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Fig. 10. Images displaying the Time Reversal reconstruction of the 2004 Parkfield, CA earthquake. From top to bottom the images show the progressive reconstruction of the earthquake as the back propagated wave fronts coalesce at the original source
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location. This figure was made with the help of GMT software.
ods. Linear and nonlinear methods of exploiting TR were outlined, including methods to improve TR imaging by achieving super resolution. Finally, some of the primary application areas of TR were summarized.
TR has proven to be a very robust method of detecting and characterizing sources and scatterers, despite its limita- tions. The frontiers of the science of TR will likely focus on developing practical methods of beating the diffraction limit to improve the resolution of TR. Additional frontiers of TR will include characterizing and understanding com- plex source events such as earthquakes and acoustic emis- sion in the laboratory, further exploiting TR to identify and locate cracks in NDE applications especially by applying Nonlinear Elastic Wave Spectroscopy (NEWS), a large number of potential medical applications, as well as many more applications currently being studied and those yet to be discovered.
Acknowledgments
We would like to acknowledge the discussions with Robert Guyer, Jim Ten Cate, Pierre-Yves Le Bas, Donatella
Pasqualini, Alexander Sutin, Marco Scalerandi, Antonio S. Gliozzi, Koen E.-A. Van Den Abeele, and Francesco Simonetti.AT
References for further reading:
1 M. Fink, “Time reversed acoustics,” Phys. Today 50, 34-40 (1997).
2 A. Parvulescu and C. S. Clay, “Reproducibility of signal trans- mission in the ocean,” Radio Elec. Eng. 29, 223-228 (1965).
3 C. R. Giuliano, “Applications of optical phase conjugation,” Phys. Today, 34 (4), 27-35, (1981).
4 B. Y. Zel’dovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation, Springer, Berlin (1985).
5 R. D. Jackson and D. R. Dowling, “Phase conjugation in under- water acoustics,” J. Acoust. Soc. Am., 89(1), 171-181, (1991).
6 M. Fink, “Time reversal of ultrasonic fields. Part I: Basic princi-
ples,” IEEE Trans. Ultr. Ferr. Freq. Contr. 39(5), 555-566 (1992). 7 F. Wu, J-L. Thomas, and M. Fink, “Time reversal of ultrasonic fields. Part II: Experimental results,” IEEE Trans. Ultr. Ferr. Freq.
Contr. 39(5), 567-578 (1992).
8 D. Cassereau and M. Fink, “Time reversal of ultrasonic fields.
Part III: Theory of the closed TR cavity,” IEEE Trans. Ultr. Ferr.
Freq. Contr. 39(5), 579-592 (1992).
9 C. Draeger, J-C. Aime, and M. Fink, “One-channel time-reversal
in chaotic cavities: Experimental results,” J. Acoust. Soc. Amer.
105(2), 618-625 (1999).
10 J. D. Achenbach, Reciprocity in Elastodynamics (Cambridge
University Press, Cambridge, UK, 2003).
11 I. Nunez and C. Negreira, “Efficiency parameters in time rever-
sal acoustics: Applications to dispersive media and multimode wave propagation,” J. Acoust. Soc. Am. 117(3), 1202-1209 (2004).
12 A. Derode, P. Roux, and M. Fink, “Robust acoustic time reversal with high-order multiple scattering,” Phys. Rev. Lett. 75(23), 4206-4210 (1995).
13 M. F. Hamilton and D. T. Blackstock, Nonlinear Acoustics (Academic Press, San Diego, 1998).
14 K. B. Cunningham, M. F. Hamilton, A. P. Brysev, and L. M. Krutyansky, “Time-reversed sound beams of finite amplitude,” J. Acoust. Soc. Am. 109(6), 2668-2674 (2001).
15 M. Tanter, J-L. Thomas, F. Coulouvrat, and M. Fink, “Breaking of time reversal invariance in nonlinear acoustics,” Phys. Rev. E 64, 016602 (2001).
16 C. Prada, F. Wu, and M. Fink, “The iterative time reversal mir- ror: A solution to self-focusing in the pulse-echo mode,” J. Acoust. Soc. Am. 90(2), 1119-1129 (1991).
17 C. Prada, J-L. Thomas, and M. Fink, “The iterative time reversal process: Analysis of the convergence,” J. Acoust. Soc. Am. 97(1), 62-71 (1995).
18 C. Prada and M. Fink, “Eigenmodes of the time reversal opera- tor: A solution to selective focusing in multiple-target media,” Wave Motion 20, 151-163 (1994).
19 C. Prada, S. Manneville, D. Spoliansky, and M. Fink, “Decomposition of the time reversal operator: Detection and selective focusing on two scatterers,” J. Acoust. Soc. Am. 99(4) 2067-2076 (1996).
20 C. Prada and M. Fink, “Separation of interfering acoustic scat- tered signals using the invariants of the time reversal operator. Application to Lamb waves characterization,” J. Acoust. Soc. Am. 104(2), 801-807 (1998).
21 N. Mordant, C. Prada, and M. Fink, “Highly resolved detection and selective focusing in a waveguide using the D.O.R.T. method,” J. Acoust. Soc. Am. 105(5), 2634-2642 (1999).
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