An automatic workflow for risk analysis on spatial output properties using kriging‐based surrogate models—Application to stratigraphic forward modelling

Abstract

AbstractStratigraphic numerical forward process‐based models represent the formation and evolution of sedimentary basins through time. Their main deliverable is a 3D digital grid which can help to better understand the sedimentary basin infill. These models depend on several input parameters that need to be characterized for the studied basin. However, available data such as well logs and seismic data may not provide enough information to identify a unique possible value for these parameters. It is then crucial to take the uncertainty induced by this non‐uniqueness into account in the decision‐making process. As a single numerical stratigraphic forward simulation can be very time consuming, solutions are needed to limit the computational cost required to estimate such uncertainties. In particular, machine learning techniques can be used to build meta‐models that mimic the simulator and provide fast estimations of its outputs for any values of the input parameters. The key step for the efficiency of such an approach stands in the choice of the set of simulations (or training set) used to build the meta‐models: it should be informative enough to obtain accurate predictions for the output properties of interest, but also of reasonable size to limit simulation time. Then, meta‐models can be used to investigate a large number of models and make uncertainty quantification easier. Here, we focus on the prediction of spatial outputs of interest approximated from the joint use of several kriging‐based meta‐models combined to reduced basis decomposition. Sequential approaches have been proposed in the literature to identify training sets iteratively for a kriging‐based meta‐model, building upon the specific structure of such surrogates. We propose here to extend these approaches to the context of spatial output predictors. The results obtained on two synthetic test cases, representing a carbonate platform and a clastic environment, highlight the potential of the proposed approach for risk analysis to iteratively build training sets with a satisfactory efficiency in terms of simulation time and prediction accuracy.