A layered model of homogeneous and isotropic material, can be up-scaled to a transverse isotropic medium, proposed by Backus.
Backus presented an equivalent medium theory, a heterogeneous medium can be replaced by a homogeneous one that predicts wave propagation in the actual medium. Backus showed that layering on a scale much finer than the wavelength has an impact and that a number of isotropic layers can be replaced by a homogeneous transversely isotropic medium that behaves exactly in the same manner as the actual medium under static load in the infinite wavelength limit.
If each layer   is described by 5 transversely isotropic parameters , specifying the matrix
The elastic moduli for the effective medium will be
where 
 denotes the volume weighted average over all layers.
This includes isotropic layers, as the layer is isotropic if ,  and .