Review PaperNo Access

Time Reversal as a Computational Tool in Acoustics and Elastodynamics

Dan Givoli

Department of Aerospace Engineering, Technion — Israel Institute of Technology, Haifa 32000, Israel

https://doi.org/10.1142/S0218396X14300011Cited by:31 (Source: Crossref)

Abstract

In this review paper, the use of the Time Reversal (TR) method as a computational tool for solving some classes of inverse problems is surveyed. The basics of computational TR are explained, using the scalar wave equation as a simple model. The application of TR to various problems in acoustics and elastodynamics is reviewed, in a selective and biased way as it leans on the author's personal view, referring to representative articles published on the subject.

Keywords:

References

M. Fink et al. , Ultrasonic Imaging 13 , 179 ( 1991 ) . Crossref, Google Scholar
C. R. Vogel , Computational Methods for Inverse Problems ( SIAM , Philadelphia , 2002 ) . Crossref, Google Scholar
D. Colton and R. Kress , Inverse Acoustic and Electromagnetic Scattering Theory , 2nd edn. ( Springer , Berlin , 1998 ) . Crossref, Google Scholar
D. Colton , J. Coyle and P. Monk , SIAM Rev. 42 , 369 ( 2000 ) . Crossref, Web of Science, Google Scholar
Y. Pinchover and J. Rubinstein , An Introducion to Partial Differential Equations ( Cambridge U. Press , Cambridge, UK , 2005 ) . Crossref, Google Scholar
C. W. Groetsch , J. Physics: Conf. Series 73 , 012001-1 ( 2007 ) . Crossref, Google Scholar
J. L. Mueller and S. Siltanen , Linear and Nonlinear Inverse Problems with Practical Applications ( SIAM , Philadelphia , 2012 ) . Crossref, Google Scholar
D. Cassereau , P. Hannoun and M. Fink , J. de Physique 2 , 661 ( 1992 ) . Google Scholar
M. Fink and C. Prada , Inverse Problems 17 , R1 ( 2001 ) . Crossref, Web of Science, Google Scholar
N. Zhu and S. Wu , J. Comput. Acoust. 20 , 1250007-1 ( 2012 ) . Link, Web of Science, Google Scholar
C. Bardos and M. Fink , Asymptot. Anal. 29 , 157 ( 2002 ) . Web of Science, Google Scholar
P. Blomgren , G. Papanicolaou and H. Zhao , J. Acoust. Soc. Am. 111 , 230 ( 2002 ) . Crossref, Web of Science, Google Scholar
M. V. Klibanov and A. Timonov , Inverse Problems 19 , 1299 ( 2003 ) . Crossref, Web of Science, Google Scholar
H. L. Calvo , R. A. Jalabert and H. M. Pastawski , Phys. Rev. Lett. PRL 101 , ( 2008 ) . Crossref, Web of Science, Google Scholar
G. Bal and L. Ryzhik , SIAM J. Appl. Math. 63 , 1475 ( 2003 ) . Crossref, Web of Science, Google Scholar
G. Bal and L. Ryzhik , C. R. Acad. Sci. Paris: Math. Phys. 333I , 1041 ( 2001 ) . Crossref, Web of Science, Google Scholar
G. Bal and O. Pinaud , Inverse Problems 21 , 1593 ( 2005 ) . Crossref, Web of Science, Google Scholar
G. Papanicolaou , L. Ryzhik and K. Solna , SIAM J. Appl. Math. 64 , 1133 ( 2004 ) . Crossref, Web of Science, Google Scholar
L. Borcea et al. , Inverse Problems 18 , 1247 ( 2002 ) . Crossref, Web of Science, Google Scholar
L. Borcea , G. Papanicolaou and C. Tsogka , Inverse Problems 19 , S139 ( 2003 ) . Crossref, Web of Science, Google Scholar
G. Derveaux , G. Papanicolaou and C. Tsogka , J. Acoust. Soc. Am. 121 , 2071 ( 2007 ) . Crossref, Web of Science, Google Scholar
J. P. Fouque , J. Garnier and A. Nachbin , SIAM J. Appl. Math. 64 , 1810 ( 2004 ) . Crossref, Web of Science, Google Scholar
J. Garnier and G. Papanicolaou , SIAM J. Applied Math. 67 , 1718 ( 2007 ) . Crossref, Web of Science, Google Scholar
A. Derode et al. , J. Comput. Acoust. 9 , 993 ( 2001 ) . Link, Web of Science, Google Scholar
K. D. LePage , J. Comput. Acoust. 9 , 1455 ( 2001 ) . Link, Web of Science, Google Scholar
D. Givoli and E. Turkel , Comput. Meth. Appl. Mech. Engng. 216 , 223 ( 2012 ) . Crossref, Web of Science, Google Scholar
G. Bal and R. Verástegui , SIAM Multiscale model. Simul. 2 , 639 ( 2004 ) . Crossref, Web of Science, Google Scholar
D. Liu et al. , IEEE Trans. Antennas & Propag. 55 , 344 ( 2007 ) . Crossref, Web of Science, Google Scholar
L. Liu , D. G. Albert and D. K. Wilson , J. Geophys. Eng. 4 , 276 ( 2007 ) . Crossref, Web of Science, Google Scholar
M. F. Dahl , A. Kirpichnikova and M. Lassas , SIAM J. Control & Optimization 48 , 839 ( 2009 ) . Crossref, Web of Science, Google Scholar
K. Bingham et al. , Inverse Problems & Imaging 2 , 63 ( 2008 ) . Crossref, Web of Science, Google Scholar
H. C. Song et al. , J. Acoust. Soc. Am. 116 , 762 ( 2004 ) . Crossref, Web of Science, Google Scholar
D. J. van Manen , A. Curtis and J. O. A. Robertsson , Geophys. 71 , S147 ( 2006 ) . Crossref, Web of Science, Google Scholar
D. Stich et al. , Geoph. J. Int. 177 , 543 ( 2009 ) . Crossref, Web of Science, Google Scholar
J. Claerbout , Imaging the Earth's Interior ( Blackwell Sci. Pub. , London , 1985 ) . Google Scholar
F. Assous et al. , Inverse Problems 27 , ( 2011 ) . Crossref, Web of Science, Google Scholar
C. W. Gardiner , Handbook of Stochastic Methods 3 ( Springer , Berlin , 1985 ) . Google Scholar
I. Levi, Time reversal for elastic wave refocusing and scatterer identification (MSc Thesis, Dept. of Applied Mathematics, Tel Aviv University, Tel Aviv, Oct. 2013) . Google Scholar
W. C. Chew and T. M. Habashy , J. Opt. Soc. Am. A 2 , 808 ( 1985 ) . Crossref, Google Scholar
L. B. Liu et al. , J. Comput. Acoust. 20 , 1240003-1 ( 2012 ) . Link, Web of Science, Google Scholar
B. M. Harker and B. E. Anderson , J. Acoust. Soc. Am. 133 , EL351 ( 2013 ) . Crossref, Web of Science, Google Scholar
C. L. Chen , Y. L. Li and F. G. Yuan , Shock and Vib. 20 , 561 ( 2013 ) . Crossref, Web of Science, Google Scholar
H. Ammari et al. , European J. Appl. Math. 24 , 565 ( 2013 ) . Crossref, Web of Science, Google Scholar
A. Deneuve et al. , J. Fluid Mech. 642 , 181 ( 2010 ) . Crossref, Web of Science, Google Scholar
E. Bavu and A. Berry , Acta Acustica United with Acustica 95 , 595 ( 2009 ) . Crossref, Web of Science, Google Scholar
J. M. Parot , Applied Acoustics 69 , 311 ( 2008 ) . Crossref, Web of Science, Google Scholar
J. P. Fouque et al. , Wave Motion 42 , 238 ( 2005 ) . Crossref, Web of Science, Google Scholar
S. Kremers et al. , Solid Earth 2 , 95 ( 2011 ) . Crossref, Web of Science, Google Scholar
D. H. Chambers and J. G. Berryman , Phys. Rev. Lett. 92 , ( 2004 ) . Crossref, Web of Science, Google Scholar
A. Buerkle and K. Sarabandi , IEEE Trans. Antenn. & Propag. 57 , 3628 ( 2009 ) . Crossref, Web of Science, Google Scholar
E. Amitt, D. Givoli and E. Turkel, Time reversal for crack identification, Computational Mechanics, DOI 10.1007/s0046601409962, to appear . Google Scholar
C. Prada , J. Thomas and M. Fink , J. Acoust. Soc. Am. 97 , 62 ( 1995 ) . Crossref, Web of Science, Google Scholar
G. Montaldo , M. Tanter and M. Fink , J. Acoust. Soc. Am. 115 , 776 ( 2004 ) . Crossref, Web of Science, Google Scholar
E. Barbieri and M. Meo , Wave Motion 47 , 452 ( 2010 ) . Crossref, Web of Science, Google Scholar
C. Ben Amar et al. , SIAM J. Applied Math. 67 , 777 ( 2007 ) . Crossref, Web of Science, Google Scholar
B. L. G. Jonsson et al. , SIAM J. Appl. Math. 64 , 1954 ( 2004 ) . Crossref, Web of Science, Google Scholar
J. Blitz and G. Simpson , Ultrasonic Methods of Nondestructive Testing ( Springer , Berlin , 1996 ) . Google Scholar
B. W. Drinkwater and P. D. Wilcox , NDT & E Int. 39 , 525 ( 2006 ) . Crossref, Web of Science, Google Scholar
G. E. Stavroulakis , Inverse and Crack Identification Problems in Engineering Mechanics ( Kluwer , Dordrecht, Netherlands , 2001 ) . Crossref, Google Scholar
G. R. Liu and X. Han , Computational Inverse Techniques in Nondestructive Evaluation ( CRC Press , London , 2003 ) . Crossref, Google Scholar
J. L. Zhu , Y. Zhang and X. Z. Liu , Wave Motion 51 , 146 ( 2014 ) . Crossref, Web of Science, Google Scholar
H. W. Park , J. Sound & Vibr. 332 , 2672 ( 2013 ) . Crossref, Web of Science, Google Scholar
Y. Labyed and L. J. Huang , IEEE Trans. Ultrasonics Reffo. Freq. Control 59 , 2186 ( 2012 ) . Web of Science, Google Scholar
F. K. Gruber , E. A. Marengo and A. J. Devaney , J. Acoust. Soc. Am. 115 , 3042 ( 2004 ) . Crossref, Web of Science, Google Scholar
A. J. Devaney , E. A. Marengo and F. K. Gruber , J. Acoust. Soc. Am. 118 , 3129 ( 2005 ) . Crossref, Web of Science, Google Scholar
S. K. Lehman and A. J. Devaney , J. Acoust. Soc. Am. 113 , 2742 ( 2003 ) . Crossref, Web of Science, Google Scholar
Y. Jun and U. Lee , J. Mech. Sci. & Tech. 26 , 53 ( 2012 ) . Crossref, Web of Science, Google Scholar
T. Goursolle et al. , J. Acoust. Soc. Am. 122 , 3220 ( 2007 ) . Crossref, Web of Science, Google Scholar
G. Zumpano and M. Meo , Int. J. Solids & Struct. 44 , 3666 ( 2007 ) . Crossref, Web of Science, Google Scholar
C. Larmat et al. , Geophys. Res. Lett. 33 , 1 ( 2006 ) . Crossref, Web of Science, Google Scholar
B. Artman , I. Podladtchikov and B. Witten , Geoph. Prospecting 58 , 861 ( 2010 ) . Crossref, Web of Science, Google Scholar
C. S. Larmat, R. A. Guyer and P. A. Johnson, Physics Today 63(8), 31 (2010). Crossref, Web of Science, Google Scholar
F. A. da Silva Neto et al. , Geophys. 76 , S143 ( 2011 ) . Crossref, Web of Science, Google Scholar
E. Tessmer , Geophys. 76 , S177 ( 2011 ) . Crossref, Web of Science, Google Scholar
C. Baldassari et al. , Geophys. Prosp. 59 , 907 ( 2011 ) . Crossref, Web of Science, Google Scholar
J. E. Anderson , L. J. Tan and D. Wang , Geophys. 77 , S93 ( 2012 ) . Crossref, Web of Science, Google Scholar
I. Lokmer et al. , Geophys. Res. Let. 36 , L12308 ( 2009 ) . Crossref, Web of Science, Google Scholar
J. Tromp , C. Tape and Q. Y. Liu , Geophys. J. Int. 160 , 195 ( 2005 ) . Crossref, Web of Science, Google Scholar
Y. Ying and L. Ma , J. Comput. Acoust. 18 , 227 ( 2010 ) . Link, Web of Science, Google Scholar
Y.-H. Hsieh and G.-P. Too , J. Comput. Acoust. 21 , 1350008-1 ( 2013 ) . Link, Web of Science, Google Scholar
T. J. R. Hughes , The Finite Element Method ( Prentice Hall , Englewood Cliffs, N.J. , 1987 ) . Google Scholar