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Coupled acoustic-elastic finite element modeling of underwater sound propagation

Youngjae Shin1 ,  Won-Ki Kim2 ,  Eunpyo Lim3 ,  Youngseok Lee3 ,  Jaehwan Oh3 ,  Dawoon Lee4 ,  Ho Seuk Bae4*
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1 Department of Geology, Gyeongsang National University, Jinju, Republic of Korea
2 Department of Earth & Environmental Sciences, Chungbuk National University, Cheongju, Republic of Korea
3 Oceanographic Division, Sekwang Engineering Consultants Co., Ltd., Seoul, Republic of Korea
4 5th R&D Institute, Agency for Defense Development, Changwon, Republic of Korea
JSE, 026100045 https://doi.org/10.36922/JSE026100045
Received: 3 March 2026 | Revised: 17 April 2026 | Accepted: 23 April 2026 | Published online: 20 May 2026
© 2026 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License ( https://creativecommons.org/licenses/by/4.0/ )
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Abstract

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.

Keywords
Finite element method
Acoustic-elastic coupling
Transmission loss
Underwater sound propagation
Curvilinear mesh
Funding
This work was supported by the Agency for Defense Development by the Korean Government (UE240520DD).
Conflict of interest
The authors declare they have no competing interests.
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Journal of Seismic Exploration, Electronic ISSN: 0963-0651 Print ISSN: 0963-0651, Published by AccScience Publishing
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