1D waves in a random poroelastic medium with large fluctuations

Abstract We examine the problem of wave propagation in a random poroelastic medium. The porous medium is modelled as a Biot poroelastic solid whose constitutive parameters fluctuate substantially over finite distances. Our main results are asymptotic analytical expressions for the mean velocity-stress wave; this solution incorporates two distinct length scales. The effect of the fluctuations appears on the regular depth coordinate while the parameters of the effective medium arise on a shorter scale of distance. Thus the method that we apply, the theory of averaging, allows us to give a rigorous derivation of the effective medium parameters. It also provides the correction terms which are caused by the fluctuations in the random medium; we find that the relative effect of the latter increases in proportion to ω1/2 where ω denotes the wave frequency. We also show that the fluctuations introduce significant attenuation of the fast Biot compressional wave and dispersion of the slow Biot wave. These results a...