Oscillatory numerical experiments in finely layered anisotropic viscoelastic media

A finely layered medium behaves as a homogeneous anisotropic medium at long wavelengths. When each layer is a transversely isotropic viscoelastic (TIV) medium, attenuation anisotropy can be described by a generalization of Backus averaging to the lossy case. We introduce a method to compute the complex and frequency-dependent stiffnesses of the equivalent viscoelastic, homogeneous, transversely isotropic medium from numerical simulations of oscillatory (harmonic) tests based on a space–frequency domain finite-element (FE) method. We apply the methodology to a periodic sequence of shale and limestone thin layers and determine the energy velocities and quality factors of the qP-, qSV- and SH-wave modes as a function of frequency and propagation direction. The agreement between theory and numerical experiments is very good when the long-wavelength condition is satisfied.