The effects of finite scattering area on validity criteria for scattering models

The correlation length of a rough interface is often used as a criterion for the validity of many approximate scattering models such as small roughness perturbation theory or the Kirchhoff approximation. A common input to these models is the power spectrum of the surface, which usually follows a band-limited power-law form (i.e., a von Karman spectrum). The fractal-like behavior of a von Karman surface breaks down at some outer scale which is closely related to the correlation length. First-order terms in approximate scattering models will not be sufficient when interface roughness correlation lengths are much larger than an acoustic wavelength. Given that first-order perturbation theory has generally been accepted as sufficient to predict scattered levels, the use of the true geophysical correlation length as a criterion for determining the validity of scattering models is suspect. In contrast to the infinite surface assumption used in most scattering models, scattering measurements are always made on patches of finite size; results of finite transmit pulses and beamwidths. In terms of correlation length, these finite-sized patches will act to window the roughness seen by the incident acoustic pulse, possibly negating the usefulness of using the true geophysical correlation length as a validity criterion. In this work we present results of a study on the link between the behavior of seafloor roughness power spectra and the finite windows resulting from measurement systems.