Aperture correlation of a fractal fracture
A rough-walled facture is modeled by fractal geometry. In the fractal fracture model, the rock surfaces are characterized by a fractal dimension D between 2 and 3, with lower D for smoother surfaces and higher D for rougher surfaces. The mismatch due to shear displacement between two mirror-image fractal surfaces determines the fracture aperture distribution. An analytic equation is derived for the varioram ..gamma../sub f/(r) describing the spatial correlation of the aperture of a fractal fracture. The aperture of a smooth fracture with low D is highly correlated over distances much larger than the shear displacement. The aperture of a rough fracture with high D becomes uncorrelated within a range shorter than the shear displacement. Near the origin, r = 0, of the variogram, the variogram is proportional to r/sup 6-2//sup D/. For the special case of Brownian fractal with D = 2.5, the variogram is proportional to r, which is the same r dependence exhibited by the spherical model widely used in geostatistical analyses. copyright American Geophysical Union 1988
- Research Organization:
- Earth Sciences Division, Lawrence Berkeley Laboratory, University of California, Berkeley
- OSTI ID:
- 5269342
- Journal Information:
- J. Geophys. Res.; (United States), Journal Name: J. Geophys. Res.; (United States) Vol. 93:B3; ISSN JGREA
- Country of Publication:
- United States
- Language:
- English
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