Tetrascatt Model: Born Approximation for the Estimation of Acoustic Dispersion of Fluid-Like Objects of Arbitrary Geometries

Abstract

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).