In the long-wavelength approximation it has been shown in several papers within the last 20 years that an elastic medium composed of alternating homogeneous isotropic layers of two different constituents is equivalent both kinematically and dynamically to a homogeneous transversely isotropic medium. Such a fact excludes uniqueness in inverting seismic data for these particular cases. A comparison of the seismic responses of the equivalent media is made by constructing synthetic seismograms using the reflectivity (numerical integration) method and the asymptotic ray approach. For the sake of simplicity the SH case only is considered. The preferable approach when considering media of this type is found to be the asymptotic ray approximation as the CPU time required is a fraction of that used in the reflectivity method for comparable results.

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