In geophysics, a common assumption is that the rock formations of the crust are locally polar anisotropic (transversely isotropic); this is the simplest case of geophysical interest.  Backus upscaling is often used to determine the effective transversely isotropic elastic constants of layered media for long wavelength seismic waves.
Assumptions that are made in the Backus approximation are:
* All materials are linearly elastic
* No sources of intrinsic energy dissipation (e.g. friction)
* Valid in the infinite wavelength limit, hence good results only if layer thickness is much smaller than wavelength
* The statistics of distribution of layer elastic properties are stationary, i.e., there is no correlated trend in these properties.
For shorter wavelengths, the behavior of seismic waves is described using the superposition of plane waves.  Transversely isotropic media support three types of elastic plane waves:
* a quasi-P wave (polarization direction almost equal to propagation direction)
* a quasi-S wave
* a S-wave (polarized orthogonal to the quasi-S wave, to the symmetry axis, and to the direction of propagation).
Solutions to wave propagation problems in such media may be constructed from these plane waves, using Fourier synthesis.