Use of the distorted wave Born approximation to predict scattering by inhomogeneous objects: Application to squid

Abstract

A new method has been developed to predict acoustic scattering by weakly scattering objects with three-dimensional variability in sound speed and density. This variability can take the form of inhomogeneities within the body of the scatterer and/or geometries where the acoustic wave passes through part of the scattering body, into the surrounding medium, and back into the body. This method applies the distorted wave Born approximation ͑DWBA͒ using a numerical approach that rigorously accounts for the phase changes within a scattering volume. Ranges of validity with respect to material properties and numerical considerations are first explored through comparisons with modal-series-based predictions of scattering by fluid-filled spherical and cylindrical fluid shells. The method is then applied to squid and incorporates high resolution spiral computerized tomography ͑SCT͒ scans of the complex morphology of the organism. Target strength predictions based on the SCT scans are compared with published backscattering data from live, freely swimming and tethered squid. The new method shows significant improvement for both singleorientation and orientation-averaged scattering predictions over the DWBA-homogeneousprolate-spheroid model.

Orientation dependence of broadband acoustic backscattering from live squid

“…The length of the prolate spheroid, L, was determined by matching the total volume of the homogeneous (no sea-water-filled cavities in the mantle cavity) squid digital representation to the volume of the prolate spheroid. Details of the inhomogeneities in the squid body and the scaling issues can be found in Jones et al (2009).…”

“…This integral can be solved analytically for simple objects, such as spheres and cylinders (Stanton et al, 1998a), and is particularly useful for numerically modeling the scattering from bodies with arbitrary shapes (Lavery et al, 2002) and material properties (Jones et al, 2009). In this study, two DWBA-based models are compared: (1) an analytical model with a simple geometry (smooth prolate spheroid) and homogeneous material properties, and (2) a numerical model which involves three-dimensional digitization of the squid and inhomogeneous material properties.…”

“…A total of seven individuals (Table I) were used and nine successful acoustic measurements were made. Spiral computed tomography (SCT) images obtained by Jones et al (2009) were used in this study to produce realistic digital representations of the three-dimensional shape of the squid. The SCT images were obtained for a single, live, anesthetized squid and a single, dead, previously frozen squid, both of the same species as those used in the experiment.…”

“…Data collected in this study have been compared to model predictions given by the analytical DWBA prolate spheroid model and the three-dimensional DWBA numerical model which takes into account inhomogeneous, fluid-like material properties, and realistic squid shape, obtained using computed tomography (CT) scans (Jones et al, 2009).…”

“…These models include the exact modal-series solution for a liquid prolate spheroid (Arnaya and Sano, 1990;Mukai et al, 2000), the Kirchhoff ray-mode model (Kang et al, 2006), and the distorted-wave Born approximation (DWBA) formulation applied analytically using a simple prolate spheroid shape (Mukai et al, 2000) or numerically with a realistic three-dimensional geometry (Jones et al, 2009). The development and assessment of these models are particularly important for the study of squid, since controlled acoustic experiments are not practical for many commercially important species of squid due to the difficulties in specimen handling.…”