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Multiscale analysis of waves reflected by granular media: Acoustic experiments on glass beads and effective medium theories

Abstract : The wavelet response is a multiscale method based on the continuous wavelet transform. We use it to characterize the acoustic reflectivity of a layer of glass beads with diameter d = 1 mm randomly arranged in water. The volumetric concentration is ϕ ≃ 63% of spherical inclusions. The wavelet response is measured over a large frequency range (100 kHz ⩽ f ⩽ 5 MHz) where five different acoustic regimes are identified on the basis of scattering phenomena. A strong decrease in the reflectivity occurs when the wavelength of the incident wave is twice the bead diameter, a situation where lateral scattering is dominant. The energy ratio of the ballistic and the coda parts of the wavelet response reveals a clear transition from a ballistic propagation regime to a diffusion regime where multiple scattering occurs. The experimental data are explained with an effective medium theory approach: the reflectivity data in the low-frequency domain of the spanned frequency range are correctly reproduced with quasi-static models. For higher frequencies, more sophisticated models accounting for multiple scattering must be used. The high-frequency part of the experimental reflectivity curve may be explained by strong multiple scattering at the top of the glass beads located at the surface of the layer and corresponds to the optical geometric limit.
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Yves Le Gonidec, Dominique Gibert. Multiscale analysis of waves reflected by granular media: Acoustic experiments on glass beads and effective medium theories. Journal of Geophysical Research : Solid Earth, American Geophysical Union, 2007, 112 (B5), pp.B05103. ⟨10.1029/2006JB004518⟩. ⟨insu-00156260⟩

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