Long-wave anisotropy in stratified media: a numerical test

When a seismic signal propagates in a stratified earth, there is anisotropy if the dominant wavelength is long enough compared to the layer thickness. In this situation, the layered medium can be replaced by an equivalent nondispersive transversely isotropic medium. The present work investigates the effects of layering by wave simulation and attempts to establish quantitatively the minimum ratio for which the long-wave approximation starts to be valid. Two-constituent periodically layered media are considered and the long-wave approximation for different material compositions and different material proportion in 1-D and 2-D media are analysed. The evaluation of the minimum ratio compares snapshots and synthetic seismograms visually and through a measure of coherence. Layering induces scattering with wave dispersion or anisotropy depending upon the wavelength-to-layer thickness ratio. The mideling confirms the dispersive characteristics of the wave field, the scattering effects in the form of coda waves at short wavelengths, and the smoothed transversely isotropic behaviour at long wavelengths. -from Authors