Finite Element Modeling of Acoustic Scattering From Fluid and Elastic Rough Interfaces

Abstract

Quantifying acoustic scattering from rough interfaces is critical for reverberation modeling, acoustic sediment characterization, and propagation modeling. In this study, a finite element (FE) scattering model is developed. The model computes the plane wave scattering strength for an ensemble of rough power-law surfaces for ocean bottoms described as fluid and elastic. The FE model is compared with two models based on approximations to the Helmholtz-Kirchhoff integral: the Kirchhoff approximation (KA) and the perturbation theory (PT). In the case of a fluid-like bottom, the KA and FE models agree except at small grazing angles. The PT and FE models deviate near specular especially at small angles. For the elastic case, the PT predicts the FE results well except at the intromission angle of the shear wave. The KA deviates for angles that are below the critical angle of the compressional wave. At the shear wave intromission angle, the FE model shows a more plausible solution likely due to multiple scattering events that are not accounted for in PT for the modeled roughness.

A comparison of finite element and analytic models of acoustic scattering from rough poroelastic interfaces

“…This disparity at specular is not anticipated and it is suspected that FEM would come into better agreement with the analytic models if the computational domain length was extended (leading to an increased beam waist as discussed in Ref. 10). KA is not in particularly good agreement with FEM or the other two analytic models except for angles near specular.…”

“…10 for the purposes of the present study. First, the version of Biot's equations used in this work and their associated weak forms follow those presented by Atalla et al…”

“…The FEM is adapted to the present scattering problem as described by Isakson and Chotiros. 10 For a full discussion of the considerations needed to adapt FEM to scattering from rough interfaces, the reader is directed to Ref. 10.…”

“…10, a computational domain length of 200k is used for all cases. Finally, special attention must be paid to the mesh criteria for computational domains consisting of poroelastic materials.…”

A survey on deployment techniques, localization algorithms, and research challenges for underwater acoustic sensor networks

“…Parabolic equations and finite elements are the most computationally intensive and highest fidelity models, and they can represent all aspects of acoustic propagation such as interface scattering, range dependence, and 3D effects . Specifically, parabolic equations are more suitable for highly 3D situations and finite element models are more suitable for highly range dependent waveguides …”