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

Abstract

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°.

A Kirchhoff approximation-based numerical method to compute multiple acoustic scattering of a moving source

“…It was observed that the accuracy gets better with smaller angles of scattering and higher frequencies. A good accuracy of the approximation has also been observed by Foote and Francis [18] for high frequencies in far-field backscattering of sound by fishes. They noticed that the BEM and the Kirchhoff approximation gave similar results for Helmholtz numbers ka > 4, where a is the characteristic size of the scattering object.…”

“…(10), (16) and (17) by introducing the shifted frequencies and the retarded time and by replacing the expression for the incident pressure by Eq. (18). As each integration point on the objects are considered as individual sources of their own perceived frequency, the computational cost increases exponentially with the level of scattering.…”

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

“…29 and applied in Ref. 17. This incorporates a second integral equation, the normal derivative form, which is obtained by differentiating the standard form with respect to the normal direction at the surface.…”

“…33 Experience suggests that good representation of the acoustic variables is obtained if the lengths of the sides of the elements are less than onethird of a wavelength. 17 The accuracy of geometrical representation depends on the degree of undulation of the surface, but it should be noted that the quadratic interpolation allows the sides and faces of the elements to be curved. Further details of the formulation and equations can be found in Ref.…”

“…The approach is by theoretical modeling with the boundaryelement method, applied in a preceding study to the same specimens, but under assumption there of an empty swimbladder volume corresponding to an ideal pressure-release boundary. 17 …”