Integration of Uncertain Data in Geostatistical Modelling

Most geostatistical estimation and simulation methodologies assume the experimental data as hard measurements, meaning that the measures of a given property of interest are not associated with uncertainty. The challenge of integrating uncertain experimental data at the geostatistical estimation or simulation models is not new. Several attempts have been made, either considering the uncertain data as soft data or interpreting it as inequality constraints, based on the indicator formalism or decreasing the weight of soft data in kriging procedures. This paper presents a stochastic simulation methodology where the uncertain experimental data are modelled by a probability distribution at each sample location. Data values are firstly drawn, by stochastic simulation, at these locations prior to the simulation of the rest of the grid nodes. This method is also extended to the simulation of categorical uncertain data, as well as to the simulation with uncertain block support data. To illustrate the proposed methodology, an application to a real case study of pore pressure prediction of oil reservoirs is presented, as well as an upscaling problem.