Modeling three-dimensional underwater acoustic propagation over multi-layered fluid seabeds using the equivalent source method

This paper develops an efficient three-dimensional (3D) underwater acoustic propagation model with multi-layered fluid seabeds based on the equivalent source method (ESM). It solves the Helmholtz equation exactly by a superposition of fields generated by equivalent sources. A linear system coupling ESM equations is derived by imposing boundary conditions and solved iteratively using the generalized minimum residual method. Unlike a direct ESM solver, matrix-vector products in each iteration are evaluated by a pre-corrected fast Fourier transformation (PFFT), significantly reducing the numerical cost and enabling efficient solution of 3D large-scale propagation. Moreover, sound speed profiles can be taken into account by dividing the water column into sub-layers, each of which requires an individual PFFT procedure using an FFT subgrid scheme. Simulations of propagation over a Gaussian canyon validate the PFFT-accelerated ESM (PFFT-ESM). The capability of the PFFT-ESM for 3D scattering problems is demonstrated by further presenting the Gaussian canyon simulations with corrugated surface waves.