Coupled acoustic-elastic finite element modeling of underwater sound propagation

Underwater sound propagation modeling is fundamental to sonar design and marine exploration. The parabolic equation (PE) method has been the dominant tool, but carries inherent limitations: the one-way approximation neglects backscattered energy, acoustic-only implementations ignore shear-wave conversion at the fluid-solid interface, and range-marching discretization approximates irregular bathymetry as a staircase boundary. These limitations become significant at low frequencies (below 200 Hz), where acoustic wavelengths reach 7.5–30 m and a substantial fraction of energy penetrates into the elastic seabed, exciting both compressional and shear waves. This study develops a two-dimensional frequency-domain finite element model coupling the Helmholtz equation in the water column with the Navier equation in the elastic seabed, with pressure and normal displacement continuity enforced at the fluid-solid interface. Irregular bathymetry is represented by a terrain-following curvilinear mesh via transfinite interpolation, eliminating staircase errors. A perfectly matched layer truncates open boundaries. Validation against RAMGEO for a Pekeris waveguide yields a mean absolute error of 1.8 dB (mean bias −0.17 dB). In a lossless comparison, mean |ΔTL| between acoustic-only and coupled models is approximately 6 dB, nearly independent of frequency across 50–200 Hz. Under realistic attenuation, mean |ΔTL| ranges from 0.8 dB (soft sediment) to 5.1 dB (hard bottom), with local maxima exceeding 10 dB at interference nulls. Staircase meshes yield displacement errors of 53–116% and pressure errors of 23–24% versus the curvilinear solution. The proposed model provides a rigorous forward engine for accurate transmission loss prediction in complex shallow-water environments.