary cokriging, consisting of a joint estimation of both types of data; 4) lognormal kriging associated with a filtering procedure; and 5) indicator kriging to determine the e-type estimate of the grades.The study concludes that the kriging techniques are not very sensitive to the level of sampling error, and that the quantity of data prevails over their quality. Only the reference estimation from the hard data subset shows a significant loss of precision with respect to the other situations. Therefore, the imprecise measurements should never be discarded in the estimation paradigm, despite their poor quality. Furthermore, in the examples under study, simple methods perform well: a kriging with all the data pooled together or a separate kriging with each type of measurement are efficient for estimating the block grades, although they are theoretically not perfectly sound. There is no need to seek more complicated techniques such as cokriging or indicator kriging.In practice, determining whether a sampling campaign is deficient or not requires further information, in particular, taking sampling duplicates or re-assaying existing pulps. Comparing the grade distributions of two campaigns via quantile-quantile plots is generally not enough to conclude on the existence of data imprecision. Comparing their sample variograms is a more powerful tool, since a measurement error is reflected by a higher nugget effect. Calibration samples (for which both the error-free and imprecise measurements are available) or twin drill holes are required to model the type of imprecision.