A technique for revealing scale-dependent patterns in fracture spacing data

Journal of Geophysical Research: Solid Earth

Volumn 119, Issue 7, 2014, Pages 5979-5986

  Roy, Ankur ^a   Perfect, Edmund ^b   Dunne, William M ^b   McKay, Larry D ^b  

^a STANFORD UNIVERSITY   (United States)

^b UNIVERSITY OF TENNESSEE   (United States)

Author keywords

binary data; clustering; fractal; fractures; lacunarity

Indexed keywords

CLUSTER ANALYSIS; DATA SET; FRACTAL ANALYSIS; FRACTURE NETWORK; SPATIAL DATA;

EID: 84906271503     PISSN: 21699313     EISSN: 21699356     Source Type: Journal    
DOI: 10.1002/2013JB010647     Document Type: Article

References (24)

1. Allain, C., and, M. Cloitre, (1991), Characterizing the lacunarity of random and deterministic fractal sets, Phys. Rev. A, 44 (6), 3552-3558.
2. Barton, C. C., (1995), Fractal analysis of scaling and spatial clustering of fractures, in Fractals in the Earth Sciences, edited by, C. C. Barton, and, P. R. La Pointe, pp. 141-177, Plenum Press, New York.
3. Boadu, F. K., and, L. T. Long, (1994), The fractal character of fracture spacing and RQD, Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 31 (2), 127-134. (Pubitemid 24427227)
4. Chiles, J. P., (1988), Fractal and geostatistical methods for modeling of a fracture network, Math. Geol., 20 (6), 631-654.
5. Gillespie, P. A., C. B. Howard, J. J. Walsh, and, J. Watterson, (1993), Measurement and characterization of spatial distributions of fractures, Tectonophysics, 226, 113-141. (Pubitemid 24423211)
6. Gillespie, P. A., J. D. Johnston, M. A. Loriga, K. J. McCaffrey, J. J. Walsh, and, J. Watterson, (1999), Influence of layering in vein systematics in line samples, in Fractures, Fluid Flow and Mineralization, Spec. Publ., vol. 155, edited by, K. J. W. McCaffrey, L. Lonergan, and, J. J. Wilkinson, pp. 35-56, Geological Society, London, U. K.
7. Gillespie, P. A., J. J. Walsh, J. Watterson, C. G. Bonson, and, T. Manzocchi, (2001), Scaling relationships of joint and vein arrays from The Burren, Co. Clare, Ireland, J. Struct. Geol., 23, 183-201. (Pubitemid 32320393)
8. Gomez, L., (2007), Characterization of the spatial alignment of opening-mode fractures, PhD dissertation, 844 pp., The University of Texas at Austin.
9. Kruhl, J. H., (2013), Fractal-geometry techniques in the quantification of complex rock structures: A special view on scaling regimes, inhomogeneity and anisotropy, J. Struct. Geol., 46, 2-21.
10. La Pointe, P. R., and, J. A. Hudson, (1985), Characterization and Interpretation of Rock Mass Joint Patterns, Spec. Pap., vol. 199, 37 pp., Geol. Soc. Am., Boulder, Colo.
11. Narr, W., and, J. Suppe, (1991), Joints spacing in sedimentary rocks, J. Struct. Geol., 13 (9), 1037-1048.
12. Odling, N. E., et al. (1999), Variations in fracture system geometry and their implications for fluid flow in fractured hydrocarbon reservoirs, Pet. Geosci., 5, 373-384. (Pubitemid 30063582)
13. Ortega, O., R. Marrett, and, S. E. Laubcah, (2006), A scale-independent approach to fracture intensity and average spacing measurement, AAPG Bull., 90 (2), 193-208. (Pubitemid 43263675)
14. Plotnick, R. E., (1995), Introduction to fractals, in Nonlinear Dynamics and Fractals: New Numerical Techniques in for Sedimentary Data, SEPM Short Course, vol. 36, edited by, G. V. Middleton, R. E. Plotnick, and, D. Rubin, pp. 1-28, SEPM, Tulsa, Okla.
15. Plotnick, R. E., R. H. Gardner, and, R. V. O'Neill, (1993), Lacunarity indices as measures of landscape texture, Landscape Ecol., 8 (3), 201-2011.
16. Plotnick, R. E., R. H. Gardner, W. W. Hargrove, K. Prestegaard, and, M. Perlmutter, (1996), Lacunarity analysis: A general technique for the analysis of spatial patterns, Phys. Rev. E., 53 (5), 5461-5468. (Pubitemid 126598823)
17. Priest, S. D., and, J. A. Hudson, (1976), Discontinuity spacings in rock, Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 13, 135-148.
18. Riley, P., B. Tikoff, and, A. B. Murray, (2011), Quantification of fracture networks in non-layered, massive rock using synthetic and natural data sets, Tectonophysics, 505, 44-56.
19. Rohrbaugh, M. B., W. M. Dunne, and, M. Mauldon, (2002), Estimating fracture trace intensity, density and mean length using circular scan lines and windows, AAPG Bull., 86 (12), 2089-2104. (Pubitemid 36211541)
20. Roy, A., (2013), Scale-dependent heterogeneity in fracture data sets and grayscale images, PhD dissertation, University of Tennessee-Knoxville, 117 pp. [Available at http://trace.tennessee.edu/utk-graddiss/2476.]
21. Roy, A., and, E. Perfect, (2012), Multifractal scaling of grayscale patterns: Lacunarity and correlation dimension, Abstract 1476857 presented at 2012 Fall Meeting, AGU, San Francisco, Calif., 3-7 Dec.
22. Roy, A., E. Perfect, W. M. Dunne, N. E. Odling, and, J. Kim, (2010), Lacunarity analysis of fracture networks: Evidence for scale-dependent clustering, J. Struct. Geol., 32, 1444-1449.
23. Snow, D. T., (1969), Anisotropic permeability of fractured media, Water Resour. Res., 5 (6), 1273-1289, doi: 10.1029/WR005i006p01273.
24. Velde, B., J. Dubois, G. Touchard, and, A. Badri, (1990), Fractal analysis of fractures in rocks, Tectonophysics, 179, 345-352.