A spectrally discretized wide-angle parabolic equation model for simulating acoustic propagation in laterally inhomogeneous oceans.

Sound waves can be used to carry out underwater activities. Rapidly and accurately simulating sound propagation is the basis for underwater detection. The wide-angle parabolic model has a good computational speed and accuracy and is currently the main numerical model for mid- and low-frequency sound propagation. The classical wide-angle parabolic equation model is discretized by the finite difference method and a low-order difference scheme is generally adopted. In this paper, a wide-angle parabolic equation model based on a spectral method is proposed. The depth operators of each layer are discretized via the Chebyshev spectral method and then assembled into a global matrix for the forward step. Lateral inhomogeneity is addressed by updating the global depth matrix while stepping forward. In the proposed spectral algorithm, both soft and hard seabeds can be accurately simulated by imposing boundary conditions, and the perfectly matched layer technique is used to truncate the unbounded acoustic half-space. Several representative numerical experiments prove the accuracy and efficiency of the proposed algorithm. However, the spectral method requires that the thickness of the layers does not change during the forward step. Thus, the current spectral algorithm cannot simulate waveguides with terrain undulation, which is its main limitation.