Integration of Soft Data Into Geostatistical Simulation of Categorical Variables - Carle, Steven F.; Fogg, Graham E. (Frontiers in Earth Science, 2020)
Abundant uncertain or indirect “soft data” (e.g., geologic interpretation, driller’s logs, geophysical logs or imaging, etc.) offer indirect constraints or soft conditioning to stochastic models of subsurface categorical variables such as hydrogeologic units or facies. Previous geostatistical simulation algorithms have not fully addressed the impact of data uncertainty in formulation of the (co)kriging equations and the objective function in simulated annealing (or quenching). This paper introduces the geostatistical simulation code tsim-s, which accounts for categorical data uncertainty through a data “hardness” parameter. In generating geostatistical realizations with tsim-s, the uncertainty inherent to soft conditioning is factored into both (1) the data declustering and spatial correlation functions in cokriging and (2) the acceptance probability for change of category in simulated quenching. The degree to which soft data constrains an individual quantified by mapping category probabilities derived from multiple realizations. In addition to point or borehole data, arrays of data (e.g. as derived from a depth-dependency function, probability map, or “prior” realization) can also be used as soft conditioning. The tsim-s algorithm provides a theoretically sound and general framework for integrating datasets of variable location, resolution, and uncertainty into geostatistical simulation of categorial variables.