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Calculation of the Derivatives of the Ray Coordinates with Respect to the Initial Parameters in the Inhomogeneous Two-Dimensional Media

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Radiophysics and Quantum Electronics Aims and scope

We consider the theory of numerical calculation of the fields in inhomogeneous two-dimensional media in the geometrical-optics approximation. Analytical formulas describing transformation of the matrix of the derivatives of the ray coordinates with respect to the initial parameters during the ray reflection from the curvilinear surfaces located in the medium are obtained. The numerically calculated derivatives are compared with those given by the obtained formulas. Asymptotic expressions for the amplitudes of the fields reflected from the large-curvature bodies are derived.

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References

  1. L. M. Brekhovskikh and Yu. P. Lysanov, Fundamentals of Ocean Acoustics, Springer, New York (2003).

    Google Scholar 

  2. A. L. Virovlyansky, Ray Theory of the Long-Range Propagation of Sound in the Ocean, [in Russian], Inst. Appl. Phys., Nizhny Novgorod (2006).

    Google Scholar 

  3. F.B. Jensen, W. A. Kuperman, M. B. Porter, and H. Schmidt, Computational Ocean Acoustics, Springer, New-York (2011).

    Book  MATH  Google Scholar 

  4. V. A. Borovikov and B. Ye. Kinber, Geometrical Theory of Diffraction, IEE, London (1994).

    Book  MATH  Google Scholar 

  5. Yu. A. Kravtsov and Yu. I. Orlov, Geometrical Optics of Inhomogeneous Media, Springer-Verlag Berlin (1990).

    Book  Google Scholar 

  6. I.P. Smirnov, ArXiv: 1212.6068v1 [math-ph] (2012).

  7. I.P. Smirnov and A. A. Khil’ko, Akust. Zh., 41, No. 1, 139 (1995).

    Google Scholar 

  8. A. N. Tikhonov and V. Ya. Arsenin, Solutions of Ill-Posed Problems, Wiley, New York (1977).

    Google Scholar 

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Authors and Affiliations

  1. Institute of Applied Physics of the Russian Academy of Sciences, Nizhny Novgorod, Russia

    I. P. Smirnov

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  1. I. P. Smirnov
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Correspondence to I. P. Smirnov.

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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 56, Nos. 2, pp. 85–95, February 2013.

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Smirnov, I.P. Calculation of the Derivatives of the Ray Coordinates with Respect to the Initial Parameters in the Inhomogeneous Two-Dimensional Media. Radiophys Quantum El 56, 78–87 (2013). https://doi.org/10.1007/s11141-013-9417-1

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  • DOI: https://doi.org/10.1007/s11141-013-9417-1

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