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Energy streamlines for qualitative inverse scattering in fluids and solids
R Aramini1, G Caviglia, M Piana
1Dipartimento di Matematica, Università di Genova, via Dodecaneso 35, 16146 Genova, Italy. aramini@dima.unige.it
The Journal of the Acoustical Society of America
|April 17, 2012
Summary
Energy streamlines visualize acoustic energy flow. This study shows the linear sampling method for inverse scattering in solids arises from energy conservation along these streamlines.
Area of Science:
- Acoustics
- Solid Mechanics
- Wave Propagation
Background:
- Energy streamlines, integral curves of the time-averaged power-flux density vector, visualize energy propagation in acoustic fields.
- The linear sampling method is a qualitative technique used in acoustic inverse scattering problems.
Purpose of the Study:
- To provide a physical interpretation of the linear sampling method in the context of elastic wave propagation.
- To connect the linear sampling method to fundamental physical principles in an isotropic homogeneous solid matrix.
Main Methods:
- Review of the role of energy streamlines in acoustic inverse scattering.
- Formulation of a physical interpretation for the linear sampling method in solid media.
- Analysis based on the conservation of energy along energy flow streamline tubes.
Main Results:
- Demonstration that the linear sampling method in this context is a consequence of energy conservation.
- Identification of energy streamline tubes as the relevant structures for this conservation principle.
- Extension of the understanding of energy streamlines to elastic wave phenomena in solids.
Conclusions:
- The linear sampling method for acoustic inverse scattering in isotropic homogeneous solids is physically underpinned by energy conservation.
- Energy streamlines provide a valuable framework for understanding wave energy transport and inverse scattering phenomena in elastic media.
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