Generalized Taylor expansion of the waveguide invariant for a homogenous waveguide with variable bathymetry (L)

Area of Science:

• Underwater acoustics
• Acoustic signal processing
• Oceanography

Background:

• Range estimation in waveguides is crucial for underwater applications.
• Previous methods utilized the waveguide invariant (β) with an eighth-order Taylor expansion.
• Variable bathymetry and range dependency complicate accurate estimations.

Purpose of the Study:

• To extend range estimation methods by introducing a generalized Taylor expansion for the waveguide invariant (β).
• To enable flexible order selection for improved convergence to analytic expressions.
• To gain new insights into the convergence rates of the waveguide invariant approximation.

Main Methods:

• Incorporation of a generalized Taylor expansion for the waveguide invariant (β).
• Flexible order selection for the Taylor expansion.
• Validation using experimental acoustic data.

Main Results:

• The generalized Taylor expansion allows for flexible order selection, aiding convergence.
• Low-order approximations are effective, particularly at longer ranges.
• Reduced angular dependency was observed at longer ranges, validating the extended method.

Conclusions:

• The generalized Taylor expansion offers a more adaptable approach to range estimation in complex waveguides.
• The method effectively reduces angular dependency, enhancing accuracy in underwater acoustic scenarios.
• Low-order approximations provide a computationally efficient and accurate solution for range estimation.