Validity of the sonar equation and Babinet’s principle for scattering in a stratified medium

Abstract

The sonar equation rests on the assumption that received sound pressure level after scattering can be written in decibels as a sum of four terms: source level, transmission loss from the source to the target, target strength, and transmission loss from the target to the receiver. This assumption is generally not valid for scattering in a shallow water waveguide and can lead to large errors and inconsistencies in estimating a target's scattering properties as well as its limiting range of detection. By application of coherent waveguide scattering theory, the sonar equation is found to become approximately valid in a shallow water waveguide when the object's complex scatter function is roughly constant over the equivalent horizontal grazing angles +/- delta psi spanned by the dominant waveguide modes. This is approximately true (1) for all objects of spatial extent L and wavelength lambda when 2delta psi<lambda/2L and (2) for spheres and certain other rounded objects in nonforward scatter azimuths, even when (1) does not hold. The sonar equation may be made valid by lowering the active frequency of operation in a waveguide. This is often desirable because it greatly simplifies the analysis necessary for target classification and localization. Similarly, conditions are given for when Babinet's principle becomes approximately valid in a shallow water waveguide.

Ocean Acoustic Waveguide Remote Sensing (OAWRS) of marine ecosystems

“…Frequency should also be low enough for the received acoustic field scattered from any given fish to be expressible as the product of the 3 factors 'transmission to the given fish', 'scattering from the fish', and 'transmission from the fish' (Appendix C). At CFFS wavelengths, this factorization is typically not possible because propagation and scattering effects are convolved together in an ocean waveguide (Ratilal et al 2002). Frequencies should be chosen so that acoustic attenuation from propagation through the fish is negligible even over long ranges.…”

Forward acoustic scattering by moving objects: Theory and experiment

“…Each incoming mode is composed of one down-going component with amplitude A n (r 0 ) and incident elevation angle α n , and one up-going component with amplitude B n (r 0 ) and incident elevation angle -α n , respectively. Each scattered mode is also composed of a pair of plane waves, the down-going plane wave with amplitude B m (r) and elevation angle α m , the up-going plane wave with amplitude A m (r) and elevation angle -α m [12]. Each of the four terms in eq.…”

“…The normal mode model [11,12] is employed to simulate the forward scattering field with an object crossing the source-receiver line and a physical interpretation is given. Furthermore, we designed and conducted lake experiments at range-to-depth ratios up to about 190, much farther than reported experiments.…”

Mean and covariance of the forward field propagated through a stratified ocean waveguide with three-dimensional random inhomogeneities

“…Equation ͑2͒ is applicable when the source and receiver ranges are sufficiently far from the target that the plane wave scatter function description is valid. 5,52,54 For a single shell, the incident field has modal plane wave amplitudes given by, 1,5,51…”