Structural Interpretation of Sparse Fault Data Using Graph Theory and Geological Rules

Structural uncertainty exists when associating sparse fault interpretations made from two-dimensional seismic lines or limited outcrop observations. Here, a graph formalism is proposed that describes the problem of associating spatial fault evidence. A combinatorial analysis, relying on this formalism, shows that the number of association scenarios is given by the Bell number, and increases exponentially with the number of pieces of evidence. As a result, the complete exploration of uncertainties is computationally highly challenging. The available prior geological knowledge is expressed by numerical rules to reduce the number of scenarios, and the graph formalism makes structural interpretation easier to reproduce than manual interpretation. The Bron–Kerbosch algorithm, which finds maximal cliques in undirected graphs, is used to detect major possible structures. This framework opens the way to a numerically assisted exploration of uncertainties during structural interpretation.