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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2001, Volume 4, Number 3, Pages 259–268 (Mi sjvm399)  

This article is cited in 24 scientific papers (total in 24 papers)

Numerical solution of the inverse problem for a system of elasticity with the aftereffect for a vertically inhomogeneous medium

A. L. Karchevskya, A. G. Fatianovb

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
b Institute of Computational Mathematics and Mathematical Geophysics (Computing Center), Siberian Branch of the Russian Academy of Sciences
References:
Abstract: In this paper, the results of numerical solution of a 1-D inverse problem for a system of elasticity with the aftereffect for a vertically inhomogeneous medium are presented. The Boltzmann model is chosen to take into account the aftereffect. The purpose of the inverse problem is to reconstruct the longitudinal and transverse velocities by using the known longitudinal and transverse displacements at the surface. A series of model calculations is carried out, and the results of reconstructions of a velocity model of the medium typical for Western Siberia are presented.
Received: 12.04.2000
Revised: 31.10.2000
Bibliographic databases:
Document Type: Article
UDC: 517.956.3
Language: Russian
Citation: A. L. Karchevsky, A. G. Fatianov, “Numerical solution of the inverse problem for a system of elasticity with the aftereffect for a vertically inhomogeneous medium”, Sib. Zh. Vychisl. Mat., 4:3 (2001), 259–268
Citation in format AMSBIB
\Bibitem{KarFat01}
\by A.~L.~Karchevsky, A.~G.~Fatianov
\paper Numerical solution of the inverse problem for a~system of elasticity with the aftereffect for a~vertically inhomogeneous medium
\jour Sib. Zh. Vychisl. Mat.
\yr 2001
\vol 4
\issue 3
\pages 259--268
\mathnet{http://mi.mathnet.ru/sjvm399}
\zmath{https://zbmath.org/?q=an:0982.86004}
Linking options:
  • https://www.mathnet.ru/eng/sjvm399
  • https://www.mathnet.ru/eng/sjvm/v4/i3/p259
  • This publication is cited in the following 24 articles:
    1. Durdumurod K. Durdiev, Zhavlon Z. Nuriddinov, “Global solvability of a kernel determination problem in 2D heat equation with memory”, Zhurn. SFU. Ser. Matem. i fiz., 18:1 (2025), 14–24  mathnet
    2. U. D. Durdiev, A. A. Rakhmonov, “Obratnaya zadacha dlya differentsialnogo uravneniya chetvertogo poryadka s drobnym operatorom Kaputo”, Izv. vuzov. Matem., 2024, no. 9, 22–33  mathnet  crossref
    3. D. K. Durdiev, J. Sh. Safarov, J. Sh. Safarov, “Inverse Problem for an Integrodifferential Equation of the Hyperbolic Type protect in a Rectangular Domain”, Math. Notes, 114:2 (2023), 199–211  mathnet  crossref  crossref  mathscinet
    4. U. D. Durdiev, “Obratnaya zadacha ob istochnike dlya uravneniya vynuzhdennykh kolebanii balki”, Izv. vuzov. Matem., 2023, no. 8, 10–22  mathnet  crossref
    5. U. D. Durdiev, Z. R. Bozorov, “Nonlocal inverse problem for determining the unknown coefficient in the beam vibration equation”, J. Appl. Industr. Math., 17:2 (2023), 281–290  mathnet  crossref  crossref
    6. D. K. Durdiev, Kh. Kh. Turdiev, “Zadacha opredeleniya yader v sisteme integro-differentsialnykh uravnenii akustiki”, Dalnevost. matem. zhurn., 23:2 (2023), 190–210  mathnet  crossref
    7. Durdiev D.K., Zhumaev Zh.Zh., “Memory Kernel Reconstruction Problems in the Integro-Differential Equation of Rigid Heat Conductor”, Math. Meth. Appl. Sci., 45:14 (2022), 8374–8388  crossref  mathscinet  isi  scopus
    8. Zh. D. Totieva, “Coefficient reconstruction problem for the two-dimensional viscoelasticity equation in a weakly horizontally inhomogeneous medium”, Theoret. and Math. Phys., 213:2 (2022), 1477–1494  mathnet  crossref  crossref  mathscinet  adsnasa
    9. G. M. Mitrofanov, A. L. Karchevskii, “Matematicheskoe modelirovanie dlya tonkosloistykh uprugikh sred v seismorazvedke”, Sib. zhurn. industr. matem., 25:3 (2022), 120–134  mathnet  crossref
    10. A. A. Rakhmonov, U. D. Durdiev, Z. R. Bozorov, “Problem of determining the speed of sound and the memory of an anisotropic medium”, Theoret. and Math. Phys., 207:1 (2021), 494–513  mathnet  crossref  crossref  adsnasa  isi
    11. Zh. D. Totieva, “Linearizovannaya dvumernaya obratnaya zadacha opredeleniya yadra uravneniya vyazkouprugosti”, Vladikavk. matem. zhurn., 23:2 (2021), 87–103  mathnet  crossref
    12. Z. R. Bozorov, “The problem of determining the two-dimensional kernel of a viscoelasticity equation”, J. Appl. Industr. Math., 14:1 (2020), 20–36  mathnet  crossref  crossref  elib
    13. D. K. Durdiev, A. A. Rahmonov, “The problem of determining the 2D-kernel in a system of integro-differential equations of a viscoelastic porous medium”, J. Appl. Industr. Math., 14:2 (2020), 281–295  mathnet  crossref  crossref  elib
    14. U. D. Durdiev, “Chislennoe opredelenie zavisimosti dielektricheskoi pronitsaemosti sloistoi sredy ot vremennoi chastoty”, Sib. elektron. matem. izv., 17 (2020), 179–189  mathnet  crossref
    15. Durdiev D.K., Rahmonov A.A., “a 2D Kernel Determination Problem in a Visco-Elastic Porous Medium With a Weakly Horizontally Inhomogeneity”, Math. Meth. Appl. Sci., 43:15 (2020), 8776–8796  crossref  mathscinet  zmath  isi  scopus
    16. Bozorov Z.R., “Numerical Determining a Memory Function of a Horizontally-Stratified Elastic Medium With Aftereffect”, Eurasian J. Math. Comput. Appl., 8:2 (2020), 28–40  crossref  mathscinet  isi  scopus
    17. U. D. Durdiev, “An inverse problem for the system of viscoelasticity equations in homogeneous anisotropic media”, J. Appl. Industr. Math., 13:4 (2019), 623–628  mathnet  crossref  crossref
    18. A. A. Sedipkov, “Application of spectral methods to inverse dynamic problem of seismicity of a stratified medium”, J. Appl. Industr. Math., 12:4 (2018), 738–748  mathnet  crossref  crossref  elib  elib
    19. A. A. Sedipkov, “Pryamaya i obratnaya zadachi akusticheskogo zondirovaniya v sloistoi srede s razryvnymi parametrami”, Sib. zhurn. industr. matem., 17:1 (2014), 120–134  mathnet  mathscinet
    20. A. L. Karchevsky, “Reconstruction of pressure and shear velocities and boundaries of thin layers in a thinly stratified layer”, Num. Anal. Appl., 5:1 (2012), 54–67  mathnet  crossref  elib
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