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Unified double- and single-sided homogeneous Green's function representations.

Kees Wapenaar1, Joost van der Neut1, Evert Slob1

  • 1Department of Geoscience and Engineering , Delft University of Technology , 2600 GA Delft, The Netherlands.

Proceedings. Mathematical, Physical, and Engineering Sciences
|July 21, 2016
PubMed
Summary
This summary is machine-generated.

This study introduces a new single-sided homogeneous Green's function representation for wave propagation in complex media. This method accurately accounts for multiple scattering, improving wave imaging and inverse scattering applications.

Keywords:
Green’s functionfocusingholographic imagingrepresentationtime-reversal acousticswave propagation and scattering

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Area of Science:

  • Wave theory
  • Acoustics
  • Quantum mechanics
  • Electromagnetics
  • Elastodynamics

Background:

  • Homogeneous Green's function is key in wave theory, typically represented by closed boundary integrals.
  • Practical applications often require approximating these with open boundary integrals, limiting accuracy in scattering scenarios.
  • Strongly inhomogeneous media pose challenges due to severe multiple scattering effects.

Purpose of the Study:

  • Derive novel double- and single-sided homogeneous Green's function representations.
  • Develop a single-sided method that correctly handles multiple scattering for one-sided accessible media.
  • Introduce a unified notation applicable across various wave types.

Main Methods:

  • Derivation of double- and single-sided Green's function representations.
  • Utilizing a focusing function in the single-sided representation, replacing the backward propagating Green's function.
  • Retrieving the focusing function from reflection measurements at the accessible boundary.

Main Results:

  • Successful derivation of unified single- and double-sided homogeneous Green's function representations.
  • The single-sided representation accurately models multiple scattering in inhomogeneous media.
  • Demonstrated applicability across acoustic, quantum-mechanical, electromagnetic, and elastodynamic waves.

Conclusions:

  • The unified single-sided homogeneous Green's function representation offers a robust solution for wave propagation analysis in complex, one-sided accessible media.
  • This method overcomes limitations of traditional approximations by accurately handling multiple scattering.
  • Potential applications include advanced holographic imaging, inverse scattering, time-reversed wave propagation, and interferometric retrieval.