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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
Summary
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.
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.
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