The academic field of "economic geology" seems to cover the exploitation of resources rather than stewardship of the resources [TOD link]. If somebody in this research area had actually wanted to or had the charter to, they could have done an impartial study of resource depletion based on some rather simple models. The fact that a branch of this field is called "geostatistics" makes one think that somebody must be doing original research. But looking at the Wiki entry for geostatistics and the Wiki entry for the "father" of geostatistics, Matheron, you find lots of controversy.
And then, following the links, you also find that a web-site exists with the URL http://www.geostatscam.com, subtitled "Geostatistics: From human error to scientific fraud" . The engineer who runs the site, Jan Merks, makes the strong claims that the specialty of geostatistics consists of "voodoo statistics" and "scientific fraud". Granted, it looks like this criticism resides mainly in the context of mineral mining and perhaps petroleum extraction is not really a part of this field, but it makes you wonder what exactly constitutes research in geostatistics. A sample of Merks' charges:
From what I understand about the technique known as "kriging", it seems to provide a way to interpolate potential mineral deposits from sampled spatial measurements in surrounding areas. The criticism leveled on this technique rests on the observation that geostatisticians never want to provide a sound estimate of the variance of their interpolation. According to Merks, they at best create a phony variance to justify their estimate. If this is indeed so, I would agree that we should seriously look into what weird interpolations geostatistics considers as science.Degrees of freedom fighters amongst professional engineers and geoscientists are addicted to Matheron's junk science of geostatistics. Hardcore krigers and cocksure smoothers turned mineral exploration into a game of chance with the stakes of mining investors.
As a counter-example, in all the models I use for oil depletion, I always use a huge variance consistent with the Maximum Entropy Principle. An assumed variance such as this maximizes the disorder, and provides the best estimate for reasoning under uncertainty. In other words, if you don't know the variance, you have too assume the worst case. The bad kriging estimates seem to basically say that if point A has X mineral grade and point B has Y mineral grade, then point C halfway between A and B has (X+Y)/2 mineral grade. From what I understand, unless you have a real spatial correlation between the points (which apparently no one verifies) no way can you do a naive interpolation like this. I have written papers on spatial correlation and always start by looking for the presence or lack of statistical independence between separated points.
So if geostatistics treats probability and statistics like a cook interpolates half-a-cup of bleached flour, the field has serious problems. It brings up the rather obvious question, why do they teach this? Do they realize the sad fact that exploration works at best as a pure crap-shoot and you might as well get the fresh eager graduates out in the field with nothing more than a pair of dice? Are the rockhead geologists that jaded?
H G Wells predicted that statistical thinking would become as important as the ability to read and write. Would Wells have embraced the nouveau pseudo science of interpolation without justification with the same unbridled passion as the world's mining industry did? [from Merks website]