The convolution point is a good one - I vaguely remember that from undergraduate functional analysis now you mention it. WebHubbleTelescope has been doing some interesting modeling where you take the discovery curve and convolute it to get the production curve, but as far as I can tell he more or less handcrafts the convolution function to make the past history fit. It's not clear here why there'd be enough layers of convolution to produce such good agreement with the Gaussian across several orders of magnitude. OTOH, it seems like there must be some central limit theorem type reasoning here. It would solve a problem in my mind - I would expect the logistic to be a rough approximation to oil production, but the degree of fit with the US production is surprising, and I can't think of any good reason why it should work so precisely. If there's really a central limit story for why the US production is Gaussian, then it's just down to the fact that the logistic derivative and Gaussian are pretty similar shapes.