Mathematical Geology

, Volume 28, Issue 5, pp 625–656 | Cite as

Topological and geometric characterization of fault networks using 3-dimensional Generalized maps

  • Yvon Halbwachs
  • Gabriel Courrioux
  • Xavier Renaud
  • Philippe Repusseau


The consistent geometric and topological representation of a fault network is possible through a method based on the implementation of 3-dimensional Generalized maps (3-G-map) enabling all subdivisions of space to be represented. The fault network is modeled as an assemblage of polygonal faces from a set of geometric data on the faults and a knowledge of the relationships between the faults. The resultant model is expressed in terms of a 3-G-map in which volume, surface, and topological information is constructed taking into account computed intersections between faults and known interception relations. The fault network can be edited through an interactive 3-D viewer which provides several tools for navigating within the 3-G-map. Information relevant to a fault network, such as block geometry, connectivity, adjacencies, and connectivity relationships, can be obtained by exploring the data structure of the 3-G-map. The fault network architecture is made comprehensive through interactive modeling and visualization.

Key Words

3D-modeling n-generalized-maps fault network 


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  1. Anderson, J., Shapiro, A. M., and Bear, J., 1984, A stochastic model of a fractured rock conditioned by measured information: Water Resources Res., v. 20, no. 1, p. 79–88.Google Scholar
  2. Ansaldi, S., Floriani, L., and Falsidieno, B., 1985, Geometric modeling of solid objects by using a free adjacency graph representation: Computer Graphics, v. 19, no. 3, p. 131–139.Google Scholar
  3. Auerbach, S., and Schaeben, H., 1990, Computer-aided design of geologic surfaces and bodies: Math. Geology, v. 22, no. 8, p. 957–987.Google Scholar
  4. Baecher, G. B., 1983, Statistical analysis of rock mass fracturing: Math. Geology, v. 15, no. 2, p. 328–348.Google Scholar
  5. Bertrand, Y., 1992, Spécification algébrique et réalisation l'un modeleur interactif d'objets géométriques volumiques: unpubl. doctoral dissertation, Louis Pasteur University, Strasbourg, France, 255 p.Google Scholar
  6. Bertrand, Y., Dufourd, J. F., Françon, J., and Lienhardt, P., 1992, Modélisation Volumique à Base Topologique: Actes MICAD 92, Paris, v. 1, p. 59–74.Google Scholar
  7. Bertrand, Y., Lienhardt, P., Françon, J., and Dufourd, J. F., 1993, 3-dimensional manifold modeling using generalized maps: Rept. 93-03, Louis Pasteur University, Strasbourg, France, 46 p.Google Scholar
  8. Billaux, D., Chilès, J. P., Hestir, K., and Long, J., 1989, Three dimensional statistical modelling of a fractured rock mass—an example from the Fanay-Augères mine: Rock Mechanic Mining Science Abstract, v. 26, no. 3/4, p. 281–299.Google Scholar
  9. Chilès, J. P., 1989a, Three-dimensional geometric modelling of a fracture network,in Buxton, B. E., ed., Geostatistical, sensitivity, and uncertainty methods for ground water flow and radionuclide transport modeling: Battelle Press, Columbus, Ohio, p. 361–385.Google Scholar
  10. Chilès, J. P., 1989b, Modélisation géométrique de réseaux de fractures,in Armstrong, M., ed., Geostatistics: Klurver, Dordrecht, The Netherlands, v. 1, p. 57–76.Google Scholar
  11. Conrad, F., and Jacquin, C., 1973, Représentation d'un réseau bidimensionnel de fractures par un modèle probabiliste. Application au calcul des grandeurs géométriques des blocs matriciels: Revue de l'I.F.P., v. XXVIII, no. 6, p. 843–890.Google Scholar
  12. Dershorvitz, W. S., and Einstein, H. H., 1988, Characterizing rock joint geometry with joint system models: Rock Mechanics and Rock Engineering, v. 21, no. 1, p. 21–51.Google Scholar
  13. Dufourd, J. F., 1991, Formal specification of topological subdivisions using hypermaps: CAD, v. 23, no. 2, p. 99–116.Google Scholar
  14. Dufourd, J. F., Gross, C., and Spehner, J. C., 1989, A digitisation algorithm for the entry of planar maps: Proc. Comp. Graphics Intern., Leeds U.K., p. 649–662.Google Scholar
  15. Gervais, F., Chilès, J. P., and Gentier, S., 1992, Geostatistical analysis and hierarchical modeling of a fracture network in a stratified rock mass: Proc. Conference on Fractured and Jointed Rock Mass, Preprints, v. 1, p. 158–165.Google Scholar
  16. Lamboglia, K., 1993, Modélisation géométrique à base d'objets non-manifold: unpubl. doctoral dissertation, University of Nancy I, France, 140 p.Google Scholar
  17. Lee, J. S., Veneziano, D., and Einstein, H. H., 1990, Hierarchical fracture trace model: Proc. 31st U.S. Symposium on Rock Mechanics, Balkema, Rotterdam, p. 228–236.Google Scholar
  18. Lienhardt, P., 1989, Subdivision ofN-dimensional spaces andN-dimensional generalized maps: Proc. 5th ACM Symposium on Computational Geometry, Saarbrucken, Germany, p. 228–236.Google Scholar
  19. Lienhardt, P., 1991, Topological models for boundary representation: a comparison withN-dimensional generalized maps: CAD, v. 23, no. 1, p. 59–87.Google Scholar
  20. Lienhardt, P., 1994,N-dimensional generalized maps and cellular quasi-manifolds: Intern. Jour. Computational Geometry and Applications, v. 4, no. 3, p. 275–324.Google Scholar
  21. Mallet, J. L., 1989, Discrete smooth interpolation: ACM Transactions on Graphics, v. 8, no. 2, p. 121–144.Google Scholar
  22. Pigot, S., 1992, A topological model for a 3-D spatial information system,in Proc. of the 5th Intern. Symposium on Spatial Data Handling, Charleston, South Carolina, p. 344–359.Google Scholar
  23. Pigot, S., 1994, Generalized singular 3-cell complexes,in Proc. 6th Intern. Symposium on Spatial Data Handling, Edinburgh, p. 89–111.Google Scholar
  24. Renard, P., and Courrioux, G., 1994, 3-D Geometric modeling of a faulted domain: the Soultz horst examples (Alsace, France): Computers & Geosciences, v. 20, no. 9, p. 1379–1390.Google Scholar
  25. Siehl, A., Ruber, O., Valdivia-Machego, M., and Klaff, J., 1992, Geological maps derived from interactive spatial modeling: Geol. Jb., A 122, p. 273–289.Google Scholar
  26. Spehner, J. C., 1991. Merging in maps and pavings: Theoretical Computer Science, v. 86, no. 2, p. 205–232.Google Scholar
  27. Verschuren, M., 1991, 3-D modeling of a complex fault pattern on an entry level 2-D workstation: Lecture Notes in Earth Sciences,in Pflug, R., and Harbaugh, J. W., eds., Computer Graphics in Geology—3D Computer Graphics in Modeling Geological Structures and Simulating Geologic Processes: Springer-Verlag, Berlin, p. 83–88.Google Scholar
  28. Weiler, K., 1986, Topological structure for geometric modeling: unpubl. doctoral dissertation, Rensselaer Polytechnic Institute, 340 p.Google Scholar
  29. Zoraster, S., and Ebisch, K., 1990, Incorporating fault geometry into geological horizon models: Geobyte, v. 5, no. 2, p. 30–36.Google Scholar

Copyright information

© International Association for Mathematical Geology 1996

Authors and Affiliations

  • Yvon Halbwachs
    • 1
  • Gabriel Courrioux
    • 2
  • Xavier Renaud
    • 2
  • Philippe Repusseau
    • 2
  1. 1.Centre de Recherche en InformatiqueUniversité Louis-PasteurStrasbourg CedexFrance
  2. 2.Bureau de Recherches Géologiques et MinièresOrléans Cedex 2France

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