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Acoustic waves are essential tools for guiding underwater activities. For many years, numerical modeling of ocean acoustic propagation has been a major research focus in underwater acoustics. Normal mode theory, one of the earliest and most extensively studied methods in this field, is renowned for its well-established theoretical framework. The core of normal mode theory involves the numerical solution of modal equations. In classical normal mode models, these equations are typically discretized using low-order finite difference methods, which, while broadly applicable, suffer from a limited convergence rate. The spectral element method, widely used in the seismic field, is recognized for its spectral precision and flexibility. In this article, we propose a normal mode model discretized using the spectral element method. The weak form of the modal equation directly satisfies boundary and interface conditions without requiring additional operations. The entire computational domain can be divided into segments of varying number and length, configured according to environmental conditions. The perfectly matched layer technique is employed to simulate acoustic half-space boundary conditions, effectively addressing the high computational costs and numerical instability associated with traditional artificial absorbing layers. Based on these algorithms, we have developed a numerical program (SEM). This research verifies the accuracy of the spectral element model through three different types of numerical experiments.
Zhang et al. (Fri,) studied this question.