David T. I. Francis

A gradient formulation of the Helmholtz integral equation for acoustic radiation and scattering

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.

Comparing Kirchhoff-approximation and boundary-element models for computing gadoid target strengths

To establish the validity of the boundary-element method (BEM) 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 degrees.

Calibration sphere for low-frequency parametric sonars

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.

Depth-dependent target strengths of gadoids by the boundary-element method.

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 (BEM) 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.

Comparisons among ten models of acoustic backscattering used in aquatic ecosystem research

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.

Broadband Ultrasonic Target Strengths of Hollow Ceramic Flotation Spheres

The target strengths of hollow ceramic flotation spheres manufactured by DeepSea Power and Light, Inc., and tested to a pressure equivalent of 12,000 m have been measured as a function of frequency over the bands 10-150 kHz. The spheres are made of alumina, purity 99.9%, with diameter 91.44 plusmn 0.2 mm, nominal thickness 1.3 mm, mass 140 plusmn 1 g. The target strength spectra have also been calculated theoretically assuming a mass density of 3.984 g/cm3, longitudinal-and transverse-wave sound speeds of 11000 and 6510 m/s, respectively. Measurements and computations are compared. Potential applications of the sphere as a standard acoustic target are noted.

The development of a low frequency barrel-stave transducer for tomographic applications using finite element and boundary element modelling

Ocean acoustic tomography requires wide bandwidth, compact, and efficient low frequency sources of sound. The paper describes the design process for such a transducer in which the principal objectives are a centre frequency of 400 Hz and a bandwidth of 100 Hz, in as compact a device as possible. A finite element method is used to model the structure, and this is coupled to a boundary element method to predict the performance in water. Quadratic elements are used throughout, and treatment of the piezoelectric properties of the driver is included. Both convex and concave barrel shapes are considered, and the effects of various parameters are determined; these include the thickness and curvature of the staves, the number of staves, and the overall size of the device. A design is presented which theoretically meets the specified objectives.<<ETX>>

Calibration of broadband sonar systems using multiple standard targets

A seven‐octave active sonar system spanning the nominal frequency range 25‐3200 kHz was deployed in Norwegian waters for the purpose of measuring the acoustic scattering characteristics of a range of marine organisms. This system transmitted linear frequency‐modulated (LFM) signals in order to achieve good range resolution and to obtain spectral information on resolved targets. Total system performance was variously measured in situ and ex situ, depending on the particular octave band, using standard‐target spheres. This enabled the frequency response of the entire system to be determined and the sidelobe level of the matched‐filter receiver to be reduced. The effects of the deep nulls encountered in the backscattered spectrum of target spheres were partially reduced by using a string of up to six spheres of different sizes and material properties. Typical results will be presented showing that such calibration procedures are sensitive the relative alignment of the sonar‐target and to sound‐speed profile ...

Spheres for calibrating high‐frequency broadband echo sounders

The notion of standard‐sphere broadband calibration [Dragonette et al., J. Acoust. Soc. Am. 69, 1186 (1981)] is being realized for a new echo sounding system that spans the seven‐octave range 25 kHz to 3.2 MHz. Spheres formed of tungsten carbide with 6% cobalt binder, with 10‐ and 20‐mm diameters, have been measured in the laboratory to determine their backscattering spectra over the approximate frequency ranges 0.85–1.3 MHz and 2.9–3.6 MHz. This allows exploration of the wave number radius (ka) product over the nominal ranges 18–28, 36–56, 61–75, and 122–150. Comparison with theoretical expectation, as derived from the standard modal solution using published values for the material properties, is quite good. Confidence in the computations thus enables favorable regions of the backscattering spectra to be sought and exploited in choosing optimal diameters, as has earlier been the case with spheres for calibrating resonant transducers. In the course of checking computations, it was discovered that two inde...

Modeling the target strength of Calanus finmarchicus

The boundary element method is applied to the copepod Calanus finmarchicus, treated as a composite body, with fluidlike oil sac embedded in a fluidlike, mostly transparent prosome. The generally complex shapes of the two bodies are modeled on the basis of the actual dorsal‐ and lateral‐aspect cross sections, as observed by videomicroscopy with the living, unanaesthetized animal encased in a droplet of sea water. Physical properties of the two bodies, namely mass density and longitudinal‐wave sound speed, are derived through a combination of measurement and inference. Computations of backscattering cross section as a function of orientation and frequency are presented over the range 25 kHz to 3.2 MHz for a number of specimens. A sensitivity analysis is performed to quantify some uncertainty in the assumed values of the physical properties. [Support by the following is acknowledged: EU through RTD Contract No. MAS3‐CT95‐0031, Norwegian Research Council through Grant No. 113809/122, and Bergen Large‐Scale Facility (LSF) for Marine Pelagic Food Chain Research.]