Friday, August 24, 2012

Metrology in mining and metallurgy

Trans Tech Publication printed Volume 4 in its series on Bulk Materials Handling in 1985. It was called Sampling and Weighing of Bulk Solids. An unauthorized translation into Mandarin surfaced in November 1989. We do have a Canadian copyright on Metrology in Mining and Metallurgy. This text will also deal in detail with mineral exploration. It will do so because the Bre-X fraud was by far the worst salting scam I have ever unscrambled. I did it for Barrick Gold Corporation several months before Bre-X’s boss salter wound up in the Kalimantan jungle. That’s but one reason why I have registered the Canadian copyright for Metrology in Mining and Metallurgy.  

What has put my work on the map was the interleaved sampling protocol for mineral concentrates. The same protocol underpins the design of a mechanical sampling system to determine trace elements in cathode copper. I know how to derive 95% confidence limits for metal grades and contents of reserves and of proven parts of resources. Page 120 of my textbook in Section 4.5 Propagation of Variances gives the variance of a general function as defined in probability theory. One would expect a scholar with a PhD in epidemiology and biostatistics to be familiar with the properties of variances and the concept of degrees of freedom. I had given a pair of copies of Sampling and Weighing of Bulk Solids to Dr Martha Piper and she gave both to Professor Dr Alastair J Sinclair, PEng, PGeo. Dr Piper could have but did not give a copy to Dr M Klawe, her Dean of Science in those days. UBC’s library in 2011 finally put a copy of my book on one of its shelves. Why it took much too long would make a story in itself at this stage.

UBC’s Department of Geological Sciences took a liking to Matheron’s new science of geostatistics. It came about when Professor Dr Alastair J Sinclair, PEng, PGeo thought that his students stood to benefit more from Matheronian geostatistics than from applied statistics. Dr Piper might have been aware that one-to-one correspondence between functions and variances is sine qua non in applied statistics. All it would have taken in those days was a brief call to Professor Dr Nathan Divinsky.

A peculiar event took place at the Department of Geological Sciences on November 22, 1989. That’s when Dr A J Sinclair greeted those who took my short course on Sampling Precious Metal Deposits, Metrology - A New Look.  CIM Bulletin had earlier entrusted Sinclair with the review of Precision Estimates for Ore Reserves. He had initialed his review with AJS:131 on November 15, 1989. What may have troubled Professor Dr Alastair J Sinclair, PEng, PGeo was that Matheron’s science of geostatistics had left us cold. It may explain why he hopped in and out of Room 330A like a jack-in-the-box. But he could have asked the odd question during my talk. For Sir R A Fisher’s sake!

One-to-one correspondence between functions and variances was as far beyond the grasps of David and of Sinclair in 1989 as it was beyond Matheron’s grasp in 1952. The question is why variances of distance-weighted averages are still missing in 2012. It is true that the distance-weighted average itself was never lost but had merely morphed into a kriged estimate. But its variance had vanished when Matheron and his disciples had cooked up geostatistics.

The attachment to my letter of November 30, 1994 to Mr John Drury, CIM Ad Hoc Reserve Definitions Committee, shows how to derive the variance of a mass of metal in crushed ore or insitu ore.

ISO/DIS 13543-Determination of Mass of Contained Metal in the Lot

Borehole statistics with spreadsheet software
SME Volume 308, Transactions 2000

It had come about that the new science of geostatistics called for a mind-numbing step. Matheron and his minions stripped the variance off the distance-weighted average and called what was left a kriged estimate. The miracle of that stripped variance was embraced at UBC with as much zeal as it was at Stanford. Professor Dr A J Journel was asked why Fisher’s F-test was not applied to test for spatial dependence between measured values in ordered sets. His reply has graced my website since 2003. Journel seems to encourage those who assume, krige, smooth and rig the rules of applied statistics with impunity!

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