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A self-consistent scheme has recently been implemented to study wave propagation through a variety of materials with microstructure such as, for example, anisotropic matrix containing a random array of aligned spheroidal inclusions, and its limiting case of penny-shaped cracks. Dispersion and attenuation curves calculated using this method show a characteristic resonance behaviour as a function of frequency that is independent of the wave type and the angle of incidence in almost all cases. Also, there is a frequency dependence of the azimuthal behaviour of the speed and attenuation coefficients in some cases. At low frequencies, very similar results may be found by employing the method of smoothing or the quasicrystalline approximation. But only the self-consistent method has been developed to yield wave speeds and attenuation for finite frequencies.

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