Abstract
Fractures in a porous rock can be modelled as very thin and highly porous layers in a porous background. Elastic moduli of such a fractured medium can be obtained using the result of Norris (1993) for wave propagation in periodically layered poroelastic media. When this porous fractured system is dry, it is equivalent to a transversely isotropic dry elastic porous material with linear-slip interfaces. When saturated with a liquid this system exhibits significant attenuation and velocity dispersion due to wave-induced fluid flow between pores and fractures. The characteristic frequency of such attenuation and dispersion depends on the background permeability, fluid viscosity, as well as fracture density and spacing. The theoretical results are in good agreement with numerical simulations using the reflectivity algorithm generalized to poroelasticity. For randomly distributed microfractures the frequency dependent anisotropy can be modelled using a combination of low frequency predictions based on anisotropic Gassmann equations and a frequency correction based on the dispersion relationship of Hudson et al. (1996). Comparison with laboratory experiments confirms that this combined model gives an accurate prediction of saturated elastic properties and angular dependencies of elastic wave velocities versus frequency.
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