A study on kriging small blocks

Professor Dr Margaret Armstrong ranks high amongst geostatistical scholars. In contrast, Mr Normand Champigny has earned a Certificate of sorts and turned into a gifted CIM Member. CIM Bulletin published this small block study in March 1989. What the authors had discovered was that “kriged estimates for very small blocks are over-smoothed”, and that “mine planners often insist on kriging very small blocks!” Good grief! The problem is not so much that mine planners have not been taught how to test for spatial dependence between measured values in ordered sets. The real problem is that Professor Matheron did not know how to test for spatial dependence between measured values, and how to count degrees of freedom! So it was not at all surprising when Matheron flunked his PhD thesis in 1970! Yet, in 1974 Matheron was ready to teach “Brownian motion along straight lines!” He has been hailed as the Founder of Spatial Statistics! For crying out loud!

Professor Dr Margaret Armstrong had figured out what Matheron had failed to grasp! After completing a Master’s degree in mathematical statistics at the University of Queensland, she took off to the City of Lights. She qualified for a PhD in geostatistics after the distance-weighted average had shed its variance. Stripping variances off distance-weighted averages AKA kriged estimates has stood the test of time. Nobody ever thought about counting degrees of freedom on Matheron’s watch.

Professor Dr Roussos Dimitrakopoulos was also a graduate at the University of Queensland in Australia. Dr RD dismissed degrees of freedom but got into stringing Markov chains at McGill University in Canada. He did so because he does not know how to derive unbiased confidence limits for metal contents and grades of mineral inventories.

Professor Dr Michel David must have been pleased that mine planners were to blame for over-smoothed estimates. But he was not at all pleased that my talk about Sampling in Exploration-Theory and Practice was a first at PDAC’s meeting on March 23, 1991. He took a seat opposite my lectern and didn’t  pose a single question! Neither did other geostatistocrats!

In 1992 I visited BHP’s mining operations in Australia. The problem was BHP’s assay laboratory got significantly lower grades than its mine planners had been predicting. For crying out loud! Surely, investors should get unbiased confidence limits for metal contents and grades of mineral inventories!

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