Mathematical Geosciences

, Volume 51, Issue 8, pp 1091–1107 | Cite as

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

Fault Data Interpretation
  • G. GodefroyEmail author
  • G. Caumon
  • G. Laurent
  • F. Bonneau
Short Note


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.


Structural interpretation Fault network Graph processing 



This work was performed within the framework of the RING project at the Université de Lorraine. The authors are grateful to the industrial and academic sponsors of the RING-GOCAD Consortium managed by ASGA ( Software corresponding to this paper is available to sponsors in the RING software package FaultMod2. The authors acknowledge Paradigm for the SKUA-GOCAD software and API. The authors also thank D.J. Sanderson and an anonymous reviewer for their constructive comments that helped to improve the manuscript.


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Copyright information

© International Association for Mathematical Geosciences 2019

Authors and Affiliations

  1. 1.Université de Lorraine, CNRS, GeoRessources / ENSGVandoeuvre-lès-NancyFrance

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