The propagation of elastic waves is modelled in media with a random distribution of fluid-filled circular cavities, which display high physical impedance in contrast to background media. Theoretical attenuation expressions for media with circular cavities, which may be filled with any material (e.g. vacuum, fluid, elastic materials), are formulated using an ensemble treatment for first-order transmitted waves. Numerical estimates of scattering attenuation rates agree with the theoretical results well. The scattering attenuations (Q(-1)) are proportional to the scale of cavities and the number density (eta, number of cavities per area in a medium). The decrease of primary energy with the size of cavities does not result in the increase of coda energy owing to the increase of both purely backscattered waves from cavities and the trapped waves inside cavities. Scattering properties (e.g. scattering attenuation, coda energy, phase fluctuation of primary waves) in media with randomly distributed cavities are very different from those in stochastic random media. It appears that heterogeneities with high impedance in the earth may not be well represented with stochastic random heterogeneities.
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