Smith should have but didn’t ask what CRIRSCO has accomplished. It would seem some sort of semi-international reporting template has been set up. The problem is the Russian Federation has a code of its own, and China’s is sort of similar. As it stands, Crirsconians have yet to develop valuation codes for mineral properties. At the present pace, valuation codes that give unbiased confidence limits for contents and grades of reserves and resources might be ready in 2020, the year of perfect vision. It had better be based on classical statistics!
Here’s what was happening in my life when CRIRSCO came about either in 1993 or in 1994. I talked to CIM Members in Vancouver, BC, about the use and abuse of statistics in ore reserve estimation. Bre-X Minerals raised money to acquire the Busang property. Clark wanted me to go from Zero to Kriging in 30 Hours at the Mackay School of Mines. I didn’t go because her semi-variograms are rubbish. The international forum on Geostatistics for the Next Century at McGill University didn’t want to hear about The Properties of Variances. David S Robertson, PhD, PEng, CIM President, failed to, “… find support for your desire to debate.” What irked me was Jean-Michel Rendu’s 1994 Jackling Lecture on Mining geostatistics - Forty years passed. What lies ahead? He rambled on about, “…an endless list of other ‘kriging’ methods…” and prophesied geostatistics, “… is here to stay with all its strengths and weaknesses.” At that time, Rendu knew about infinite sets of kriged estimates and zero kriging variances.
Rendu’s lecture stood in sharp contrast to A Geostatistical Monograph of The Mining and Metallurgical Society of America. Robert Shurtz, a mining engineer and a friend of mine, wrote The Geostatistics Machine and the Drill Core Paradox. Harry Parker, a Stanford-bred geostat sage, was to find fault in Shurtz’s work. This great debate got nowhere because neither grasped the properties of variances. Otherwise, both of them could have put in plain words why kriging variances drop off. A few of Parker’s geostat pals had already found out why in 1989.
Figure 2 is rather odd in the sense that, “The kriging variance rises up to a maximum and then drops off.” That’s precisely what Armstrong and Champigny wrote in A Study of Kriging Small Blocks published in CIM Bulletin of March 1989. What I saw kriging variances do is what real variances never do. Armstrong and Champigny alleged kriging variances drop off because mine planners over-smooth small blocks. More research brought to light that kriged block estimates and actual grades were “uncorrelated.” That would make a random number generator of sorts for kriged block grades. It was David himself who approved that blatant nonsense for publication in CIM Bulletin.
Figure 2 gives kriging variances as a function of variogram ranges. As such, it was more telling than Parker’s. Neither Shurtz nor Parker scrutinized Armstrong and Champigny’s 1989 A Study of Kriging Small Blocks. Otherwise, Shurtz might have pointed out Parker’s kriging variances looked a touch over-smoothed. Neither did Parker confess he does over-smooth the odd time.
Corrected and uncorrected sampling variograms for Bre-X’s bonanza grade borehole BSSE198 show where spatial dependence between bogus gold grades of crushed, salted and ordered core samples from this borehole dissipates into randomness. The adjective “corrected” implies that the variance of selecting a test portion of a crushed and salted core sample, and the variance of analyzing such a test portion, are extraneous to the in situ variance of gold in Bre-X’s Busang resource. Subtracting the sum of extraneous variances gives an unbiased estimate for the intrinsic variance of bogus gold in Busang’s phantom gold resource. Fisher’s F-test proved this intrinsic variance to be statistically identical to zero.
Harry Parker and Jean-Michel Rendu appear to speak for the Society for Mining, Metallurgy and Exploration (SME) in the USA. What it takes to cook up ballpark reserves and resources are soothsayers who know how to failingly infer mineralization between boreholes, hardcore krigers and cocksure smoothers. What CRIRSCO ought to have done after the Bre-X fraud is set up an ISO Technical Committee on reserve and resource estimation. It’s never too late to do it! GIGO may be a bit dated but Garbage In does stand the test of time. Nowadays, Good Graphics Bad Statistics Out is a much more likely outcome. What a pity that GIGGBSO lacks GIGO’s punch!