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Representation theorems and Green's function retrieval for scattering in acoustic media.
Ivan Vasconcelos1, Roel Snieder, Huub Douma
1ION Geophysical, GXT Imaging Solutions, 1st Floor, Integra House, Vicarage Road, Egham, Surrey TW20 9JZ, United Kingdom.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 13, 2009
Summary
New reciprocity theorems simplify acoustic scattering problems. These convolution- and correlation-type theorems aid in analyzing forward and inverse scattering, offering experimental advantages for retrieving scattered wave responses.
Area of Science:
- Acoustics
- Wave Propagation
- Mathematical Physics
Background:
- Reciprocity theorems are fundamental in wave physics.
- Perturbed acoustic media present challenges in scattering analysis.
- Green's functions are crucial for wave description.
Purpose of the Study:
- To develop novel reciprocity theorems for perturbed acoustic media.
- To provide tools for analyzing forward and inverse scattering problems.
- To enable efficient retrieval of scattered wave responses.
Main Methods:
- Derivation of convolution- and correlation-type reciprocity theorems.
- Utilizing Green's functions for perturbed and unperturbed waves.
- Application of representation theorems for scattered waves.
Main Results:
- Convolution-type theorems yield scattering integrals analogous to Lippmann-Schwinger equation.
- Correlation-type theorems enable scattering response retrieval via cross-correlations.
- Scattered-wave response extraction via cross-correlations does not require energy equipartitioning.
Conclusions:
- The developed reciprocity theorems offer a unified framework for scattering problems.
- Cross-correlation methods provide experimental advantages for remote scatterer analysis.
- The approach is validated with analytic and numerical examples in acoustics and seismology.
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