We perform theoretical analysis of the method of field focusing in a randomly inhomogeneous waveguide using reradiation of the received signal with time reversal. The simplest case where point sources and receivers are used for emission and reception is considered. As an example, the waveguide is chosen which simulates an underwater sound channel with refractive-index fluctuations caused by random internal waves. In underwater acoustics, the considered method of field focusing is usually applied at relatively short distances that are shorter than or about 10 km. This work deals with much longer paths, along which sound waves propagate under conditions of well-developed ray and wave chaos. Main attention is given to studying the width of the focal spot and the field amplitude at its center. It is shown that the amplitude distribution in the vertical section of the focal spot and the peak amplitude value at its center can be estimated analytically using the stochastic ray theory.
Similar content being viewed by others
References
J.-P. Fouque, J. Garnier, G. Papanicolaou, and K. Solna, Wave Propagation and Time Reversal in Randomly Layered Media, Springer Science, Berlin (2007).
M. Fink and C. Prada, Inverse Problems, 17, R1 (2001).
D. R. Jackson and D. R. Dowling, J. Acoust. Soc. Am., 89, No. 1, 171 (1991).
P. Blomgrena, G. Papanicolaou, and H. Zhaoc, J. Acoust. Soc. Am., 111, No. 1, 230 (2002).
S. M. Rytov, Yu. A. Kravtsov, and V. I. Tatarskii, Principles of Statistical Radiophysics, Vols. 3 and 4, Springer-Verlag, Berlin (1989).
A. Ishimaru, Wave Propagation and Scattering in Random Media, Vol. 2, Academic Press, New York (1978).
D. R. Dowling and D. R. Jackson, J. Acoust. Soc. Am.. 91, No. 6, 3257 (1992).
V. A. Zverev, P. I. Korotin, and A. A. Stromkov, Acoust. Phys., 54, No. 1, 58 (2008).
V. A. Zverev, P. I. Korotin, and A. A. Stromkov, Acoust. Phys., 54, No. 5, 711 (2008).
A. Derode, A. Tourin, and M. Fink, J. Acoust. Soc. Am., 107, No. 6, 2987 (2000).
S. Kim, W. A. Kuperman, W. S. Hodkiss, et al., J. Acoust. Soc. Am., 115, No. 4, 1525 (2004).
M. G. Brown, J. A. Colosi, S. Tomsovic, et al., J. Acoust. Soc. Am., 113, No. 5, 2533 (2003).
F. J. Beron-Vera, M. G. Brown, J. A. Colosi, et al., J. Acoust. Soc. Am., 114, No. 3, 1226 (2003).
A. L. Virovlyansky, Acoust. Phys., 51, No. 1, 71 (2005).
A. L. Virovlyansky, A.Yu. Kazarova, and L.Ya. Lyubavin, J. Acoust. Soc. Am., 121, No. 5, 2542 (2007).
D. Makarov, S. Prants, A. Virovlyansky, and G. Zaslavsky, Ray and Wave Chaos in Ocean Acoustics, Word Scientific, Singapore (2010).
S. M. Flatte, ed., Sound Transmission through a Fluctuating Ocean, Cambridge Univ. Press, Cambridge (1979).
J. A. Colosi and M. G. Brown, J. Acoust. Soc. Am., 103, 2232 (1998).
L. M. Brekhovskikh and Yu. P. Lysanov, Fundamentals of Ocean Acoustics, Springer-Verlag, New York (2003).
F. D. Tappert, Lecture Notes in Physics. Vol. 70. Wave Propagation and Underwater Acoustics, Springer-Verlag, Berlin (1977), p. 224.
F.B. Jensen, W. A. Kuperman, M. B. Porter, and H. Schmidt, Computational Ocean Acoustics, Woodbur, New York (1994).
K. B. Smith, J. Comp. Acoust., 9, No. 1, 243 (2001).
L. D. Landau and E. M. Lifshitz, Mechanics, Butterworth-Heinemann, New York (1976).
S. S.Abdullaev and G. M. Zaslavskii, Sov. Phys. Uspekhi [in Russian], 34, No. 8, 645 (1991).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 54, No. 5, pp. 368–380, May 2011.
Rights and permissions
About this article
Cite this article
Virovlyansky, A.L., Kazarova, A.Y. & Lyubavin, L.Y. Focusing of acoustic fields in a randomly inhomogeneous waveguide by using the time reversal method. Radiophys Quantum El 54, 334–345 (2011). https://doi.org/10.1007/s11141-011-9294-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11141-011-9294-4