  A theory for multiple scattering of elastic waves is presented in a random
medium bounded by two ideal free surfaces, whose horizontal size is infinite
and whose transverse size is smaller than the mean free path of the waves. This
geometry is relevant for seismic wave propagation in the Earth crust. We derive
a time-dependent, quasi-2D radiative transfer equation, that describes the
coupling of the eigenmodes of the layer (surface Rayleigh waves, SH waves, and
Lamb waves). Expressions are found that relate the small-scale fluctuations to
the life time of the modes and to their coupling rates. We discuss a diffusion
approximation that simplifies the mathematics of this model significantly, and
which should apply at large lapse times. Finally, coherent backscattering is
studied within the quasi-2D radiative transfer equation for different source
and detection configurations.
