The wavenumber integration model is considered to be the most accurate algorithm for arbitrary horizontally stratified media in computational ocean acoustics. In contrast to the normal mode approach, it considers not only the discrete wavenumber spectrum but also the continuous spectrum components, eliminating errors in the model approximation for horizontally stratified media. Traditionally, analytical and semianalytical methods have been used to solve the depth-separated wave equation in the wavenumber integration method, and numerical solutions have generally focused on the finite difference method and the finite element method. In this paper, an algorithm for solving the depth equation using the Chebyshev--Tau spectral method combined with a domain decomposition strategy is proposed, and a numerical program named WISpec is developed accordingly. The proposed algorithm can simulate not only the sound field excited by a point source but also the sound field excited by an infinite line source. The key idea of the algorithm is to first discretize the depth equations for each layer via the Chebyshev--Tau spectral method and then solve the equations for each layer simultaneously by incorporating boundary and interface conditions. Several representative numerical experiments are devised to test the accuracy and speed of WISpec. The high consistency of the results of different software programs running under the same configuration proves that the numerical algorithm proposed in this paper is accurate, reliable and numerically stable.

翻译：波数积分模型被认为是计算海洋声学中任意水平分层介质最精确的算法。与简正波方法不同，它不仅考虑离散波数谱，还包含连续谱成分，从而消除了水平分层介质模型近似中的误差。传统上，波数积分方法中深度分离波动方程的解多采用解析和半解析方法，数值解则主要集中于有限差分法和有限元法。本文提出了一种基于切比雪夫-陶谱方法结合区域分解策略求解深度方程的算法，并据此开发了名为WISpec的数值程序。该算法不仅能模拟点源激发的声场，还能模拟无限长线源激发的声场。其核心思路是：首先通过切比雪夫-陶谱方法对各层的深度方程进行离散化，然后结合边界和界面条件联立求解各层方程。我们设计了多项代表性数值实验来测试WISpec的精度和速度。在同一配置下运行不同软件所获结果的高度一致性，证明本文提出的数值算法准确、可靠且数值稳定。