Intrinsic anisotropy and thin multilayering - Two anisotropy effects combined

Abstract

Elastic wave propagation in 1-D randomly layered media is characterized by frequency-dependent anisotropy. We study the transmission of obliquely incident plane qP and qSV waves propagating through a thick 1-D randomly multilayered stack embedded between two identical homogeneous half-spaces and allow each individual layer to be transversely isotropic. Theoretical and numerical investigations show that the presence of intrinsic anisotropy in addition to thin multilayering causes a shift of the phase velocities towards higher values when compared with a stack of isotropic layers with the same vertical-incidence velocity (provided that the background velocity normal to the symmetry axis exceeds that along the symmetry axis). The magnitude of the shift depends on the magnitude of the intrinsic anisotropy and increases with increasing angle of incidence. The frequency dependence of the phase velocities is only changed if the intrinsic anisotropy is not constant but varies along the symmetry axis. The influence of the intrinsic anisotropy on the phase velocities is quite strong in comparison with multilayering effects, even if the velocity and density fluctuations in the thin-layer stack are much larger. In the small fluctuation approximation the three effects, background anisotropy, static anisotropy due to multilayering, and frequency-dependent anisotropy due to multilayering, provide additive contributions to the vertical slowness. In this approximation the effects are also additive in terms of the phase velocity. The attenuation coefficients for both qP and qSV waves are controlled exclusively by frequency-dependent multilayering effects. However, the intrinsic anisotropy influences the attenuation coefficients in the case that it is fluctuating, since fluctuations of the intrinsic anisotropy affect the phase velocities in the single layers, leading to an increase in internal scattering. This effect can be rather pronounced for large incidence angles.