A porosity-based Biot model for acoustic waves in snow

Phase velocities and attenuation in snow can not be explained by the widely used elastic or viscoelastic models for acoustic wave propagation. Instead, Biot's model of wave propagation in porous materials should be used. However, the application of Biot's model is complicated by the large property space of the underlying porous material. Here the properties of ice and air as well as empirical relationships are used to define the properties of snow as a function of porosity. Based on these relations, phase velocities and plane wave attenuation of shear- and compressional-waves as functions of porosity or density are predicted. For light snow the peculiarity was found that the velocity of the first compressional wave is lower than the second compressional wave that is commonly referred to as the "slow" wave. The reversal of the velocities comes with an increase of attenuation for the first compressional wave. This is in line with the common observation that sound is strongly absorbed in light snow. The results have important implications for the use of acoustic waves to evaluate snow properties and to numerically simulate wave propagation in snow.