Stochastic stratigraphic correlation of multiple wells seen as a Directed Acyclic Graph creation problem

International audienceThe correlation of one-dimensional stratigraphic sections (such as well data) has implication in the spatio-temporal analysis of sedimentary systems, source-to-sink calculations, and natural resource quantification. Therefore, capturing uncertainties in stratigraphic correlation can be consequential, but it raises combinatorial challenges, especially in the presence of multiple wells. Inspired by multiple sequence alignment methods in bioinformatics, we propose a hierarchical multiple well correlation method which produces several likely stratigraphic correlation scenarios from a possibly large set of vertical or subvertical wells. One of the main ideas is to consider sets of correlations between wells as a directed acyclic transition graph. In this graph, the nodes represent stratigraphic units and the edges represent the possible vertical succession of these units. In the proposed method, groups of wells are correlated in parallel by associating larger and larger clusters defined by traversing a proximity tree. Each correlation between two groups of wells is achieved by a variant of the n-best Dynamic Time Warping method which considers the transition graphs instead of the wells themselves. Because the graph size increases exponentially as new wells are added to the correlation set, the graphs are pruned to keep the number of solutions manageable. Results on synthetic cases show that the method allows a laptop computer to find a reasonable set of solutions in a few minutes, for 20 wells containing an average of 118 samples on each well. We also show that changes in the correlation rules and the correlation constraints have a significant influence on the obtained result space. For a particular study, this suggests an important scope for further research is to define formal stratigraphic correlation rules adapted to the observations and to the stratigraphic concepts deemed appropriate by sedimentologists