f Backus averaging, scattering and drift

In certain kinds of finely-layered media seismic waves propagate as if the medium was replaced by its homogeneous transversely isotropic equilivant whose elastic constants are given by the averaging formulae of Backus (1962). These formulae were obtained under the assumtion that the distrubution of the properties of the layers is statistically stationary on the scale of the averaging length, 1, which must itself be much less than a wavelength.