Geometric stochastic ray propagation using the special Euclidean group.

Area of Science:

• Ocean acoustics
• Wave propagation physics
• Stochastic modeling

Background:

• Accurate modeling of sound propagation in the ocean is crucial for sonar and underwater communication.
• Ocean sound speed profiles are inherently variable, introducing uncertainty into acoustic ray tracing.
• Existing models often struggle to fully capture the complex effects of this uncertainty on sound paths.

Purpose of the Study:

• To develop a novel stochastic model for ray trajectory propagation in media with uncertain sound speed profiles.
• To frame acoustic ray propagation as a geometric fractal Brownian motion process.
• To quantify the impact of sound speed profile uncertainty on ray deviations.

Main Methods:

• Framing ray propagation as a fractal Brownian motion on the special Euclidean group SE(2).
• Incorporating diffusion parameters that are functions of sound speed profile uncertainty.
• Applying the model to established sound speed profiles (Munk profile) and complex scenarios (double-ducted profile in the Beaufort Sea).

Main Results:

• Demonstrated a method to model stochastic ray deviations caused by sound speed variations.
• Quantified ray path uncertainty using diffusion parameters derived from profile uncertainty.
• Successfully applied the model to different oceanic sound speed environments.

Conclusions:

• The proposed fractal Brownian motion framework provides a robust method for modeling acoustic ray propagation in uncertain ocean environments.
• The diffusion parameters effectively capture the impact of sound speed variability on ray trajectories.
• This approach enhances the predictability of sound paths in complex underwater acoustics scenarios.