This paper proposes a propagation model to calculate the three-dimensional (3-D) sound scattering from transversely symmetric sea surface waves in both deep and shallow water using the equivalent source method (ESM). The 3-D sound field is calculated by integrating an assembly of two-dimensional (2-D) transformed fields with different out-of-plane wavenumbers through a cosine transform. Each 2-D solution is calculated using the ESM incorporating a complex image method that can efficiently and accurately solve the 2-D water/seabed Green's function. The oscillatory cosine integral is accurately calculated using a segmented integral scheme requiring relatively few 2-D solutions, which can be further improved through the use of parallel computation. The model is validated by comparison with a 3-D Helmholtz-Kirchhoff method for deep water and a finite element method for a shallow water wedge with both a fluid and an elastic seabed. The model is as accurate as the finite element approach but more numerically efficient, which enables Monte Carlo simulations to be performed for random rough surfaces in order to study the scattering effects at a reasonable computational cost. Also, 3-D pulse propagation in the shallow water wedge is demonstrated to understand the out-of-plane scattering effects further.

中文翻译：

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使用等效声源法在深水和浅水中从横向对称表面波进行三维声散射。

本文提出了一种传播模型，利用等效源法（ESM）计算深水和浅水中横向对称海面波的三维（3-D）声散射。3-D声场是通过余弦变换对具有不同平面外波数的二维（2-D）变换场的集合进行积分来计算的。每个二维解决方案都是使用结合了复杂图像方法的ESM计算得出的，该方法可以有效，准确地解决二维水/海底格林函数。振荡余弦积分是使用要求相对较少的2D解的分段积分方案精确计算的，可以通过使用并行计算来进一步改善。通过与针对深水的3-D Helmholtz-Kirchhoff方法和针对具有流体和弹性海床的浅水楔形的有限元方法进行比较，对模型进行了验证。该模型与有限元方法一样准确，但是在数值上更有效，这使可以对随机粗糙表面执行蒙特卡洛模拟，从而以合理的计算成本来研究散射效应。此外，演示了在浅水楔形中进行3-D脉冲传播以进一步了解面外散射效果。这样就可以对随机粗糙表面执行蒙特卡洛模拟，以便以合理的计算成本研究散射效应。此外，演示了在浅水楔形中进行3-D脉冲传播以进一步了解面外散射效果。这样就可以对随机粗糙表面执行蒙特卡洛模拟，以便以合理的计算成本研究散射效应。此外，演示了在浅水楔形中进行3-D脉冲传播以进一步了解面外散射效果。