Astronomy and Astrophysics – Astronomy
Scientific paper
Feb 2003
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003geoji.152..344t&link_type=abstract
Geophysical Journal International, Volume 152, Issue 2, pp. 344-352.
Astronomy and Astrophysics
Astronomy
Anisotropy, Cracked Media, Porosity
Scientific paper
An effective medium theory typically requires the description of a mean crack shape. In general, for simplicity, this is taken to be a flat, circular (`penny-shaped') crack. However, this places an unnecessary limitation on the theory, when it is perhaps more realistic to describe a crack in terms of having a bounded width and an otherwise ellipsoidal shape. The generalization of the method of smoothing, as proposed by Hudson (1994, Geophys. J. Int.,117, 555-561) , to extend his original model (Hudson, 1980. Math. proc. Camb. phil. Soc.,88, 371-384), has been used to study the role of the crack width and the ratio of the two larger dimensions in determining the properties of the effective medium. In general, this leads to a description of the medium as having orthorhombic symmetry, and provides a suitable description of a material where the crack dimensions are restricted in one direction owing to, for example, bed-limiting effects, while remaining unconfined in other directions. An elliptical flat crack limit is determined, analoguous to the circular crack description of the original Hudson model. In addition to the isolated crack description, the theory is extended to include the fluid flow mechanism of Tod (2001, Geophys. J. Int.,146, 249-263) that models the flow as being dominated by crack-to-crack flow and is valid for low matrix porosities and over a large range of frequencies, provided that the wavelength is much greater than the crack dimensions.
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