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This study integrates source and receiver directivity for wave scattering over rough surfaces, providing clear physical interpretations. Derived covariances and variances aid in extracting surface roughness parameters.

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Area of Science:

  • Oceanography
  • Acoustics
  • Wave Scattering

Background:

  • Wave scattering models often omit source and receiver directivity.
  • Integrating directivity provides clearer physical interpretations of scattering phenomena.

Purpose of the Study:

  • To develop integral solutions for wave scattering over slightly rough surfaces that incorporate source and receiver directivity.
  • To derive spatial covariances and variances for specular echoes in a multibeam-subbottom-profiler configuration.
  • To establish a method for extracting surface roughness parameters.

Main Methods:

  • Integrating point source and point receiver solutions over source and receiver apertures.
  • Deriving scintillation, time-of-arrival, and direction-of-arrival spatial covariances.
  • Obtaining algebraic expressions for variances with Gaussian autocorrelation and apodization functions.
  • Numerical evaluation of surface integrals and comparison with 3D numerical experiments.

Main Results:

  • Integral solutions with clear physical interpretations were achieved by incorporating directivity.
  • Surface integrals for covariances were derived and numerically evaluated.
  • Algebraic expressions for variances were obtained for specific roughness and array functions.
  • Numerical results closely matched estimates from a realistic 3D numerical experiment.

Conclusions:

  • The integration of source and receiver directivity offers a physically interpretable approach to wave scattering.
  • The derived covariances and variances are applicable to multibeam-subbottom-profiler systems.
  • A simple inversion scheme effectively extracts roughness parameters from experimental signals.