Acoustic scattering comparison of Kirchhoff approximation to Rayleigh-Fourier method for sinusoidal surface waves at low grazing angles

Recovery of coherent reflection from rough-surface scattered acoustic fields via the frequency-difference autoproduct

The acoustic field reflected from a random rough surface loses coherence with the incident field in the Kirchhoff approximation as kh cos θ increases, where k is the incident field wavenumber, h is the root mean square roughness height, and θ is the incidence angle. Thus, for fixed rough-surface properties and incidence angle, a reflected field at lower wavenumber should retain more coherence. Recent results suggest that the frequency-difference autoproduct formed from complex acoustic field amplitudes at two nearby frequencies can recover acoustic information at the difference of those frequencies even when the difference frequency is below the recorded field's bandwidth. Herein analytical, computational, and experimental results are presented for the extent to which the frequency-difference autoproduct recovers coherence from randomly rough-surface-scattered constituent fields that have lost coherence. The analytical results, developed from the Kirchhoff approximation and formal ensemble averaging over randomly rough surfaces with Gaussian height distributions and Gaussian correlation functions, indicate that the coherence of the rough-surface-reflected frequency-difference autoproduct depends on the surface correlation length and Δkh cos θ, where Δk is the difference of the autoproduct's constituent field wavenumbers. These results compare favorably with Monte Carlo simulations of rough surface scattering, and with laboratory experiments involving long surface correlation lengths where 1  ≤kh cos θ≤ 3.

Scattering of low-frequency acoustic waves from a moving source by the sea surface

This paper examines the scattering of a monochromatic acoustic wave by sea-surface gravity waves in the 1-200 Hz frequency range. The source is moving in a straight line at a constant speed, and the acoustic waves are traveling upward in a refractive channel. Considering the scales of the problem, the small perturbation method coupled with the normal-mode theory and an asymptotic analysis are used to derive the first-order scattered pressure field p₁. This method, established by Labianca and Harper [J. Acoust. Soc. Am. 61(2), 378-389 (1977)], allows p₁ to be expressed with normal-mode functions, which are computed numerically using the in-house modal propagation code MOCTESUMA for any sound-speed profile. The pressure field is calculated in a deep-water configuration with a moving source inside a summer thermocline. First, the spatial distribution of p₁ is found to follow the diffraction grating formula. Particular attention is drawn to the border between the propagative and evanescent regimes in which singularities in the theory lead to computational difficulties. Subsequently, the power spectral density of the pressure field is computed and the Doppler sidebands, asymmetrically shifted from the carrier frequency, are examined.

Acoustic Scattering Models from Rough Surfaces: A Brief Review and Recent Advances

This paper proposes a brief review of acoustic wave scattering models from rough surfaces. This review is intended to provide an up-to-date survey of the analytical approximate or semi-analytical methods that are encountered in acoustic scattering from random rough surfaces. Thus, this review focuses only on the scattering of acoustic waves and does not deal with the transmission through a rough interface of waves within a solid material. The main used approximations are classified here into two types: the two historical approximations (Kirchhoff approximation and the perturbation theory) and some sound propagation models more suitable for grazing observation angles on rough surfaces, such as the small slope approximation, the integral equation method and the parabolic equation. The use of the existing approximations in the scientific literature and their validity are highlighted. Rough surfaces with Gaussian height distribution are usually considered in the models hypotheses. Rather few comparisons between models and measurements have been found in the literature. Some new criteria have been recently determined for the validity of the Kirchhoff approximation, which is one of the most used models, owing to its implementation simplicity.