A comparison between wave propagation in water-saturated and air-saturated porous materials

Abstract

The classical Biot theory [J. Acoust. Soc. Am. 28, 168 (1956)] predicts the existence of three waves that can propagate in a fluid-saturated porous material: A fast compressional wave, a slow compressional wave, and a shear wave. Through use of this theory, propagation characteristics within water-filled and air-filled materials were compared in the 10 Hz–100 kHz band. Numerical calculations show that the ratio of fluid to solid motion for the slow compressional wave is around 2 in water-filled sand, but greater than 300 in air-filled sand. In addition, calculations of plane wave transmission from a fluid into a fluid-saturated porous solid were investigated. The calculations show that when the fluid is water, nearly all of the incident energy is transferred to the reflected wave and to the transmitted fast compressional wave that is traveling mainly in the solid frame. Only a slight frequency dependence occurs in the energy transfer. When the fluid is air, however, the interaction of the waves with the boundary becomes strongly dependent upon frequency, and most of the incident energy is transferred to the reflected wave and to the transmitted slow compressional wave traveling mainly in the pores. These theoretical results justify the different approaches used to treat reflections from porous materials in underwater and aeroacoustics. For reflections, air-filled soil or snow can be approximately modeled as a modified fluid (ignoring motion in the frame) rather than as a viscoelastic solid (ignoring motion in the pores), the approximation commonly used to model saturated undersea sediments.