Suggestion Box ESTIMATING RESERVES

On this continent, in most deposits that contain significant amounts of gold in its native form, gold particles display a completely randomized probability distribution, which can be approximated with the Poisson distribution. As a result, geostatistical techniques, even if the most powerful computer and the most advanced software were utilized, could not possibly improve the precision for contained gold beyond limits that are imposed by the theory of mathematical probability and applied statistics.

Papers that deal with the application of geostatistics to deposits containing native gold indeed mention that the single particle or nugget effect often renders the technique ineffective. The conclusion is not surprising since the “sphere of influence” of a nugget is zero.

It is entirely possible, of course, that the probability of encountering a particle with a similar mass in close proximity is higher than the expectation for such particles throughout the deposit. Nevertheless, random variations in the distances between gold particles and in their mass make it extremely difficult to estimate ore reserves with an acceptable degree of precision. Therefore, the risk to obtain a lower grade during production remains high.

It would seem that significance is sometimes attached to a seesaw semi- variogram that essentially falls within the confidence range for the variance of the complete data set (that silly sill value). Under those conditions, eac h variance term is statistically identical to the variance for the completely randomized set of gold assays, which implies that such a “semi-variogram” only reflects the effect of random variations in the measurement process. Attempts to apply Fourier analysis to these variance terms are cute but an exercise in futility. For how could one possibly develop a deterministic model to compute the outcome for a throw with a coin, or any other stochastic process for that matter?

One might debate whether the advent of heap leaching low-grade gold ores is, at least partially, responsible for continued efforts to apply geostatistics to gold deposits on this continent. Perhaps one would expect that gold is more homogeneously distributed in a low-grade deposit. However, in terms of its co-efficient of variation, the gold in a low-grade deposit is not necessarily more homogeneous than in a high-grade deposit. Actually, the set of paired gold assays that are each determined in chips from either upper or lower strata of blastholes in a block hardly ever display a significant correlation. Bad Omen

The lack of correlation between the grades in upper and lower strata of blastholes within blocks is a bad omen for the probability of encountering a significant correlation between blastholes. In fact, the first term of each semi-variogram for the gold assays in blastholes along the length of a block is rarely lower than the variance for the completely randomized set of gold assays. The question is then how a significant correlation could possibly exist between gold assays in widely- spaced drill holes in a deposit if gold assays in closely-spaced blastholes within its blocks are statistically independent.

Champigny makes reference to the premise that sampling or analytical problems should not occur. However, during preparation of samples, in particular, systematic errors are often introduced, and loss of information inevitably occurs. Yet, the occurrence of gold assays should be beyond question, and their precision should be carefully optimized. Ore reserve estimates that are based on biased and imprecise gold assays are misleading in the extreme and create a vast potential for disaster to both owners and investors.

A notorious source of systematic errors is the friction pulverizer, which should never be used to comminute to analytical fineness any sample that may contain native metals. Its grinding surfaces become so hot that native metals settle solidly until the pulverizer cools down, at which time abrasive slag, quartz sand, or the first sample of a set may remove the deposits. Systematic errors of 10% to 25% have been observed in float and jig concentrates, but much less information is available on exploration samples.

Comminuted samples should be properly mixed prior to division to ensure that the variance of division does not exceed the variance of analysis. For the comminution process causes changes in composition and distribution variances. Comminution increases the number of particles in a sample, and reduces its composition variance, while mixing reduces its distribution variance. Actually, for a perfectly homogenized sample, the distribution variance is zero.

Despite claims to the contrary, splitting drill core sections into halves not only accounts for the single largest variance component in the measurement process, but it is also subject to human discretion and thus a potential source for systematic errors. After all, drill core can often be split in such a manner that the most promising half is systematically selected and then submitted to the assay laboratory for further preparation and analysis. The practice of cutting high grades is deceptive, discriminator y and disturbing. It should, therefore, be replaced by a logical approach that forms an integral part of a statistical quality control program. Its objective should be to obtain unbiased assays with acceptable and affordable precision characteristics for each stage of the measurement process. A sensible methodology for replacing an outlier, or a roque value, with a reliable and realistic estimate is a key element for an effective exploration program. Conventional statistical techniques also provide powerful tools to the management team.

The most suitable model to estimate ore reserves for gold deposits on this continent may well be based on computing the composite variance for the gold content of each block of ore which can be estimated from the variances of its volume, density and metal grade.

The cumulative composite variance for a set of blocks could then be used to calculate the lower confidence limit for contained gold in any combination of blocks at a predetermined probability level.

I hope my comments in this space make a minor contribution to the continuing effort to compute more reliable ore reserve estimations. I might mention that I am writing a text on “The Metrology of Precious Metals,” which will be published in 1991, and I feel confident that the textbook will make a much more profound contribution to this subject. J. W. Merks is president of Matrix Consultants, which provides consulting services in metrology (the science of measurement) to the mining industry in Canada and abroad. He has written a textbook entitled Sampling and Weighing of Bulk Solids.

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