Sound scattering by several zooplankton groups. II. Scattering models

Abstract

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

Distribution, patchiness, and behavior of Antarctic zooplankton, assessed using multi-frequency acoustic techniques

“…Discrepancies also exist in the predictions of the scattering by individual krill (i.e., target strength) from the semiempirical model developed by Greene et al (1991) that is in common use for krill surveys and theoretical models based on scattering physics (e.g., Stanton et al, 1993Stanton et al, , 1998McGehee et al, 1998). Target strength is a critical quantity in making abundance estimates from acoustic data, and the Greene et al (1991) model marked a substantial improvement over earlier target strength models developed during the BIOMASS program (see review in Miller and Hampton, 1989), but these discrepancies have yet to be fully reconciled.…”

“…In this study, however, we average volume backscattering over large depth ranges and horizontal intervals, and thereby average over a very large number of animals. When scattering is averaged over a distribution of animal lengths, the dips in target strength at particular size ranges are substantially reduced in magnitude, to 5 dB or less (Stanton et al, 1998;Stanton and Chu, 2000). Furthermore, the exact sizes of animals encountered in this study are such that the potential confounding effect of animal size on the relationship between volume backscattering and biomass is relatively small: the lengths of most of the net-sampled taxa (e.g., copepods, pteropods, siphonophores, and small euphausiids) were much smaller than the length at which the first dip in the target strength vs. size relationship occurs.…”

“…For most of the dominant taxa, the models of acoustic scattering used here have been experimentally validated through comparisons of model predictions to measured target strengths of actual individual organisms (Stanton et al, 1998; …”

“…Expected echo intensities, or backscattering cross-sections (abs), were estimated based on the length of each individual determined by silhouette analysis and models of acoustic scattering appropriate to the individual's taxonomic group. These models were developed by Stanton et al (1994Stanton et al ( , 1998, are reviewed in Stanton and Chu (2000), and are sensitive to numerous parameters in addition to animal length, including animal orientation and material properties (Chu et al, 2000a; …”

“…In the case of euphausiids (the order encompassing Antarctic krill), the shape has typically been modeled as some kind of deformed cylinder. Scattering is integrated along the lengthwise axis of the cylinder, taking into account the phase shift arising from deformation of this axis due to curvature and variations in cross-sectional radius Stanton et al, 1993;McGehee et al, 1998;Stanton et al, 1998;Demer and Conti, 2003). Lavery et al (2002) employed the DWBA to estimate scattering as the volume integral over a fully 3-D representation of the animal derived from computerized tomography.…”