It’s high time to try and read Agterberg’s state of mind in his tribute to the life and times of Professor Dr George Matheron. It taught me so much more about his way of thinking than I had learned when we talked in the early 1990s. Neither could I have found out what I needed to know had the Centre de Géosciences (CG) not posted Matheron’s works on its website. When I looked at CG’s spiced up website for the first time I found out that he wrote his Note statistique No 1 in 1954. So, it seems safe to assume Matheron thought he was working with statistics. His thoughts are accessible again since CG’s website is back online.
Agterberg said in his tribute that Matheron “commenced work on regionalized random variables inspired by De Wijs and Krige.” Let’s take a look at Matheron’s very first paper and try to figure out what he did in his Formule des Minerais Connexes. He tested for associative dependence between lead and silver grades in lead ore. He derived length-weighted average lead and silver grades of core samples that varied in lengths. What he didn’t do was derive variances of length-weighted average lead and silver grades. Neither did he test for spatial dependence between metal grades of ordered core samples. He didn’t give his primary data but scribbled a few stats in this 1954 paper. He didn’t refer to De Wijs or to Krige. In fact, Matheron rarely referred to the works of others.
Where’s the Central Limit Theorem?
Matheron was a master at working with symbols. Yet, he wouldn’t have made the grade in statistics because the Central Limit Theorem was beyond his grasp. The Founder of Spatial Statistics did indeed have a long way to go in 1954. So, he penned nothing but Notes Statistique until 1959. That's when he tucked Note géostatisque No 20 tightly behind Note statistique No19. So, why did he switch from stats to geostats? It took quite a while to explain but here’s what Matheron said in 1978. He did it because “geologists stress structure” and “statisticians stress randomness.” That sort of drivel does stand the test of time in Matheron’s Foreword to Mining Geostatistics just as much as Journel’s mad zero kriging variance does in Section V.A. Theory of Kriging.
What did D G Krige do that so inspired young Matheron? In 1954 Krige had looked at, “A statistical approach to some mine valuation problems on the Witwatersrand.” It still reads like real statistics, doesn’t it? In 1960 he did reflect, “On the departure of ore value distributions from the lognormal model in South African gold mines.” Isn't that the nasty reality at gold mines? So, Krige did indeed work with statistics in those days. He may since have had some epiphany because he cooked up in 1976, “A review of the development of geostatistics.” This is why Krige was highly qualified to put a preface to David’s 1977 Geostatistical Ore Reserve Estimation with its infinite set of simulated values in Section 12.2 Conditional Simulations.
Why did H J De Wijs wind up in Agterberg’s tribute to Matheron? Agterberg had found out in 1958 that De Wijs worked with formulas that “differed drastically from those used by mathematical statisticians.” Agterberg preferred “the conventional method of serial correlation.” Why would Agterberg talk about mathematical statistics and serial correlation in 1958 when he himself had stripped the variance of his own distance-weighted average point grade in 1970 and in 1974? Agterberg ought to explain why in 2009!
De Wijs brought vector analysis without confidence limits to mining engineering at the Technical University of Delft in the Netherlands when he left Bolivia after the Second World War. Jan Visman worked at the Dutch coal mines during the war and surfaced with tuberculosis, a novel approach to sampling theory and practice, and a huge set of test results determined in samples taken from heterogeneous sampling units of coal. So much information, in fact, that he was encouraged to write his PhD thesis on this subject. And that’s exactly what he did! He continued to work as a mining engineer at the Dutch State Mines. When he found out that the Dutch Government was thinking of closing its coal mines he migrated to Canada in 1951. He worked briefly in Ottawa until 1955, and moved to Alberta where his formidable expertise was put to work in the coal industry.
Visman’s sampling experiment with pairs of small and large increments is described in ASTM D2234-Collection of a Gross Sample of Coal, Annex A1. Test Method for Determining the Variance Components of a Coal. Visman’s sampling theory has been quoted in a range of works. Following are some surprising references to Visman’s work, and to the lack thereof after Gy's work was widely accepted for no apparent reason.
Gy’s 1967 L’Échantillonnage des Minerais en Vrac, Tome 1 … two
Gy’s 1973 L’Échantillonnage des Minerais en Vrac, Tome 2 … eight
David’s 1977 Geostatistical Ore Reserve Estimation … two
Journel & Huijbregts’s 1978 Mining Geostatistics … zero
Clark’s 1979 Practical Geostatistics … zero
Gy’s 1979 Sampling Particulate Materials, Theory Practice … zero
Visman's sampling theory is based on the additive property of variances. None of the above works deals with the additive property of variances in a measurement hierarchy.
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