Skip to main content
Log in

Simulation of a functional solution to the acoustic tomography problem for data from quasi-point transducers

  • Acoustic Signal Processing and Computer Simulation
  • Published:
Acoustical Physics Aims and scope Submit manuscript

Abstract

Two variants of a functional-analytical algorithm intended for solving inverse tomography problems are discussed and numerically carried out. The acoustic fields that are transmitted and received by transducers, which are equivalent to point ones, serve as experimental data. These data are used to calculate the classical or generalized scattering amplitude, and the scatterer characteristics are then reconstructed. The algorithm requires neither model linearization, no iterations for refining the estimates of scatterers, thus making it attractive for solving acoustic-tomography problems in different applications. The results of the numerical reconstruction of inhomogeneities in the sound velocity and absorption in a medium are presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. V. V. Goncharov, V. Yu. Zaitsev, V. M. Kurtepov, A. G. Nechaev, and A. I. Khil’ko, Acoustical Tomography of Ocean (IPF RAN, N. Novgorod, 1997) [in Russian].

    Google Scholar 

  2. K. Chadan and P. C. Sabatier, Inverse Problems in Quantum Scattering Theory (Springer-Verlag, Berlin, 1977).

    Book  MATH  Google Scholar 

  3. L. D. Faddeev, in Modern Problems of Mathematics, J. Soviet Math. 5, 334 (1976).

    Article  MATH  Google Scholar 

  4. R. G. Novikov and G. M. Henkin, Russian Mathem. Survey 42(3), 109 (1987).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. V. A. Burov and O. D. Rumyantseva, Sov. Phys.-Acoust. 38, 226 (1992).

    Google Scholar 

  6. V. A. Burov, S. N. Vecherin, S. A. Morozov, and O. D. Rumyantseva, Acoust. Phys. 56, 541 (2010).

    Article  ADS  Google Scholar 

  7. P. G. Grinevich and S. V. Manakov, Funct. Anal. Appl. 20, 94 (1986).

    Article  MathSciNet  MATH  Google Scholar 

  8. R. G. Novikov, Funct. Anal. Appl. 20, 246 (1986).

    Article  MATH  Google Scholar 

  9. R. G. Novikov, J. Funct. Anal. 103, 409 (1992).

    Article  MathSciNet  MATH  Google Scholar 

  10. R. G. Novikov, Phys. Lett. A 238, 73 (1998).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  11. R. G. Novikov, Proc. V. A. Steklov Inst. Math. Solitons, Geometry, Topology-On Crossroads 225, 285 (1999).

    Google Scholar 

  12. V. A. Burov, N. V. Alekseenko, and O. D. Rumyantseva, Acoust. Phys. 55, 843 (2009).

    Article  ADS  Google Scholar 

  13. R. G. Novikov, Int. Math. Res. Pap., No. 6, 287 (2005).

    Google Scholar 

  14. R. G. Novikov, J. Geom. Anal. 18, 612 (2008).

    Article  MathSciNet  MATH  Google Scholar 

  15. N. V. Alekseenko, V. A. Burov, and O. D. Rumyantseva, Acoust. Phys. 54, 407 (2008).

    Article  ADS  Google Scholar 

  16. R. G. Novikov, Func. Anal. Appl. 22, 263 (1988).

    Article  MATH  Google Scholar 

  17. R. G. Novikov and M. Santacesaria, Int. Mathem. Res. Not. (2012). doi: 10.1093/imrn/rns025

    Google Scholar 

  18. V. A. Burov, A. S. Shurup, O. D. Rumyantseva, and D. I. Zotov, Bull. Russ. Acad. Sci. Phys. 76, 1365 (2012).

    Article  Google Scholar 

  19. V. A. Burov, I. P. Prudnikova, and N. S. Sirotkina, Sov. Phys. Acoust. 38, 555 (1992).

    Google Scholar 

  20. A. I. Nachman, Annals of Math. 128, 531 (1988).

    Article  MathSciNet  MATH  Google Scholar 

  21. V. A. Burov, O. D. Rumyantseva, and A. V. Saskovets, Moscow Univ. Phys. Bull. 49, 47 (1994).

    Google Scholar 

  22. V. A. Burov and O. D. Rumyantseva, Acoust. Phys. 39,419 (1993).

    ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to V. A. Burov.

Additional information

Original Russian Text © V.A. Burov, A.S. Shurup, D.I. Zotov, O.D. Rumyantseva, 2013, published in Akusticheskii Zhurnal, 2013, Vol. 59, No. 3, pp. 391–407.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Burov, V.A., Shurup, A.S., Zotov, D.I. et al. Simulation of a functional solution to the acoustic tomography problem for data from quasi-point transducers. Acoust. Phys. 59, 345–360 (2013). https://doi.org/10.1134/S1063771013030044

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063771013030044

Keywords

Navigation