What probability law characterizes the spatial distribution of oil and gas fields in a petroleum province? How does the probability that a wildcat well will penetrate a reservoir change (if at all!) as the history of a basin unfolds?

The answers to these questions are important inputs to any model of the process of exploring for oil and gas. Some attention has been devoted to these questions, but there are deficiencies in the treatments of each.

Our objective is twofold: (1) to posit a reasonable model of the spatial distribution of petroleum reservoirs that conforms to several empirically observed facts about such distribution; and (2) to examine a simple first-order model of the exploration process that allows one to test empirically the hypothesis that, at an early stage in the exploration of a basin, the process behaves like sampling without replacement.

The techniques of inference outlined will be useful in predicting properties of an unexplored region.