Modal formulation and paraxial approximation for acoustic wave propagation in waveguides with surface perturbations

Area of Science:

• Acoustics and Wave Propagation
• Fluid Dynamics and Surface Physics
• Applied Mathematics and Computational Physics

Background:

• Deterministic surface perturbations significantly impact wave propagation in planar waveguides.
• Understanding these effects is crucial for accurate signal interpretation and subsurface imaging.
• Existing methods often lack the precision to fully characterize complex 3D surface dynamics.

Purpose of the Study:

• To develop and validate a paraxial modal approach for investigating surface perturbations in planar waveguides.
• To theoretically formulate modal amplitude sensitivity to 3D surface perturbations.
• To establish a time-harmonic inversion method for imaging dynamic surface perturbations.

Main Methods:

• Development of a modal approach within the paraxial approximation framework.
• Theoretical formulation of modal amplitude sensitivity to 3D air-water interface perturbations.
• Application of a time-harmonic inversion method using the paraxial single-scattering approximation and modal transmission matrix.

Main Results:

• The paraxial modal approach accurately predicts travel-time and amplitude fluctuations in ultrasonic waveguide experiments.
• Observed nonlinear modal amplitude fluctuations are attributed to the 3D nature of surface perturbations.
• The time-harmonic inversion method successfully images dynamic surface perturbations from experimental data.

Conclusions:

• The proposed paraxial modal approach is effective for analyzing deterministic surface perturbations in planar waveguides.
• The study demonstrates successful comparison between theoretical predictions and experimental data for wavefield fluctuations.
• The developed inversion technique provides a robust method for imaging dynamic surface changes using modal transmission data.