The Incorporation of Model Uncertainty in Geostatistical Simulation

A growing area of application for geostatistical conditional simulation is as a tool for risk analysis in mineral resource and environmental projects. In these applications accurate field measurement of a variable at a specific location is difficult and measurement of variables at all locations is impossible. Conditional simulation provides a means of generating stochastic realizations of spatial (essentially geological and/or geotechnical) variables at unsampled locations thereby quantifying the uncertainty associated with limited sampling and providing stochastic models for 'downstream' applications such as risk assessment. However, because the number of experimental data in practical applications is limited, the estimated geostatistical parameters used in the simulation are themselves uncertain. The inference of these parameters by maximum likelihood provides a means of assessing this estimation uncertainty which, in turn, can be included in the conditional simulation procedure. A case study based on transmissivity data is presented to show the methodology whereby both model selection and parameter inference are solved by maximum likelihood. The authors give an overview of their previously published work on maximum likelihood estimation of geostatistical parameters with particular reference to uncertainty analysis and its incorporation into geostatistical simulation.