First‐order perturbation solution for rough surface scattering cross section including the effects of gradients

The transition matrix relating the incident pressure field to the scattered field in a fluid above a rough surface is derived to first order using Rayleigh–Rice perturbation theory, resulting in a general expression for scattering strength. A small region bordered above by the rough surface and below by a horizontal plane intersecting the surface at its lowest point contains a lossy homogeneous fluid. Below this point, the sediment is allowed to be vertically stratified, viscoelastic, or porous, supporting shear or Biot slow waves. Gradients strongly affect the scattering cross section if they cause a substantial portion of the incident energy to be redirected toward the interface.