Abstract The modelling of sound propagation in the ocean by the solution of mode parabolic equations is discussed. Mode parabolic equations can be obtained as the one-way approximation to horizontal refraction equations for modal amplitudes. Their wide-angle capabilities depend on the order of the Pade approximation of the involved pseudo-differential operators. Various aspects of numerical solution methods for wide-angle mode parabolic equations are considered in detail, including artificial domain truncation and Cauchy initial data for the point source field approximation. The capabilities of the discussed numerical approaches are demonstrated in several important test cases, including the problems of sound propagation in a penetrable wedge and in a sea with an underwater canyon.

中文翻译：

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用于水声水平折射建模的广角模式抛物线方程及其在无界域上的数值解

摘要 讨论了通过求解模态抛物线方程来模拟海洋中的声音传播。模态抛物线方程可以作为模态振幅水平折射方程的单向近似来获得。它们的广角能力取决于所涉及的伪微分算子的 Pade 近似的阶数。详细考虑了广角模式抛物线方程数值求解方法的各个方面，包括人工域截断和点源场近似的柯西初始数据。所讨论的数值方法的能力在几个重要的测试案例中得到了证明，包括在可穿透的楔形和具有水下峡谷的海洋中的声音传播问题。