Accounting for model sensitivity in controlled (log)Gaussian geostatistical simulation

Abstract

Geostatistical simulation using controlled or stratified sampling methods, namely Latin hypercube and stratified likelihood sampling, are capable of generating representative realizations from (log)Gaussian random fields, i.e., spanning efficiently the range of values corresponding to the (log)Gaussian multivariate probability distribution. Although such realizations often serve as parameters for physical process simulators, existing controlled sampling methods do not account for model sensitivity; hence, they need not yield representative realizations of model outputs. To address this shortcoming, controlled sampling methods are embedded within a two-step simulation procedure. The first step involves stratified sampling at a set of control points where attribute values are expected to exert a large impact on model predictions and/or where uncertainty in such predictions is expected to be largest. In the second step, control point samples are used to generate attribute realizations over the entire study region using classical geostatistical simulation. The application of the proposed controlled, two-step, geostatistical simulation procedure is illustrated in a hydrogeological context via a synthetic case study involving physically-based simulation of flow and transport in a porous medium with known boundary and initial conditions over a simple geometrical domain.