Analytical and numerical scattering models with accompanying digital representations are used increasingly to predict acoustic backscatter by fish and zooplankton in research and ecosystem monitoring applications. Ten such models were applied to targets with simple geometric shapes and parameterized (e.g., size and material properties) to represent biological organisms such as zooplankton and fish, and their predictions of acoustic backscatter were compared to those from exact or approximate analytical models, i.e., benchmarks. These comparisons were made for a sphere, spherical shell, prolate spheroid, and finite cylinder, each with homogeneous composition. For each shape, four target boundary conditions were considered: rigid-fixed, pressure-release, gas-filled, and weakly scattering. Target strength (dB re 1 m(2)) was calculated as a function of insonifying frequency (f = 12 to 400 kHz) and angle of incidence (θ = 0° to 90°). In general, the numerical models (i.e., boundary- and finite-element) matched the benchmarks over the full range of simulation parameters. While inherent errors associated with the approximate analytical models were illustrated, so were the advantages as they are computationally efficient and in certain cases, outperformed the numerical models under conditions where the numerical models did not converge.

To establish the validity of the boundary-element method ͑BEM͒ for modeling scattering by swimbladder-bearing fish, the BEM is exercised in several ways. In a computation of backscattering by a 50-mm-diam spherical void in sea water at the four frequencies 38.1, 49.6, 68.4, and 120.4 kHz, agreement with the analytical solution is excellent. In computations of target strength as a function of tilt angle for each of 15 surface-adapted gadoids for which the swimbladders were earlier mapped, BEM results are in close agreement with Kirchhoff-approximation-model results at each of the same four frequencies. When averaged with respect to various tilt angle distributions and combined by regression analysis, the two models yield similar results. Comparisons with corresponding values derived from measured target strength functions of the same 15 gadoid specimens are fair, especially for the tilt angle distribution with the greatest standard deviation, namely 16°.

The depth dependence of fish target strength has mostly eluded experimental investigation because of the need to distinguish it from depth-dependent behavioral effects, which may change the orientation distribution. The boundary-element method ͑BEM͒ offers an avenue of approach. Based on detailed morphometric data on 15 gadoid swimbladders, the BEM has been exercised to determine how the orientation dependence of target strength changes with pressure under the assumption that the fish swimbladder remains constant in shape and volume. The backscattering cross section has been computed at a nominal frequency of 38 kHz as a function of orientation for each of three pressures: 1, 11, and 51 atm. Increased variability in target strength and more abundant and stronger resonances are both observed with increasing depth. The respective backscattering cross sections have been averaged with respect to each of four normal distributions of tilt angle, and the corresponding target strengths have been regressed on the logarithm of fish length. The tilt-angle-averaged backscattering cross sections at the highest pressure have also been averaged with respect to frequency over a 2-kHz band for representative conditions of insonification. For all averaging methods, the mean target strength changes only slightly with depth.

A method of overcoming the problem of nonuniqueness in the discretized Helmholtz integral equation is described, based on a partial application of the Helmholtz gradient formulation of Burton and Miller [Proc. R. Soc. London, Ser. A 323, 201–210 (1971)]. The numerical implementation is designed to be compatible with a finite-element structural analysis, and uses boundary elements of the quadratic isoparametric type. The method is illustrated for scattering from a sphere, and for radiation by a piston vibrating in the end of a cylinder, with consistent results being obtained across a wide frequency range. The additional computation is of the order of 35% of that required for the standard formulation.

The problem of calibrating parametric sonar systems at low difference frequencies used in backscattering applications is addressed. A particular parametric sonar is considered: the Simrad TOPAS PS18 Parametric Sub-bottom Profiler. This generates difference-frequency signals in the band 0.5-6 kHz. A standard target is specified according to optimization conditions based on maximizing the target strength consistent with the target strength being independent of orientation and the target being physically manageable. The second condition is expressed as the target having an immersion weight less than 200 N. The result is a 280-mm-diam sphere of aluminum. Its target strength varies from −43.4 dB at 0.5 kHz to −20.2 dB at 6 kHz. Maximum excursions in target strength over the frequency band due to uncertainty in material properties of the sphere are of order ±0.1 dB. Maximum excursions in target strength due to variations in mass density and sound speed of the immersion medium are larger, but can be eliminated by attention to the hydrographic conditions. The results are also applicable to the standard-target calibration of conventional sonars operating at low-kilohertz frequencies.