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.

A coupled-mode model is a classic approach for solving range-dependent sound propagations and is often used to provide benchmark solutions in comparison with other numerical models because of its high accuracy. Existing coupled-mode programs have disadvantages such as high computational cost, weak adaptability to complex ocean environments, and numerical instability. In this paper, a new algorithm that uses an improved range normalization of a “stair-step” and global matrix approach to address range dependence in ocean environments is designed. This algorithm uses the Chebyshev–Tau spectral method to solve the eigenpairs in the range-independent segments. The Chebyshev–Tau spectral method can converge rapidly, and the rate of convergence depends on the smoothness of the sound speed and density profiles. The main steps of the algorithm are parallelized, so parallel computing technologies are also applied for further acceleration. Based on this algorithm, an efficient program is implemented, and numerical simulations verify that this algorithm is reliable, accurate, and capable. Compared with the existing coupled-mode programs, the newly developed program is more stable and efficient with comparable accuracy and can simulate waveguides in more complex and realistic ocean environments.

With the increasing demand for underwater detection, interest in the acoustic field of range-dependent ocean waveguides is also growing. For weakly range-dependent ocean waveguides, adiabatic modes represent a compromise between accuracy and computational cost and occupy an important place in the simulation of numerical sound fields. However, either existing adiabatic-mode programs consider too few layers of media or the root-finder tends to miss roots. In addition, none of the programs can solve the acoustic field excited by a line sound source located anywhere in the plane. In this paper, we first derive an expression for the acoustic field excited by a line source by adiabatic modes and then introduce a high-precision spectral method to solve the local eigenmodes. For the lower boundary condition of the acoustic half-space, we use the eigenvalue transformation technique to transform the transcendental algebra system formed by spectral discretization into a generalized eigenvalue problem. Several representative numerical experiments are designed to verify the accuracy of the algorithm. After analyzing the parallelism, the multiprocess and multithread hybrid strategy is adopted to further accelerate the algorithm in parallel, and parallel numerical simulation is carried out on the Tianhe–2 multicore supercomputer; favorable acceleration is achieved.

Underwater acoustic propagation is a complex phenomenon in the ocean environment. Traditional methods for calculating acoustic propagation loss rely on solving complex partial differential equations. Deep learning methods, leveraging their robust nonlinear approximation capabilities, can model various physical phenomena effectively, significantly reducing computation time and cost. Despite considerable advancements in the study of various inverse underwater acoustic problems, research focused on forward physical modeling is still nascent. This study proposes an end-to-end architecture for predicting underwater acoustic transmission loss (TL). This architecture employs a data-driven approach capable of swiftly and accurately predicting the complete acoustic field. It employs a U-Net model integrated with an adaptive multi-scale dilated module, named MultiScale-DUNet, which effectively predicts by assimilating multi-scale acoustic field information. It is demonstrated that the MultiScale-DUNet is capable of predicting acoustic TL in complex two-dimensional ocean environments within the end-to-end framework. The results indicate that the MultiScale-DUNet can rapidly predict the acoustic TL while maintaining high accuracy under computationally inexpensive conditions. This end-to-end technology for predicting underwater acoustic TL holds broad application prospects in fields such as underwater exploration and real-time underwater monitoring.