Abstract
Through numerical experiments and analytical analysis, we show that a strong correlation exists between anisotropy in the material structure (i.e., the elongation of inclusions present within rocks in the different directions of space) and anisotropy in seismic attenuation (i.e., the values of the inverse quality factors associated with the anisotropic moduli that control wave propagation). This is especially true for weakly anisotropic materials where a power law is shown to relate the aspect ratios of the inclusions (i.e., the ratios of the lengths of the inclusions in the different spatial directions) to the peak attenuation ratios (i.e., the ratios of the maximum values of the quality factors describing wave attenuation in the different spatial directions). Analytical results show that small deviations from this simple power law relation are to be expected for general anisotropic materials. For axisymmetric spheroidal inclusions, a perfectly bijective analytical relation is obtained between aspect ratios of the inclusions and attenuation ratios. This relation is not a power law in general but may be considered to reduce to one as aspect ratios approach 1 (a perfect sphere).
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