An Analytical Ocean Propagation Model using Piecewise Linear Sound Speed Profile

The normal mode method is widely employed for addressing depth-dependent acoustic wave propagation, with its accuracy contingent upon the precision of the propagating wavenumbers and depth mode shapes. Typically, finite-difference and finite-element methods are utilized for such solutions. Recently, a new approach has been proposed for heterogeneous depth-dependent waveguides, utilizing the classical Rayleigh–Ritz (RR) method. This method demonstrates high accuracy from low-frequency to high-frequency ranges. However, the matrices involved for solving the eigenvalue problems necessitate numerical integrations for evaluating each element, resulting in increased computational costs. To mitigate this, a similar method (RRF) is proposed, where sound speed profiles are expressed as a sum of Fourier series. This allows for the analytical computation of each entry of the RR matrices but compromises the accuracy of the wavenumbers. This paper presents a novel technique aimed at enhancing the precision of determining wavenumbers and mode shapes, while simultaneously minimizing the computational effort without compromising the accuracy. The method involves discretizing sound speed profiles using piecewise linear functions and deriving closed-form solutions for RR matrix elements, while also accounting for sound speed attenuation. Various examples are examined to evaluate the proposed method, demonstrating its capability to compute propagating radial wavenumbers with significantly improved accuracy and reduced computational cost, often achieving improvements of one or two orders of magnitude. Additionally, comparisons of transmission losses at fixed depth indicate accuracy comparable to existing solutions, without any noticeable visual discrepancies.