Quantifying three dimensional effects in acoustic rough surface scattering
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Interface roughness can have a significant effect on the scattering of sound energy, and therefore an understanding of the effects of roughness is essential to making predictions of sound propagation and transmission underwater. Many models of roughness scattering currently in use are two dimensional (2D) in nature; three dimensional (3D) modeling requires significantly more time and computational resources. In this work, an effort is made to quantify the effects of 3D scattering in order to assess whether or under what conditions 3D modeling is necessary. To that end, an exact 3D roughness scattering model is developed based on a commercially available finite element package. The finite element results are compared with two approximate scattering models (the Kirchhoff approximation and first order perturbation theory) to establish the validity and regimes of applicability of each. The rough surfaces are realizations generated from power spectra measured from the sea floor. However, the surfaces are assumed to be pressure release (as on an air-water interface). Such a formulation is nonphysical, but allows the assessment of the validity of the various modeling techniques which is the focus of this work. The comparison between the models is made by calculating the ensemble average of the scattering from realizations of randomly rough surfaces. It is shown that a combination of the Kirchhoff approximation and perturbation theory models recovers the 3D finite element solution.