A Spectral Split-Step Pad\'e Method for Guided Wave Propagation

TL;DR

This paper introduces a spectral split-step Padé method using Fourier transforms for more accurate and efficient guided wave propagation modeling in ocean acoustics, especially for complex and large-scale scenarios.

Contribution

It replaces finite-difference discretization with a spectral approach using DST, enabling exact vertical operator treatment and improved accuracy for coarse grids.

Findings

Achieves higher accuracy with fewer depth points.

Handles inhomogeneities via Neumann series expansion.

Effective in deep ocean and eddy scenarios.

Abstract

In this study, a Fourier-based, split-step Pad\'e (SSP) method for solving the parabolic wave equation with applications in guided wave propagation in ocean acoustics is presented. Traditional SSP implementations rely in finite-difference discretizations of the depth-dependent differential operator. This approach limits accuracy in coarse discretizations as well as computational efficiency in dense discretizations since it does not significantly benefit from parallelization. In contrast, our proposed method replaces finite differences with a spectral representation using the discrete sine transform (DST). This enables an exact treatment of the vertical operator under homogeneous boundary conditions. For non-constant sound speed, we use a Neumann series expansion to treat inhomogeneities as perturbations. Numerical experiments demonstrate the method's accuracy in range-independent media and rage-dependent scenarios, including propagation in deep ocean with Munk profile and in the presence of a parametrized synoptic eddy. Compared to finite-difference SSP methods, the Fourier-based approach achieves higher accuracy with fewer depth discretization points and avoids the resolution bottleneck associated with sharp field features, making it well-suited for large-scale, high-frequency wave propagation problems in ocean environments.