Measurements of ultrasound velocity and attenuation in numerical anisotropic porous media compared to Biot’s and multiple scattering models

•Velocities and attenuation coefficients measurements in numerical anisotropic porous structures – like bone – are proposed.•Results are confronted with Biot’s model and multiple scattering theory (ISA).•The ISA well describes one wave propagation velocities and attenuation for low solid fraction but fails otherwise.•Biot’s theory does not predict any of the attenuation observed but fairly predicts velocities.•Smooth transition from one to two waves as the propagation rotates from parallel to perpendicular to the main direction. This article quantitatively investigates ultrasound propagation in numerical anisotropic porous media with finite-difference simulations in 3D. The propagation media consist of clusters of ellipsoidal scatterers randomly distributed in water, mimicking the anisotropic structure of cancellous bone. Velocities and attenuation coefficients of the ensemble-averaged transmitted wave (also known as the coherent wave) are measured in various configurations. As in real cancellous bone, one or two longitudinal modes emerge, depending on the micro-structure. The results are confronted with two standard theoretical approaches: Biot’s theory, usually invoked in porous media, and the Independent Scattering Approximation (ISA), a classical first-order approach of multiple scattering theory. On the one hand, when only one longitudinal wave is observed, it is found that at porosities higher than 90% the ISA successfully predicts the attenuation coefficient (unlike Biot’s theory), as well as the existence of negative dispersion. On the other hand, the ISA is not well suited to study two-wave propagation, unlike Biot’s model, at least as far as wave speeds are concerned. No free fitting parameters were used for the application of Biot’s theory. Finally we investigate the phase-shift between waves in the fluid and the solid structure, and compare them to Biot’s predictions of in-phase and out-of-phase motions.