Creaming-and the Likelihood of Discovering Further Giant Petroleum Fields

The applied context of this paper is the exploration for undiscovered resources, like oil accumulations in different deposits, where the most promising deposits are likely to be drilled first, so-called creaming. This means that the observed sequence of discoveries over time in a region, say the Norwegian Continental Shelf, exhibits a decaying pattern. A log normal size distribution may fit available data well, but cannot be used directly for prediction purposes in the creaming context, since the observations are not a random sample from the assumed unknown parent distribution. The paper studies a creaming model in the context of sampling with probabilities in proportion to size, for which a lognormal size distribution has nice analytical features. The theory is applied to the prediction of remaining oil accumulations on the mature part of the Norwegian Continental Shelf.