We analyze compressional wave attenuation in fluid-saturated porous material with porous inclusions having different compressibility and very different spatial scale in comparison with the background. Such a medium exhibits attenuation due to wave-induced fluid flow across the interface between inclusion and background. We show that overall wave attenuation is governed by the superposition of two coupled fluid-diffusion processes. Associated with two characteristic spatial scales, we compute two cross-over frequencies that separate three different frequency regimes. We give a physical explanation for an intermediate range of frequencies, where attenuation scales with square-root of frequency.<br>The potential application of this model is in estimation of the background permeability as well as inclusion scale (thickness) by identifying these frequencies from the attenuation measurement.


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