The impact of finite ensonified area on the scattering cross section

The definition of the scattering cross section for the pressure field scattered by a rough interface uses the underlying assumption that the ensonified area does not affect its shape. This assumptions holds so long as the incident field is a good approximation of a plane wave, which situation occurs when the ensonified area is large compared to a wavelength. In the opposite situation, when the ensonified dimensions approaches a wavelength, the incident plane wave assumption does not hold and the cross section can depart from modeled behavior. This research uses the Perturbation approximation to derive a model for the low grazing-angle behavior of the scattering cross section. The primary results are 1) the appearance of an additive Lambertian term, and 2) a separation of scales imposed by the acoustic resolution. This separation can then be used as a criterion for the application of the composite roughness model. Model results are checked against direct numerical solution of the governing integral equations. Implications for inversion of seafloor parameters based on acoustic scattering experiments is discussed.