AUTHOR=Carle Steven F. , Fogg Graham E. 

TITLE=Integration of Soft Data Into Geostatistical Simulation of Categorical Variables

JOURNAL=Frontiers in Earth Science

VOLUME=Volume 8 - 2020

YEAR=2020

URL=https://www.frontiersin.org/journals/earth-science/articles/10.3389/feart.2020.565707

DOI=10.3389/feart.2020.565707

ISSN=2296-6463

ABSTRACT=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.