Acoustic pulse propagation in a non-ideal shallow-water model

TL;DR

This paper presents a comprehensive theoretical framework for modeling acoustic pulse propagation in non-ideal shallow-water environments, incorporating dissipation, stratification, and boundary interactions for more realistic predictions.

Contribution

It introduces an -pseudodifferential operator formulation and Hamiltonian formalism to account for non-ideal effects in shallow-water acoustic wave modeling.

Findings

Extended semiclassical and ray-based theories with dissipative effects

Derived single-mode equations for amplitude and phase evolution

Validated models with analytical and numerical examples

Abstract

This study develops a theoretical framework for modeling acoustic pulse propagation in a non-ideal shallow-water waveguide. We derive an {\epsilon}-pseudodifferential operator ({\epsilon}-PDO) formulation from the general three-dimensional wave equation, that accounts for vertical stratification, bottom interaction, and slow horizontal inhomogeneity. Using the operator separation of variables method and the WKB-ansatz, we obtain single-mode equations describing the evolution of amplitude and phase along rays. The approach incorporates non-self-adjoint operators to model energy leakage through the bottom and introduces a Hamiltonian formalism for eikonal and transport equations, enabling the computation of amplitude, time, and phase fronts. Analytical and numerical examples are provided for different boundary conditions, including Neumann (ideal), self-adjoint, and partially reflecting interfaces. The results extend previous semiclassical and ray-based theories of wave propagation by including dissipative effects and improving the physical realism of shallow-water acoustic modeling.