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Joint reconstruction of the speed of sound, absorption, and flows by the Novikov–Agaltsov functional algorithm

  • Acoustic Signal Processing. Computer Simulation
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Abstract

Numerical implementation of the two-dimensional functional-analytical Novikov–Agaltsov algorithm is considered and its possibilities are discussed. This algorithm is intended for reconstructing combined scalar-vector inhomogeneities describing spatial distributions of the speed of sound, absorption, and vector flow field. The results of the numerical simulation of the algorithm in the single- and multifrequency probing modes are presented. The obtained results illustrate an acceptable accuracy and interference resistance of the obtained estimates, which illustrates the application prospects of the algorithm in practical problems of acoustic tomography.

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References

  1. W. Munk, P. Worcester, and C. Wunsch, Ocean Acoustic Tomography (Cambridge Univ., New York, 1995).

    Book  Google Scholar 

  2. V. V. Goncharov, V. Yu. Zaitsev, V. M. Kurtepov, A. G. Nechaev, and A. I. Khil’ko, Ocean Acoustical Tomography (Inst. Prikl. Fiz. Ross. Akad. Nauk, N. Novgorod, 1997) [in Russian].

    Google Scholar 

  3. V. A. Burov, T. V. Gracheva, S. N. Sergeev, and A. S. Shurup, Acoust. Phys. 54 (2), 246–260 (2008).

    Article  ADS  Google Scholar 

  4. V. A. Burov, S. N. Sergeev, and A. S. Shurup, Acoust. Phys. 57 (3), 344–358 (2011).

    Article  ADS  Google Scholar 

  5. D. Rouseff and K.B. Winters, Inverse Problems 10 (3), 687–697 (1994).

    Article  ADS  MathSciNet  Google Scholar 

  6. S. J. Norton, J. Acoust. Soc. Am. 105 (5), 2717–2721 (1999).

    Article  ADS  Google Scholar 

  7. S. J. Norton, IEEE Trans. Image Process. 1 (3), 406–412 (1992).

    Article  ADS  Google Scholar 

  8. M. N. Rychagov and H. Ermert, J. Acoust. Soc. Am. 99 (5), 3029–3035 (1996).

    Article  ADS  Google Scholar 

  9. O. D. Rumyantseva and A. S. Shurup, Acoust. Phys. 63 (1), 95–103 (2017).

    Article  ADS  Google Scholar 

  10. V. V. Krylov, Foundations of the Theory of Sound Transmission and Scattering (Mos. Gos. Univ., Moscow, 1988) [in Russian].

    Google Scholar 

  11. V. E. Ostashev, Sound Propagation in Moving Media (Nauka, Moscow, 1992) [in Russian].

    MATH  Google Scholar 

  12. R. G. Novikov, J. Funct. Anal. 103 (2), 409–463 (1992).

    Article  MathSciNet  Google Scholar 

  13. A. D. Agaltsov and R. G. Novikov, J. Math. Phys. 55 (10), 103502 (2014). https://hal.archives-ouvertes.fr/hal-00939283v1

    Article  ADS  MathSciNet  Google Scholar 

  14. A. D. Agaltsov, Eurasian J. Math. Comp. Appl. 4 (1), 4–11 (2016). http://arxiv.org/abs/1512.06367

    Google Scholar 

  15. V. A. Burov, A. S. Shurup, D. I. Zotov, and O. D. Rumyantseva, Acoust. Phys. 59 (3), 345–360 (2013).

    Article  ADS  Google Scholar 

  16. R. G. Novikov and M. Santacesaria, Intern. Math. Research Notices 2013 (6), 1205–1229 (2013). http:// imrn.oxfordjournals.org/content/2013/6/1205.abstract

    Article  Google Scholar 

  17. V. A. Burov, N. V. Alekseenko, and O. D. Rumyantseva, Acoust. Phys. 55 (6), 843–856 (2009).

    Article  ADS  Google Scholar 

  18. L. D. Faddeev, in Contemporary Problems of Mathematics (VINITI, Moscow, 1974), vol. 3, pp. 93–180 [in Russian]; J. Sov. Math. 5, 334–396 (1976).

    Google Scholar 

  19. S. V. Manakov, Phys. D: Nonlinear Phenom. 3 (1–2), 420–427 (1981).

    Article  ADS  MathSciNet  Google Scholar 

  20. P. G. Grinevich and R. G. Novikov, Sov. Math., Dokl. 33 (1), 9–12 (1986).

    Google Scholar 

  21. R. G. Novikov and G. M. Henkin, Russ. Math. Surveys 42 (3), 109–180 (1987).

    Article  ADS  Google Scholar 

  22. V. A. Burov, S. N. Vecherin, S. A. Morozov, and O. D. Rumyantseva, Acoust. Phys. 56 (4), 541–559 (2010).

    Article  ADS  Google Scholar 

  23. A. D. Agaltsov, Bull. Sci. Mathém. 139 (8), 937–942 (2015).

    Article  MathSciNet  Google Scholar 

  24. G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers: Definitions, Theorems, and Formulas for Reference and Review (McGraw-Hill, New York, 1968; Nauka, Moscow, 1984).

    MATH  Google Scholar 

  25. O. D. Rumyantseva, V. A. Burov, A. L. Konyushkin, and N. A. Sharapov, Acoust. Phys. 55 (4–5), 613–629 (2009).

    Article  ADS  Google Scholar 

  26. Physical Principles of Medical Ultrasonics. Second Edition, Ed. by C. R. Hill, J. C. Bamber, and G. R. ter Haar, (Wiley, 2004; Mir, Moscow, 2008).

  27. V. A. Burov and O. D. Rumyantseva, Sov. Phys. Acoust. 38 (3), 226–230 (1992).

    Google Scholar 

  28. V. A. Burov and O. D. Rumyantseva, Acoust. Phys. 39 (5), 419–424 (1993).

    ADS  Google Scholar 

  29. N. V. Alekseenko, V. A. Burov, O. D. Rumyantseva, Acoust. Phys. 54 (3), 407–419 (2008).

    Article  ADS  Google Scholar 

  30. A. A. Goryunov and A. V. Saskovets, Inverse Scattering Problems in Acoustics (Mos. Gos. Univ., Moscow, 1989) [in Russian].

    Google Scholar 

  31. V. A. Burov, D. I. Zotov, and O. D. Rumyantseva, Acoust. Phys. 61 (2), 231–248 (2015).

    Article  ADS  Google Scholar 

  32. D. I. Zotov, A. S. Shurup, and O. D. Rumyantseva, Bull. Russ. Acad. Sci.: Phys. 81 (1), 101–105 (2017).

    Article  Google Scholar 

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Authors and Affiliations

  1. Moscow State University, Moscow, 119991, Russia

    A. S. Shurup & O. D. Rumyantseva

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  1. A. S. Shurup
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  2. O. D. Rumyantseva
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Correspondence to A. S. Shurup.

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Original Russian Text © A.S. Shurup, O.D. Rumyantseva, 2017, published in Akusticheskii Zhurnal, 2017, Vol. 63, No. 6, pp. 700–718.

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Shurup, A.S., Rumyantseva, O.D. Joint reconstruction of the speed of sound, absorption, and flows by the Novikov–Agaltsov functional algorithm. Acoust. Phys. 63, 751–768 (2017). https://doi.org/10.1134/S1063771017060136

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  • DOI: https://doi.org/10.1134/S1063771017060136

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