A relation between multipath group velocity, mode number, and ray cycle distance

Area of Science:

• Underwater acoustics
• Wave propagation physics
• Oceanography

Background:

• The study of sound propagation in underwater environments is crucial for various applications.
• Understanding wave phenomena in range-dependent environments presents significant challenges.
• Existing models often require complex computations for accurate predictions.

Purpose of the Study:

• To establish an exact equivalence between Weston's ray invariant and the Wentzel-Kramers-Brillouin phase integral.
• To derive a novel formula for group velocity using ray cycle distance and mode number.
• To demonstrate the applicability and validity of the derived formula in variable ocean conditions.

Main Methods:

• Analysis of a ray element to reformulate the ray invariant.
• Derivation of a group velocity formula based on ray cycle distance and time.
• Inclusion of the Airy phase within the ray-based approach.
• Numerical validation against a normal mode model for variable sound speed and bathymetry.

Main Results:

• Weston's ray invariant is shown to be equivalent to the Wentzel-Kramers-Brillouin phase integral for ducted normal modes.
• A new formula for group velocity is derived, expressed in terms of ray cycle distance and mode number.
• The derived formula accurately predicts group velocities, including the Airy phase, in range-dependent environments.
• Numerical simulations confirm the formula's validity for variable sound speed and bathymetry.

Conclusions:

• The derived ray-based formula provides a simplified yet accurate method for calculating group velocity in underwater acoustics.
• This approach offers a valuable tool for analyzing complex acoustic phenomena in realistic ocean environments.
• The formula has broad applicability in areas such as active sonar, signal processing, and underwater communication systems.