Juan D. Gonzalez

Modeling the acoustic scattering response due to penetrable objects of arbitrary shapes, such as those of many marine organisms, can be computationally intensive, often requiring high-performance computing equipment when considering a completely general situation. However, when the physical properties (sound speed and density) of the scatterer are similar to those of the surrounding medium, the Born approximation provides a computationally efficient way to calculate it. For simple geometrical shapes like spheres and spheroids, the acoustic scattering in the far field evaluated through the Born approximation recipe results in a formula that has been historically employed to predict the response of weakly scattering organisms, such as zooplankton. Further, the Born approximation has been extended to bodies whose geometry can be described as a collection of noncircular rings centered on a smooth curve. In this work, we have developed a numerical approach to calculate the far-field backscattering by arbitrary 3D objects under the Born approximation. The object's geometry is represented by a volumetric mesh composed of tetrahedrons, and the computation is efficiently performed through analytical 3D integration, yielding a solution expressed in terms of elementary functions. On a current desktop PC the model can compute the scattering from meshes with millions of elements in a matter of minutes. This model is able to compute the scattering from a complex shape 200× faster than other methods like the Boundary Element Method, without compromising the numeric quality of the solution. The method's correctness has been successfully validated against benchmark solutions. Additionally, we present acoustic scattering results for species with complex geometries. To enable other researchers to use and validate the method, a computational package named tetrascatt was developed in the R programming language and published in the CRAN (Comprehensive R Archive Network).

The Kirchhoff approximation (K-A) to calculate the acoustic backscattering of a complex structure can be evaluated using a discretized version of its surface (i.e, a mesh). From the computational viewpoint, the most handy approach is the one based on flat facets. However, in the high-frequency range, where the K-A provides good agreement and is therefore applicable, it requires a mesh with such a large number of facets that it turns impractical. To avoid these difficulties, a mesh of curved triangles can be used to model the scatterer’s complex structure. Previous computational implementations reported in the literature did not accomplish satisfactory results for high frequency. In this work, we propose a numerical model based upon an iterative integration using Gauss–Legendre rules. The model was validated against exact solutions and led us to achieve adequate results in the high-frequency range.

Engraulis anchoita is a physostomous fish with a dual chambered swimbladder (sb). In situ target strength (TS) measurements on this species are only possible at night, when anchovies disperse forming a scattering layer near the sea surface. A survey data series comprising more than 50000 single target detections, recorded from 1995 to 2008, was analyzed in order to study the species specific TS at 38 kHz. A TS vs. fish total length (L) equation was obtained from the in situ measurements (TS = 31.9 log L – 82.4 dB; r2= 0.78). When the slope of the regression line was forced to 20 into the TS equation, the resulting value for the constant term (b20) was −68.6 dB. In any case, these results indicate an average difference of +3 dB (higher TS values) when compared with the general model suggested for clupeoid fish. The TS measurements obtained inside the nighttime sound scattering layer exhibited a negative trend with depth. An empirical depth dependence term for the anchovy TS equation was obtained through a three parameter least square fitting of the data [TS = 31.3 log L – 79.6 dB – 4.74 log (1 + z/10); r2 = 0.74]. Anatomical data obtained through high resolution X-Ray Computed Tomography was employed as input for a Prolate Spheroidal Model (PSM). Theoretical TS vs. tilt angle functions were obtained considering the compression of the sb at different depths and under the assumption of different contraction rates. The TS functions were then averaged over different fish tilt angle distributions and used to derive theoretical depth dependence curves of average fish TS. The implications of the adopted sb contraction rate and tilt angle distribution are discussed by comparing the modelled TS(z) curves against the empirical data.

The prolate spheroidal model is reexamined to simulate the backscattered target strength by a fish through coherent treatment of the swimbladder (gas-filled spheroid) and fish body (liquid-filled spheroid). The wavelength/fish size applicability range of the model is expanded via implementation of non-traditional algorithms to calculate the prolate spheroidal radial functions. Results demonstrate the relevance of including the fish body backscatter contribution and the random nature of fish behavior to obtain good agreement between model predictions and measurements. The model was tested by comparison with direct measurements of acoustic backscattering target strength of caged fish (Percichthys trucha) using a 38 kHz split-beam echosounder. Reported values of measured maximum and averaged target strength (in the intensity domain) from gadoids (bladdered fish) and mackerel (bladderless fish) were also compared with model predictions. In all cases, a good agreement was obtained when comparing simulated and measured results.