Three-dimensional sound scattering from transversely symmetric surface waves in deep and shallow water using the equivalent source method.

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.