A statistical scaling model for fracture network geometry, with validation on a multiscale mapping of a joint network (Hornelen Basin, Norway)

Journal of Geophysical Research: Solid Earth

Volumn 107, Issue 6, 2002, Pages

  Bour, Olivier ^a   Davy, Philippe ^a   Darcel, Caroline ^a   Odling, Noëlle ^b  

^a UNIVERSITÉ DE RENNES 1   (France)

^b UNIVERSITY OF LEEDS   (United Kingdom)

Author keywords

Faults; Fractal; Fractures; Geometry; Length distribution; Scaling laws

Indexed keywords

FRACTURE NETWORK; GEOMETRY; JOINT; MAPPING; STATISTICAL ANALYSIS;

HORNELEN BASIN; NORWAY;

EID: 0037054712     PISSN: 21699313     EISSN: 21699356     Source Type: Journal    
DOI: None     Document Type: Article

References (47)

1. Ackermann, R. V., and R. W. Schlische, Anticlustering of small normal faults around larger faults, Geology, 25(12), 1127-1130, 1997.
2. Acuna, J. A., and Y. C. Yortsos, Application of fractal geometry to the study of networks of fractures and their pressure transient, Water Resour. Res., 31, 527-540, 1995.
3. Allègre, C. J., J. L. Lemouel, and A. Provost, Scaling rules in rock fracture and possible implications for earthquake prediction, Nature, 297, 47-49, 1982.
4. Barton, C. C., and E. Larsen, Fractal geometry of two-dimensional fracture networks at Yucca Mountain, southwestern Nevada, in Proceedings of the International Symposium on Fundamentals of Rock Joints, edited by O. Stephannson, pp. 77-84, Centek, Bjorkliden, Sweden, 1985.
5. Berkowitz, B., O. Bour, P. Davy, and N. Odling, Scaling of fracture connectivity in geological formations, Geophys. Res. Lett., 27(14), 2061-2064, 2000.
6. Bonnet, E., O. Bour, N. E. Odling, P. Davy, I. Main, P. Cowie, and B. Berkowitz, Scaling of Fracture Systems in Geological Media, Rev. Geophys., 39(3), 347-383, 2001.
7. Bour, O., Transferts de fluides dans les milieux fracturés: Effects d'échelle, Mém. Géosci. Rennes, 80, 288 pp., 1997.
8. Bour, O., and P. Davy, Connectivity of random fault networks following a power-law fault length distribution, Water Resour. Res., 33, 1567-1583, 1997.
9. Bour, O., and P. Davy, On the connectivity of three-dimensional fault networks, Water Resour. Res., 34, 2611-2622, 1998.
10. Bour, O., and P. Davy, Clustering and size distribution of fault patterns: Theory and measurements, Geophys. Res. Lett., 26(13), 2001-2004, 1999.
11. Castaing, C., et al., Scaling relationships in intraplate fracture systems related to Red Sea rifting, Tectonophysics, 261, 291-314, 1996.
12. Childs, C., J. J. Walsh, and J. Watterson, A method for estimation of the density of fault displacements below the limits of seismic resolution in reservoir formations, in North Sea Oil and Gas Reservoirs, vol. II, edited by A. T. Buller et al., pp. 309-318, Graham and Trotman, Norwell, Mass., 1990.
13. Clark, R. M., S. J. D. Cox, and G. M. Laslett, Generalizations of power-law distributions applicable to sampled fault-trace length: Model choice, parameter estimation and caveats, Geophys, J. Int., 136, 357-372, 1999.
14. Davy, P., On the frequency-length distribution of the San Andreas fault system, J. Geophys. Res., 98, 12, 141-12,151, 1993.
15. Davy, P., A. Sornette, and D. Sornette, Some consequences of a proposed fractal nature of continental faulting, Nature, 348, 56-58, 1990.
16. Feder, J., Fractals, 283 pp., Plenum, New York, 1988.
17. Gautier, B. D. M., and S. D. Lake, Probabilistic modeling of faults below the limit of seismic resolution in Pelican Field, North Sea, offshore United Kingdom, AAPG. Bull., 77, 761-777, 1993.
18. Gudmunsson, A., Geometry, formation and development of tectonic fractures on the Reykjanes Peninsula, southwest Iceland, Tectonophysics, 139, 295-308, 1987.
19. Hamburger, D., O. Biham, and D. Avnir, Apparent fractality emerging from models of random distributions, Phys. Rev. E, 53, 3342-3458, 1996.
20. Heffer, K. J., and T. G. Bevan, Scaling relationships in natural fractures: data, theory, and application, in Proceedings of the 2nd European Petroleum Conference, pp. 367-376, Soc. of Pet. Eng., Tulsa, Okla., 1990.
21. Hentschel, H. G. E., and I. Proccacia, The infinite number of generalised dimensions of fractals and strange attractors, Physica D, 8, 435-444, 1983.
22. Hirata, T., Fractal dimension of fault systems in Japan: Fractal structure in rock fracture geometry at various scales, Pure Appl. Geophys., 121, 157-170, 1989.
23. King, G., The accommodation of large strains in the upper lithosphere of the Earth and other solids by self-similar fault-system, Pure Appl. Geophys., 12, 761-815, 1983.
24. LaPointe, P. R., A method to characterise fracture density and connectivity through fractal geometry, Int. J. Rock Mech. Min. Sci. Geomech., 25, 421-429, 1988.
25. Laslett, G. M., Censoring and edge effects in areal and line transect sampling of rock joint traces, Math. Geol., 14(2), 125-140, 1982.
26. Main, I. G., P. G. Meredith, P. R. Sammonds, C. Jones, Influence of fractal flaw distributions on rock deformation in the brittle field, in Deformation Mechanisms, Rheology and Tectonics, edited by R. J. Knipe and E. H. Rutter, Geol. Soc. Spec. Publ., 54, 71-79, 1990.
27. Mandelbrot, B. B., The Fractal Geometry of Nature, 468 p., W.H. Freeman, New York, 1982.
28. Marrett, R., and R. Allmendinger, Estimates of strain due to brittle faulting: Sampling of fault populations, J. Struct. Geol., 13, 735-738, 1991.
29. Odling, N. E., Network properties of a two dimensional fracture pattern, Pure Appl. Geophys., 138, 95-114, 1992.
30. Odling, N. E., Scaling and connectivity of joint systems in sandstones from western Norway, J. Struct. Geol., 19(10), 1257-1271, 1997.
31. Odling, N. E., The scaling of hydraulic conductivity in rock fracture zones, Geophys. Res. Lett., 28(15), 3019-3022, 2001.
32. Odling, N. E., et al., Variations in fracture system geometry and their implications for fluid flow in fractured hydrocarbon reservoirs, Pet. Geosci., 5, 373-384, 1999.
33. Okubo, P. G., and K. Aki, Fractal geometry in the San Andreas fault system, J. Geophys. Res., 92, 345-355, 1987.
34. Ouillon G., and D. Sornette, Unbiased multifractal analysis: Application to fault patterns, Geophys. Res. Lett., 23(23), 3409-3412, 1996.
35. Ouillon, G., C. Castaing, and D. Sornette, Hierarchical geometry of faulting, J. Geophys. Res., 101, 5477-5487, 1996a.
36. Ouillon, G., D. Sornette, A. Genter, and C. Castaing, The imaginary part of rock jointing, J. Phys. I Fr., 6, 1127-1139, 1996b.
37. Pickering, G., J. M. Bull, and D.J. Sanderson, Sampling power-law distributions, Tectonophysics, 248, 1-20, 1995.
38. Ross, B., Dispersion in fractal fracture networks, Water Resour. Res., 22, 823-827, 1986.
39. Scholz, C. H., and P. A. Cowie, Determination of total strain from faulting using slip measurements, Nature, 346, 837-839, 1990.
40. Scholz, C. H., N. H. Dawers, J. Z. Yu, M. H. Anders, P. A. Cowie, Fault growth and fault scaling laws: Preliminary results, J. Geophys. Res., 98, 21,951-21,961, 1993.
41. Segall, P., and D. D. Pollard, Joint formation in granitic rock of the Sierra Nevada, Geol. Soc. Am. Bull., 94, 563-575, 1983.
42. Sornette, A., P. Davy, and D. Sornette, Fault growth in brittle-ductile experiments and the mechanics of continental collisions, J. Geophys. Res., 98, 12,111-12,139, 1993.
43. Turcotte, D. L., A fractal model for crustal deformation; Tectonophysics, 132, 261-269, 1986.
44. Vicsek, T., Fractal Growth Phenomena, 488 pp., World Sci., River Edge, N. J., 1992.
45. Villemin, T., and C. Sunwoo, Distribution logarithmique des rejets et longueurs de failles: Exemple du bassin houiller lorrain, C. R. Acad. Sci.; 305, 1309-1312, 1987.
46. Walsh, J. J., and J. Watterson, Fractal analysis of fracture pattern using the standard box-counting technique: Valid and invalid methodologies, J. Struct. Geol., 15, 1509-1512, 1993.
47. Yielding, G., J. J. Walsh, and J. Watterson, The prediction of small scale faulting in reservoirs, First Break, 10, 449-460, 1992.