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On the relation between time-reversed acoustics and Green's function retrieval in space-variant and in time-variant
Kees Wapenaar1, Johannes Aichele2, Dirk-Jan van Manen2
1Delft University of Technology, Department of Geoscience and Engineering, Stevinweg 1, 2628 CN Delft, The Netherlands.
The Journal of the Acoustical Society of America
|July 2, 2026
Summary
This study compares time-reversed acoustics and Green's function retrieval methods for classical and time-variant materials. We reveal distinct wave field and source requirements for these acoustic techniques in different material types.
Area of Science:
- Acoustics
- Wave Physics
- Materials Science
Background:
- Time-reversed acoustics and Green's function retrieval are established for inhomogeneous, time-invariant materials.
- Recent extensions propose similar methods for homogeneous, time-variant materials.
Purpose of the Study:
- Investigate the mutual relation between these methods in time-variant materials.
- Compare these methods with their classical counterparts for different material types.
Main Methods:
- Utilize the similarity between wave equations for classical and time-variant materials.
- Analyze the role of causality in wave propagation and retrieval methods.
- Compare source and wave field characteristics for classical and time-variant scenarios.
Main Results:
- Classical time-reversed acoustics uses a time-reversed single-component wave field from a boundary.
- Time-variant acoustics requires a sign-reversed two-component wave field from a single time instant.
- Classical Green's function retrieval uses temporal cross-correlation.
- Time-variant Green's function retrieval involves spatial cross-correlation.
Conclusions:
- The study elucidates the distinct operational principles of time-reversed acoustics and Green's function retrieval across classical and time-variant materials.
- Understanding these differences is crucial for applying acoustic methods to dynamic material systems.
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