Cross-over frequencies of seismic attenuation in fractured porous rocks
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We analyze compressional wave attenuation in fluid saturated porous material with porous inclusions having different compressibilities and very different spatial scales in comparison with the background. Such a medium exhibits significant attenuation due to wave-induced fluid flow across the interface between inclusion and background. For the representative element containing two layers (one of them representing inclusion), 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. At low frequencies inverse quality factor scales with the first power of frequency ?, while at high frequencies the attenuation is proportional to ?12. In the intermediate range of frequencies inverse quality factor scales with ?12. These characteristic frequency regimes can be observed in all theoretical models of wave-induced attenuation, but complete physical explanation is still missing. The potential application of this model is in estimation of the background permeability as well as inclusion scale (thickness) by identifying these frequencies from attenuation measurements.
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