Multi-Scenario Interpretations From Sparse Fault Evidence Using Graph Theory And Geological Rules

The characterization of geological faults from geological and geophysical data is often subject to uncertainties, owing to data ambiguity and incomplete spatial coverage. We propose a stochastic sampling algorithm which generates fault network scenarios compatible with sparse fault evidence while honoring some geological concepts. This process is useful for reducing interpretation bias, formalizing interpretation concepts, and assessing first-order structural uncertainties. Each scenario is represented by an undirected association graph, where a fault corresponds to an isolated clique, which associates pieces of fault evidence represented as graph nodes. The simulation algorithm samples this association graph from the set of edges linking the pieces of fault evidence that may be interpreted as part of the same fault. Each edge carries a likelihood that the endpoints belong to the same fault surface, expressing some general and regional geological interpretation concepts. The algorithm is illustrated on several incomplete data sets made of three to six two-dimensional seismic lines extracted from a three-dimensional seismic image located in the Santos Basin, offshore Brazil. In all cases, the simulation method generates a large number of plausible fault networks, even when using restrictive interpretation rules. The case study experimentally confirms that retrieving the reference association is difficult due to the problem combinatorics. Restrictive and consistent rules increase the likelihood to recover the reference interpretation and reduce the diversity of the obtained realizations. We discuss how the proposed method fits in the quest to rigorously (1) address epistemic uncertainty during structural studies and (2) quantify subsurface uncertainty while preserving structural consistency.Plain Language Summary This paper presents a way to generate interpretation scenarios for geological faults from incomplete spatial observations. The method essentially solves a "connect the dots" exercise that honors the observations and geological interpretation concepts formulated as mathematical rules. The goal is to help interpreters to characterize how the lack of data affects geological structural uncertainty. The proposed method is original in the sense that it does not anchor the scenarios on a particular base case but rather uses a global characterization formulated with graph theory to generate possible fault network interpretations. The application on a faulted formation offshore Brazil where observations have been decimated shows that the method is able to consistently generate a set of interpretations encompassing the interpretation made from the full data set. It also highlights the computational challenge of the problem and the difficulty to check the results in settings where only incomplete observations exist. The proposed method, however, opens novel perspectives to address these challenges.