PART A: A model of the discovery process can be used to predict the size distribution of future petroleum discoveries in partially explored basins. The parameters of the model are estimated directly from the historical drilling record, rather than being determined by assumptions or analogies. The model is based on the concept of the area of influence of a drill hole, which states that the area of a basin exhausted by a drill hole varies with the size and shape of targets in the basin and with the density of previously drilled wells. It also uses the concept of discovery efficiency, which measures the rate of discovery within several classes of deposit size. The model was tested using 25 years of historical exploration data (1949-74) from the Denver basin. From the trend in the discovery rate (the number of discoveries per unit area exhausted), the discovery efficiencies in each class of deposit size were estimated. Using pre-1956 discovery and drilling data, the model accurately predicted the size distribution of discoveries for the 1956-74 period. PART B: A stochastic model of the discovery process has been developed to predict, using past drilling and discovery data, the distribution of future petroleum deposits in partially explored basins, and the basic mathematical properties of the model have been established. The model has two exogenous parameters, the efficiency of exploration and the effective basin size. The first parameter is the ratio of the probability that an actual exploratory well will make a discovery to the probability that a randomly sited well will make a discovery. The second parameter, the effective basin size, is the area of that part of the basin in which drillers are willing to site wells. Methods for estimating these parameters from locations of past wells and from the sizes and locations of past discoveries were derived, and the properties of estimators of the parameters were studied by simulation. PART C: This study examines the temporal properties and determinants of petroleum exploration for firms operating in the Denver basin. Expectations associated with the favorability of a specific area are modeled by using distributed lag proxy variables (of previous discoveries) and predictions from a discovery process model. In the second part of the study, a discovery process model is linked with a behavioral well-drilling model in order to predict the supply of new reserves. Results of the study indicate that the positive effects of new discoveries on drilling increase for several periods and then diminish to zero within 2? years after the deposit discovery date. Tests of alternative specifications of the argument of the distributed lag function using alternative minimum size classes of deposits produced little change in the model's explanatory power. This result suggests that, once an exploration play is underway, favorable operator expectations are sustained by the quantity of oil found per time period rather than by the discovery of specific size deposits. When predictions of the value of undiscovered deposits (generated from a discovery process model) were substituted for the expectations variable in models used to explain exploration effort, operator behavior was found to be consistent with these predictions. This result suggests that operators, on the average, were efficiently using information contained in the discovery history of the basin in carrying out their exploration plans. Comparison of the two approaches to modeling unobservable operator expectations indicates that the two models produced very similar results. The integration of the behavioral well-drilling model and discovery process model to predict the additions to reserves per unit time was successful only when the quarterly predictions were aggregated to annual values. The accuracy of the aggregated predictions was also found to be reasonably robust to errors in predictions from the behavioral well-drilling equation.