Creaming and the Likelihood of Discovering Additional Giant Petroleum Fields

The applied context of this paper is the exploration for petroleum resources, like petroleum accumulations in different deposits, where the most promising deposits are likely to be drilled first, based on some size indicators, so-called creaming. The paper explores creaming models in the context of sampling with probabilities in proportion to size, for which a lognormal size distribution has nice analytical features. It departs from the traditional paradigm in petroleum resource assessment. Instead of conceiving a finite population being depleted over time in a decaying fashion with respect to size, the situation is studied within the framework of independent observations (infinite population) and an exploration maturity-dependent creaming factor. The theoretical and practical consequences for inference on the parent population and the probabilities and expectations linked to future discoveries are studied. The theory applies to the issue of remaining sizes of petroleum resources to be found within different future discovery horizons on the mature part of the Norwegian Continental Shelf. The aim is to obtain reasonable and useful predictions, and not to provide the best possible explanation of the exploratory behavior itself.