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A depth-dependent formula for shallow water propagation.

Hüseyin Özkan Sertlek1, Michael A Ainslie2

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Summary
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This study presents an analytical solution for shallow water sound propagation, simplifying depth-dependent calculations. The Faddeeva function method accurately models sound fields without complex normal mode computations.

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Area of Science:

  • Acoustics
  • Oceanography
  • Wave Propagation

Background:

  • Shallow water sound propagation is influenced by receiver proximity to the sea surface and seabed, source depth, and complementary source depth.
  • Normal mode theory predicts depth dependence but is computationally intensive.

Purpose of the Study:

  • To develop an efficient analytical solution for predicting depth-dependent sound fields in shallow water.
  • To overcome the computational limitations of traditional normal mode theory.

Main Methods:

  • Derived an analytical solution using the Faddeeva function.
  • Converted a normal mode sum into an integral representation based on a hypothetical continuum of modes.
  • Applied the method to a Pekeris waveguide model.

Main Results:

  • The Faddeeva function approach provides accurate depth-dependent propagation results.
  • This method effectively models surface decoupling in shallow water environments.
  • The solution avoids complex calculations of eigenvalues and eigenfunctions.

Conclusions:

  • The derived analytical solution offers an efficient and accurate alternative for shallow water acoustic propagation modeling.
  • This method simplifies the prediction of sound field behavior in relation to depth and boundaries.