Wave Transmission through Random Layering with Pressure Release Boundary Conditions

This paper considers the statistical properties of the waves generated by a point source in the subsurface and transmitted towards the surface through a randomly layered medium. The problem is analyzed in a regime of separation of scales and with pressure release boundary conditions at the surface. Using a probabilistic representation of the spectral density of the waves received at the surface, the transmitted intensity is analyzed. Conserved quantities specific to the pressure release boundary conditions are evaluated and the power delay spread is computed. In particular a waveguiding effect that is produced by the reflections from the surface and from the random medium is identified and analyzed. This effect is different from the propagation in a standard waveguide from the point of view of the decay of the intensity.