  This paper concerns the derivation of radiative transfer equations for
acoustic waves propagating in a randomly fluctuating half-space in the
weak-scattering regime, and the study of boundary effects through an asymptotic
analysis of the Wigner transform of the wave solution. These radiative transfer
equations allow to model the transport of wave energy density, taking into
account the scattering by random heterogeneities. The approach builds on the
method of images, where the half-space problem is extended to a full-space,
with two symmetric sources and an even map of mechanical properties. Two
contributions to the total energy density are then identified: one similar to
the energy density propagation in a full-space, for which the resulting lack of
statistical stationarity of the medium properties has no leading-order effect;
and one supported within one wavelength of the boundary, which describes
interference effects between the waves produced by the two symmetric sources.
In the case of a homogeneous Neumann boundary conditions, this boundary effect
yields a doubling of the intensity, and in the case of homogeneous Dirichlet
boundary conditions, a canceling of that intensity.
