TIME REVERSAL IN SOLIDS at LANL
Linear and Nonlinear Elasticity

​(For a non-specialist description of time reversal, read Reversing Time to Find Wave Sources. For an in-depth overview, read our PDF from Acoustics Today.)
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SUMMARY
​Time Reversal (TR) is analogous to filming a pebble dropped into a pond and the resultant ripples emanating outward. Stop the movie and run it backwards. All of the waves propagate backwards-in-time, coalescing on the pebble impact as illustrated in the figure below.
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Snapshots of TR back-propagation observed in experiment on a metal plate, showing out-of-plane displacements.
Time steps a-b show the wave displacement field up to the focus at c.
Unlike the movie analogy, in actual TR the waves at focal time pass through each other and then
are rebroadcast as see in steps d-e.
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TIME REVERSAL WORK at LANL

• Time Reversal Home
• Source Reconstruction Using Time Reversal
• Robustness & Efficiency of Time Reversal Acoustics in Solid Media
• Audio Example of Time Reversal - Speech Privacy 
• Crack Imaging with Time Reversal - Experimental Results
• ​Time Reversal Nonlinear Elastic Wave Spectroscopy 
• Experimental Facilities and Resources
• Time Reversal of the 2004 (M9.0) Sumatra Earthquake​​

More rigorously, in any linear, time-invariant process, wave propagation may be described as a linear system with different impulse responses. If a point source at r₀ emits a Dirac pulse, the δ(t) the jth transducer will record the impulse response hj(t) that corresponds to the Green's function... ​

​Moreover, due to the principle of reciprocity, h_j(t) is also the impulse response describing the propagation of a pulse from the j^th transducer to the source. TR theory shows that it is the wave phase that makes TR focus. Phase is all we have for locating long duration, noise-like (tremor) signals because discrete arrivals don't exist.

In practice, TR can be carried out in at least three ways...

1. TR can be conducted experimentally by propagating waves forward and backwards in say, a lab sample.
2. In the case where a source is located inside a solid (e.g., Earth), one can take recorded data (re: seismic), TR the data and backpropagate it through an appropriate velocity model.
3. TR can be conducted entirely in a numerical velocity model.

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​We are exploring the possibility of applying TR to reconstruct a spatially and complex earthquake source, locating Earth tremor, as well as exploring the use of TR in NonDestructive Evaluation (NDE) applications. This work is supported by institutional support at Los Alamos (LDRD) and by commercial support.