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Mathematical scattering models are derived and compared with data from zooplankton from several gross anatomical groups-fluidlike, elastic shelled, and gas bearing. The models are based upon the acoustically inferred boundary conditions determined from laboratory backscattering data presented in part I of this series ͓Stanton et al., J. Acoust. Soc. Am. 103, 225-235 ͑1998͔͒. The models use a combination of ray theory, modal-series solution, and distorted wave Born approximation ͑DWBA͒. The formulations, which are inherently approximate, are designed to include only the dominant scattering mechanisms as determined from the experiments. The models for the fluidlike animals ͑euphausiids in this case͒ ranged from the simplest case involving two rays, which could qualitatively describe the structure of target strength versus frequency for single pings, to the most complex case involving a rough inhomogeneous asymmetrically tapered bent cylinder using the DWBA-based formulation which could predict echo levels over all angles of incidence ͑including the difficult region of end-on incidence͒. The model for the elastic shelled body ͑gastropods in this case͒ involved development of an analytical model which takes into account irregularities and discontinuities of the shell. The model for gas-bearing animals ͑siphonophores͒ is a hybrid model which is composed of the summation of the exact solution to the gas sphere and the approximate DWBA-based formulation for arbitrarily shaped fluidlike bodies. There is also a simplified ray-based model for the siphonophore. The models are applied to data involving single pings, ping-to-ping variability, and echoes averaged over many pings. (k i •r tan ) where r tan is the tangent to the body axis at point r pos ͑␤ tilt ϭ0 corresponds to broadside incidence to the disk axis at the arbitrary point on the body axis͒. ␤ tilt is not to be confused with the orientation angle, , of the body, although the two are the same when the body axis is straight. ␤ L imaginary part of L ; attenuation coefficient of Lamb wave on elastic shelled sphere

By heuristically extending the previously developed ray solution [Stanton et al. J. Acoust. Soc. Am. 94, 3454-3462 (1993)] to predict the scattering by cylinders over all angles of incidence, approximate expressions are derived which describe the echo energy due to sound scattered by finite cylinders averaged over orientation and length. Both straight and bent finite length cylinders of high aspect ratio are considered over the full range of frequencies (Rayleigh through geometric scattering). The results show that for a sufficiently broad range of orientation, the average echo is largely independent of the degree of bend--that is, the results are essentially the same for both the straight and bent cylinders of various radii of curvature (provided the bend is not too great). Also, in the limit of high frequency (i.e., the acoustic wavelength is much smaller than the cross-sectional radius of the object), the averages are independent of frequency.

Acoustic echo sounders are commonly used to survey zooplankton. An essential element in the methods is the acoustic scattering model, which relates acoustic echo data to meaningful biological parameters such as size and numerical density. Because of the importance of scattering models, there has been much development of models of increasing sophistication. With the increase in sophistication is an associated improvement in accuracy, but possibly at the cost of increased effort in implementing the model. Thus the practical question is which model provides sufficient accuracy for the scientific problem of interest. This paper presents a modelling study using a wide range of models, ranging from simple to complex representation of the animals, a synthesis of previously published laboratory scattering data from a variety of sources, and laboratory data presented for the first time. The focus is on fluid-like zooplankton (i.e., animals that do not support shear waves) with examples specific to euphausiids, shrimp, and copepods. The simplest model is the sphere with homogeneous material properties while the most complex is a high-resolution digitized form of each zooplankton taking into account surficial roughness and inhomogeneities of the material properties. The results show that there are conditions under which very simple, easy-to-use models can be used with reasonable accuracy while there are other conditions where the more complex models must be used. 2000 International Council for the Exploration of the Sea

Stanton, T. K., Chu, D., Jech, J. M., and Irish, J. D. 2010. New broadband methods for resonance classification and high-resolution imagery of fish with swimbladders using a modified commercial broadband echosounder. – ICES Journal of Marine Science, 67: 365–378. A commercial acoustic system, originally designed for seafloor applications, has been adapted for studying fish with swimbladders. The towed system contains broadband acoustic channels collectively spanning the frequency range 1.7–100 kHz, with some gaps. Using a pulse-compression technique, the range resolution of the echoes is ∼20 and 3 cm in the lower and upper ranges of the frequencies, respectively, allowing high-resolution imaging of patches and resolving fish near the seafloor. Measuring the swimbladder resonance at the lower frequencies eliminates major ambiguities normally associated with the interpretation of fish echo data: (i) the resonance frequency can be used to estimate the volume of the swimbladder (inferring the size of fish), and (ii) signals at the lower frequencies do not depend strongly on the orientation of the fish. At-sea studies of Atlantic herring demonstrate the potential for routine measurements of fish size and density, with significant improvements in accuracy over traditional high-frequency narrowband echosounders. The system also detected patches of scatterers, presumably zooplankton, at the higher frequencies. New techniques for quantitative use of broadband systems are presented, including broadband calibration and relating target strength and volume-scattering strength to quantities associated with broadband signal processing.