Facies proportion uncertainty in presence of a trend

Categorical variable modeling is of great significance for resource estimation as it defines a major aspect of geological heterogeneity and uncertainty. Stochastic simulation can be used to generate multiple equally-probable realizations that describe the uncertainty in the spatial distribution of categorical variables such as facies. These realizations reasonably sample the space of uncertainty if the input statistics are well known. However, the input statistics are often poorly defined due to sparse data. The prior parameter uncertainty related to proportions of different categories is required to achieve an accurate evaluation of the space of uncertainty. For decision making and risk analysis, it is critical to have an accurate and precise model of uncertainty associated with 3924 the subsurface geology. A methodology is proposed, implemented and checked to quantify parameter uncertainty related to facies proportions in presence of a locally varying proportion model (a trend model). Unconditional sequential indicator simulation (SIS) is employed to implement the spatial bootstrap and quantify the prior proportion uncertainty. A trend building algorithm provides multiple realizations of the trend model based on the spatial bootstrap realizations of sampled data. Passing this prior parameter uncertainty through geostatistical simulation provides a realistic posterior model of uncertainty that accounts for the data configuration, conditioning, spatial correlation, and the domain limits.