Edmundo F. Lavia

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.