Wave propagation in a layered medium when the wavelength is much greater than each layer thickness (low frequency) produces a response equivalent to that of wave propagation in an equivalent single-layer medium. This equivalent medium is transversely isotropic with symmetry about a vertical axis (VTI), and the elastic parameters are computed with the Backus averaging technique. Conversely, when the wavelength is comparable to each layer thickness (high frequency), the directional dependence of the phase velocity in the transmission response also can be simulated by replacing the layered medium with a single homogeneous medium with properties derived from a time average. It then can be treated approximately as a VTI medium. To compute the medium parameters, a method based on fitting the traveltime parameters is used. We investigated the relationship between Thomsen's anisotropic parameters ε and δ computed for the equivalent medium in the low-frequency limit and for the homogenized medium in the high-frequency limit. In our experiments, we used a medium in which layers of only two isotropic materials alternate repeatedly. For the high-frequency limit, we obtained solutions for PP- and SS-wave propagation.