An Iterative Way of Solving the Inverse Scattering Problem for an Acoustic System of Equations in an Absorptive Layered Nonhomogeneous Medium

Baev, A.V.; Gavrilov, S.V.

Авторы: Baev A.V., Gavrilov S.V.
Журнал: Moscow University Computational Mathematics and Cybernetics
Том: 42
Номер: 2
Год издания: 2018
Издательство: Allerton Press Inc.
Местоположение издательства: United States
Первая страница: 55
Последняя страница: 62
DOI: 10.3103/S0278641918020024
Аннотация: ABSTRACT An algorithm is considered for solving the inverse scattering problem of seismic waves in a layered medium. The algorithm is based on solving a nonclassical ordinary differential equation with respect to an acoustic impedance, which also contains an unknown function characterizing the dissipative properties of the medium. The uniqueness of determining of these functions and the functional dependence associating them is established by solving the inverse problem of ground seismics. Results are presented from a computing experiment on applying the proposed algorithm. REFERENCES 1. V. I. Dmitriev, “Inverse problemsin the opticsof layered media,” Comput. Math. Model. 26, 546–554 (2015). 2. A. V. Tikhonravov, M. Trubetskov, A. Gorokh, et al., “Advantages and challenges of optical coating production with indirect monochromatic monitoring,” Appl. Opt. 54, 3433–3439 (2015). 3. A. V. Baev, “On local solvability of inverse dissipative scattering problems,” J. Inverse Ill-Posed Probl. 9, 227–247 (2001). 4. A. V. Baev and N. V. Kutsenko, “Solving the inverse generalized problem of vertical seismic profiling,” Comput. Math. Model. 15, 1–18 (2004). 5. A. V. Baev and N. V. Kutsenko, “Identification of a dissipation coefficient by a variational method,” Comput. Math. Math. Phys. 46, 1796 (2006). 6. A. V. Baev and G. Yu. Mel’nikov, “Inverse dissipative problems in vertical seismic profiling,” J. Inverse Ill- Posed Probl. 7, 201–220 (1999). 7. A. V. Baev, “On local solvability of inverse scattering problems for the Klein–Gordon equation and the Dirac system,” Math. Notes 96, 286 (2014). 8. A. N. Kolmogorovand S. V. Fomin, Elements of the Theory of Functions and Functional Analysis, Dover Books on Mathematics (Nauka, Moscow,1972; Dover, New York, 1999). 9. L. A. Molotkov, The Study of Wave Propagation in Porous and Fractured Media Based on Effective Models of BIO and Layered Media (Nauka, St. Petersburg, 2001) [in Russian]. 10. A. V. Baev, “On solution of inverse boundary problem for wave equation with discontinued koefficient,” Zh. Vychisl. Mat. Mat. Fiz. 28, 1619–1633 (1988). 11. A. V. Baev, “Generalized differential equation arising in the solution of the inverse scattering problem in a layered medium,” Differ. Equat. 53, 981–988 (2017). 12. A. V. Baev, “Numerical solution of inversescatteringproblemsforequation ofacoustica in layeredmedia with absorption,” Prikl. Mat. Inform., № 54, 57–74 (2017). 13. A. N. Tikhonov, A. V. Goncharskii, V. V. Stepanov, and A. G. Yagola, Numerical Methods for the Solution of Ill-Posed Problems (Nauka, Moscow, 1990; Springer, Dordrecht, 1995).
Добавил в систему: Гаврилов Сергей Вадимович

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An Iterative Way of Solving the Inverse Scattering Problem for an Acoustic System of Equations in an Absorptive Layered Nonhomogeneous Mediumстатья

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