  In the present paper which follows our previous paper ``Mathematical models
for passive imaging I: general background'', we discuss the case of surface
waves in a medium which is stratified near its boundary at some scale
comparable to the wave length. We discuss how the propagation of such waves is
governed by effective Hamiltonians on the boundary. The results are certainly
not new, but we have been unable to find a precise reference. They are very
close to results in adiabatic theory.
