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Extrapolating Green's functions using the waveguide invariant theory.

H C Song1, Gihoon Byun1

  • 1Scripps Institution of Oceanography, La Jolla, California 92093-0238, USA.

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|May 4, 2020
PubMed
Summary
This summary is machine-generated.

The waveguide invariant (β) describes sound propagation patterns in waveguides. This property allows predicting sound behavior at new ranges using a simple formula, verified with simulations and real shallow-water data.

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Area of Science:

  • Acoustics
  • Oceanography
  • Wave Propagation

Background:

  • Sound propagation in waveguides exhibits broadband interference patterns.
  • These patterns are characterized by striations in the frequency-range plane.
  • The waveguide invariant (β) quantifies the relationship between frequency and range variations.

Purpose of the Study:

  • To describe broadband interference structure of sound propagation in a waveguide using the waveguide invariant.
  • To establish an analytic relation for extrapolating time-domain Green's functions to adjacent ranges.
  • To verify this relationship using simulations and real-world acoustic data.

Main Methods:

  • Utilizing the waveguide invariant (β) to analyze frequency-range striations.
  • Applying Fourier transform to multipath impulse response (Green's function).
  • Developing an analytic relation: g(r+Δr,t)≃g(r,α(t-Δr/c)) where α=1+β(Δr/r).
  • Verifying the relation via simulations and analysis of broadband noise from a ship in a shallow-water environment.

Main Results:

  • The waveguide invariant (β) accurately describes the stretching or shrinking of frequency patterns with range.
  • A simple analytic relation was derived to extrapolate Green's functions to adjacent ranges.
  • Experimental data from a shallow-water environment confirmed the predicted relationship with β≈0.92 for steep-angle arrivals.

Conclusions:

  • The waveguide invariant provides a powerful tool for understanding and predicting sound propagation in waveguides.
  • The derived analytic relation offers a method for efficient extrapolation of acoustic field information.
  • The findings are validated in a complex shallow-water environment, demonstrating practical applicability.