There are two major problems in the construction of a stochastic model that describes quantitatively the spatial distribution of undiscovered petroleum accumulations: a) available exploration results are biased; and, b) information associated with the locations of accumulations is incomplete. Studies in the Western Canada Sedimentary Basin (WCSB) and elsewhere indicate that the spatial characteristics of petroleum accumulations are fractal. In this paper, we propose the use of these fractal characteristics to calibrate sampling bias, thus deriving an unbiased spatial correlation (covariance function) for the stochastic modelling. The uncertainty in the modelled locations of undiscovered accumulations resulting from insufficient information is captured by equal-probable realizations of the simulation and these are subsequently converted to a probability map of petroleum occurrence. In the example, a pre-1994 exploratory data set for the Rainbow gas play in WCSB was used to derive simulation parameters. A comparison of the simulated results to post-1993 gas discoveries in the same play shows that most of the post-1993 discoveries are located in areas with high predicted probability values.