Negative velocity dispersion and attenuation in granular marine sediments.

The author proposed a gap stiffness model incorporated into the Biot model; that is, the BIMGS model. Reported large velocity dispersion is predicted by this model. However, at higher frequencies, there are some reported data for negative velocity dispersion and attenuation proportional to the first to fourth power of frequency. In this study, the velocities and attenuation in six kinds of water-saturated glass beads and four kinds of water-saturated silica sands with different grain sizes are measured in the frequency range of 80–140 kHz and 300–700 kHz. The measured results are compared with the calculated results by using the BIMGS model plus some acoustic sediment models, such as the BICSQS model plus high-frequency correction, nonlocal model, porosity dynamics model, and multiple scattering model. It is shown that the velocity dispersion and attenuation is predicted by using the BIMGS model in the range of kd ⩽ 0.5 (k is wavenumber in water, d is grain diameter) and by using the BIMGS model plus multiple scattering effects in the range of kd ⩾ 0.5, in which a negative velocity dispersion appears. Finally, the relations between the measured velocity dispersion and attenuation are confirmed by using the twice-subtracted Kramers–Kronig relations.