Spatial analysis of extension fracture systems: A process modeling approach

  • Colin C. Ferguson


Little consensus exists on how best to analyze natural fracture spacings and their sequences. Field measurements and analyses published in geotechnical literature imply fracture processes radically different from those assumed by theoretical structural geologists. The approach adopted in this paper recognizes that disruption of rock layers by layer-parallel extension results in two spacing distributions, one representing layer-fragment lengths and another separation distances between fragments. These two distributions and their sequences reflect mechanics and history of fracture and separation. Such distributions and sequences, represented by a 2 × nmatrix of lengthsL,can be analyzed using a method that is history sensitive and which yields also a scalar estimate of bulk extension, e(L).The method is illustrated by a series of Monte Carlo experiments representing a variety of fracture-and-separation processes, each with distinct implications for extension history. Resulting distributions of e(L)are process-specific, suggesting that the inverse problem of deducing fracture-and-separation history from final structure may be tractable.

Key words

spatial analysis extension fractures fracture history modeling Monte Carlo simulation structural geology 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Ashton, W. D., 1971, Distributions for gaps in road traffic: Jour. Inst. Math. Appl., v. 7, p. 37–46.Google Scholar
  2. Beloussov, V. V., 1952, Spacing of fracture in rocks: Akad. Nauk SSSR Trad. Geofiz. Inst. v. 17, p. 144.Google Scholar
  3. Biot, M. A., 1965, Mechanics of incremental deformation: John Wiley & Sons, New York, 519 p.Google Scholar
  4. Bridges, M. C., 1975, Presentation of fracture data for rock mechanics: 2nd Australia—New Zealand Conference on Geomechanics, Institute of Engineers, Australia, National Conference Publication 75/4, p. 144–148.Google Scholar
  5. Chadwick, P. K., 1975, A psychological analysis of observation in geology: Nature, London, v. 256, p. 570–573.Google Scholar
  6. Chatfield, C., 1978, Statistics for technology (2nd ed.): Chapman and Hall, London, 370 p.Google Scholar
  7. Chertkova, E. I., 1950, Some results of the modeling of tectonic faults: Akad. Nauk SSSR Izv. Ser. Geol. 14, no. 5, p. 42–44.Google Scholar
  8. Chinnery, M. A., 1966, Secondary faulting: Can. Jour. Earth Sci., v. 3, p. 163–174.Google Scholar
  9. Cobbold, P. R. and Ferguson, C. C., 1979, Description and origin of spatial periodicity in tectonic structures: Report on a Tectonic Studies Group Conference held at Nottingham University, 8 November 1978: Jour. Struct. Geol., v. 1, no. 1, p. 93–97.Google Scholar
  10. Cox, H. L., 1952, The elasticity and strength of paper and other fibrous materials: Br. Jour. Appl. Phys., v. 3, p. 72–79.Google Scholar
  11. Deere, D. U., 1963, Technical description of rock cores for engineering purposes: Rock Mech. Engr. Geol., v. 1, p. 16–22.Google Scholar
  12. Ferguson, C. C., 1981, A strain reversal method for estimating extension from fragmented rigid inclusions: Tectonophysics, v. 79, p. T43-T52.Google Scholar
  13. Ferguson, C. C. and Lloyd, G. E., 1984, Extension analysis of stretched belemnites: A comparison of methods: Tectonophysics, v. 101, p. 199–206.Google Scholar
  14. Fletcher, R. C. and Hallet, B., 1983, Unstable extension of the lithosphere: A mechanical model for Basin-and-Range structure: Jour. Geophys. Res., v. 88, no. B9, p. 7457–7466.Google Scholar
  15. Harris, S. F., Taylor, G. L., and Walper, J. J., 1960, Relation of deformational fractures in sedimentary rocks to regional and local structure: Amer. Assoc. Petrol. Geol. Bull., v. 44, p. 1853–1873.Google Scholar
  16. Hobbs, D. W., 1967, Formation of tension joints: Geol. Mag., v. 104, p. 550–556.Google Scholar
  17. Hudson, J. A. and Priest, S. D., 1979, Discontinuities and rock mass geometry: Int. Jour. Rock Mech. Min. Sci. Geomech. Abstr., v. 16, p. 339–362.Google Scholar
  18. Hudson, J. A. and Priest, S. D., 1983, Discontinuity frequency in rock masses: Int. Jour. Rock Mech. Min. Sci. Geomech. Abstr., v. 20, p. 73–89.Google Scholar
  19. Kelly, A., 1973, Strong solids: Clarendon Press, Oxford, 230 p.Google Scholar
  20. Lachenbruch, A. H., 1961, Depth and spacing of tension cracks: J. Geophys. Res., v. 66, p. 4273–4292.Google Scholar
  21. Lloyd, G. E., Ferguson, C. C., and Reading, K., 1982, A stress-transfer model for the development of extension fracture boudinage: Jour. Struct. Geol., v. 4, no. 3, p. 355–372.Google Scholar
  22. Marsaglia, G., MacLaren, M. D., and Bray, T. A., 1964, A fast procedure for generating normal random variables: Comm. Assoc. Comput. Mach., v. 7, p. 4–10.Google Scholar
  23. Merino, E., Ortoleva, P. and Strickholm, P., 1983, Generation of evenly-spaced pressuresolution seams during (late) diagenesis: A kinetic theory: Contr. Min. Pet. v. 82, p. 360–370.Google Scholar
  24. Merzer, A. M. and Freund, R., 1976, Equal spacing of strike-slip faults: Geophys. Jour. Roy. Astr. Soc., v. 45, p. 177–188.Google Scholar
  25. Paterson, M. S., 1978, Experimental rock deformation—The brittle field: Springer-Verlag, New York, 254 p.Google Scholar
  26. Piteau, D. R., 1973, Characterizing and extrapolating rock joint properties in engineering practice: Rock Mech., Supl. 2, p. 5–31.Google Scholar
  27. Priest, S. D. and Hudson, J. A., 1976, Discontinuity spacings in rock: Int. Jour. Rock Mech. Min. Sci. Geomech. Abstr., v. 13, p. 135–148.Google Scholar
  28. Pyke, R., 1965, Spacings (with Discussion): Jour. Roy. Stat. Soc. Ser. B., v. 27, p. 395–449.Google Scholar
  29. Ramberg, H. 1955, Natural and experimental boudinage: Jour. Geol., v. 63, p. 512–526.Google Scholar
  30. Rudnicki, J. W., 1980, Fracture mechanics applied to the Earth's crust: Ann. Rev. Earth Planet. Sci., v. 8, p. 489–525.Google Scholar
  31. Secor, D. T., 1968, Mechanics of natural extension fracture:in Baer, A. J. and Norris, D. K. (Eds.), Conference on Tectonics, Can. Geol. Surv. Paper 68-52, p. 3–48.Google Scholar
  32. Seidensticker, C. M., Oldow, J. S., and Ave Lallement, H. G., 1982, Development of beddingnormal boudins in the Pilot Moutains, Nevada: Tectonophysics v. 90, p. 335–349.Google Scholar
  33. Smith, R. B., 1975, Unified theory of the onset of folding, boudinage, and mullion structure: Geol. Soc. Amer. Bull., v. 86, p. 1601–1609.Google Scholar
  34. Smith, R. B., 1977, Formation of folds, boudinage, and mullions in non-Newtonian materials: Geol. Soc. Amer. Bull., v. 88, p. 312–320.Google Scholar
  35. Snow, D. T., 1968, Rock fracture spacings, openings and porosities: Proc. Amer. Soc. Civ. Engr. Soil. Mech. Found. Div., v. 94, p. 73–91.Google Scholar
  36. Sowers, G. M., 1972, Theory of spacing of extension fracture:in Pincus, H. (Ed), Geological factors in rapid excavation; Geol. Soc. Amer. Engr. Geol. (case history no. 9), p. 27–53.Google Scholar
  37. Stearns, D. W., 1968, Fracture as a mechanism of flow:in Baer, A. J. and Norris, D. K. (Eds.), Conference on tectonics: Can. Geol. Surv. Paper 68-52, p. 79–95.Google Scholar
  38. Wallis, P. F. and King, M. S., 1980, Discontinuity spacings in a crystalline rock: Int. Jour. Rock Mech. Min. Sci. Geomech. Abstr., v. 17, p. 63–66.Google Scholar

Copyright information

© Plenum Publishing Corporation 1985

Authors and Affiliations

  • Colin C. Ferguson
    • 1
  1. 1.Kansas Geological SurveyThe University of KansasLawrenceUSA

Personalised recommendations