Uncertainty assessment in an arbitrary volume without the use of geostatistical simulation.


Alvaro Riquelme, Queen's University at Kingston ; Julian Ortiz, The Robert M. Buchan Department of Mining, Queen's Universty at Kingston

Ore bodies are variable in nature, and we can only access a few locations, through sampling, to characterize their properties. In mining, important economic decisions must be made, with fairly high levels of risk, based on this very limited information: the mining method, processing equipment and setting, plan and schedule. Several issues arise when the goal is to predict the performance of a specific process. Sample quality and spatial variability inject uncertainty in the final model. This uncertainty should be taken into consideration when making decisions, rather than basing these decisions on expected average values. This is critical when extreme values have large consequences in process performance. The state-of-the-art approach to this uncertainty quantification problem is the use of stochastic simulation, which generates multiple spatial models that must be processed to understand the effect of variability in the response variable. However, this process is computationally expensive, and the results are hard to use and automate for decision-making, especially for large grid sizes. In this research, we present an approach to quantify the spatial uncertainty without resorting to the use of stochastic simulation. We developed an analytical closed-form solution that allows us to determine the variance in an arbitrary volume conditioned by sampling data, for the case of lognormal distributed variables. Analytical results show us explicitly proportional effect and the conditioning of sample data. Synthetical cases have been developed showing high accuracy in the prediction of variance when comparing with simulations results. As an example of how to transfer the in situ uncertainty into the process, an application of the procedure is showed in the case of dispersion prediction in monthly volumes of ore sent to processing plant, allowing us future reconciliation.
Keywords: Geostatistics Simulation Uncertainty