Auditing resource databases and exploration data sets over the past several decades has exposed the lead author to many instances of data averaging of multiple analyses from a single sample. These data sets were comprised of pulp or reject analyses that showed poor precision upon re-analyses. Some organizations produced a final concentration in their database that was an arithmetic average of all analyses. It was this average concentration that was used in resource grade estimation, or in anomaly definition. In these cases the reason for the re-analyses was a “rare grain” or “nugget” effect in the element being sought, usually gold.
Several years ago, one company decided to re-assay a large suite of samples that contained a nugget effect using the commonly applied metallics or screen assay method for gold. The thought was that this method would capture all the gold in the samples, thus raising the average grade from all the samples.
In fact, the opposite occurred, much to the consternation of the company’s geologists. This somewhat counter-intuitive result was created by the nugget effect in the original analyses. The original assays included some samples that had at least one large grain of gold, which produced an assay that was sometimes an order of magnitude or more above the “normal” concentration. The actual effect of the metallics assay was to reduce these “fliers” back to a realistic concentration and to marginally raise the gold content of the majority of samples. When all assays were averaged, the overall grade from the metallics assays was lower than from the original assays. The disproportionate effect of the very high-grade samples was removed from the assays, thus lowering the average grade.
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Background to This Study
Sometime after the above instance, a resource data set containing multiple gold assays for single samples was examined. The analytical data base clearly exhibited a nugget effect, as the precision of analyses was poor and visible gold had been noted in the drill core. The laboratory had commented on the poor reproducibility of the in-house assays and recommended a metallics assay procedure. The mining company did not undertake the metallics assay method, as they considered the use of multiple assays and averaging on many samples a more robust (and less costly) method than periodic metallics assaying.
The final resource grade was calculated from single assays, and from between two to five assays of one or more pulps. The company’s criteria for determining a re-assay was grade dependent: samples that originally contained more than 2 g/t gold were re-assayed from the same pulp as the original sample; samples that originally contained more than 5 g/t gold were re-assayed using the original pulp, and then using a newly prepared pulp from reject. The laboratory routinely re-assayed some of the original pulps as a form of in-house quality control. The laboratory re-assays were not grade dependent.
The nugget effect is a random phenomenon if all other factors in sampling and sample preparation are equal. In any sample pulp there should be a finite number of large gold grains. The chances of selecting one or more of these larger grains from a pulp of fixed weight, in a lessor weight used for fire assaying, is governed by the Poisson distribution. If the initial analysis did not contain a nugget, then the result could be left as is if below 2 g/t gold, or re-assayed if above 2 g/t gold, or re-assayed by the lab anyway. The weight of the original pulp was decreased by the weight used for the original analyses, so the chances of obtaining a nugget in the second assay is somewhat increased. The chance of obtaining one or more nuggets in successive assays from the same pulp therefore increases, if nuggets had not been obtained in previous analyses. In other words, the chances of getting a high grade assay goes up with the number of assays from the same pulp. Based on previous experience with the metallics test, the presence of a nugget will disproportionately affect the average of all analyses for the same sample. Therefore, the overall grade of the deposit will be compromised by averaging multiple assays of single samples.
This hypothesis required testing using a mathematical model based on Poisson statistics. A previous paper by these authors had looked at a similar statistical model (Stanley, C.R. and Smee, B.W., 1988a and b) in soil samples, proving the methodology. The model was developed and the calculations done by Dr. Stanley.
The results of this modeling were presented in a paper at the Dublin IGES, 2003. The attached PowerPoint presentation shows this presentation.
by: Barry W. Smee
Smee and Associates Consulting Ltd.
4658 Capilano Road, North Vancouver B.C. V7R 4K3
Phone 1 (604) 929-0667 Fax 1(604) 929-0662
and: Clifford R. Stanley
Department of Geology, Acadia University
Wolfville, Nova Scotia B4P 2R6, Canada
VOX (902) 585-1344, FAX (902) 585-1816
Stanley, Clifford R., and Smee, Barry W., 1988a: A test in pattern recognition: defining anomalous patterns in surficial samples which exhibit severe nugget effects. Explore, 63, 12-14.
Stanley, Clifford R., and Smee, Barry W., 1988b: A test in pattern recognition: defining anomalous patterns in surficial samples which exhibit severe nugget effects II. Explore, 65, 12-14.