The normal mode model is widely used to solve underwater acoustic propagation problems in horizontally layered waveguides. However, ocean elastic bottoms are often modeled as fluids or replaced by an equivalent reflection coefficient in most current models; for this reason, the solution of elastic modes and seismic wavefields cannot be solved. To overcome this constraint, a solving method utilizing the Chebyshev collocation method (CCM) for the seismo-acoustic normal mode model within arbitrarily layered inhomogeneous fluid-solid media is proposed. The CCM is applied to discretize the modal equations of compressional wave (P-wave) and shear wave (S-wave), along with the boundary and interface conditions. A complex matrix eigenvalue system is established by restructuring the global discrete modal equation matrix, on which proper interface conditions (fluid-solid and solid-solid) as well as boundary conditions have been enforced. Solving this eigenvalue problem yields the horizontal wavenumbers and the full-depth modal functions; the full-wavefield is then constructed by summing up contributions of each of the modes. Numerical experiments demonstrate that the proposed method accurately computes both the acoustic and seismic wavefields. Moreover, detailed analyses reveal that its accuracy is comparable to that of rpress and significantly surpasses that of kraken and krakenc.
Cai et al. (2026) studied this question.