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 find 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 the latter question by Arps and Roberts and Kaufman. Bradley and Uhler and Griffiths have touched on aspects of the former. There are deficiencies in each of these treatments.

Our objective here is two-fold: first to posit a reasonable model of the spatial distribution of petroleum reservoirs that conforms to a number of empirically observed facts about such distributions; second, 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.

We have examined some Canadian data as examples of applications. The techniques of inference are useful in predicting properties of an unexplored region.

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