Quantifying uncertainty in petroleum resources is important for development planning and decision making. Increasingly, geostatistical techniques are used to integrate diverse data sources and provide a defensible model of uncertainty. Petroleum resources are calculated from a combination of variables including thickness, porosity and saturation. Uncertainty in global petroleum resources are calculated stepwise: 1) establish the local uncertainty in each variable using a conventional Gaussian geostatistical model; 2) sample the local distributions with spatial correlation using a p-field based technique; 3) modify the p-field samples to have the correct multivariate variability using the LU technique; and, 4) assemble the distribution of uncertainty over any volume using the joint spatial/multivariate realizations. The alternatives to this technique are a simplistic Monte Carlo simulation without spatial correlation or a more complex high resolution geostatistical model. Speed and mathematical consistency are the main advantages of the proposed technique. The theoretical basis of the spatial/multivariate decomposition approach is developed with the assumptions and implementation details. A synthetic example from a realistic case study is presented showing the global uncertainty in oil-in-place over arbitrarily large areas.