Modeling of Propagation of Antiplane Acoustic Waves in Multiscale Media with Lognormal Distribution of Parameters

The effective coefficients for the problem of propagation of acoustic waves in multifractal elastic media using the subgrid modeling approach are obtained. The maximum scale of heterogeneities of the medium in question is assumed to be small as compared with the wavelength. If a isotropic medium is assumed to satisfy the improved Kolmogorov similarity hypothesis, the term for the effective coefficient of the elastic stiffness coincides with the Landau-Lifshitz-Matheron formula. Both isotropic and anisotropic media are considered. The numerical testing for the wave propagating at a distance, which is of the same order as a typical wavelength of a source, illustrates the efficiency of the approach proposed.