The problem of studying a depth-velocity seismic modelof the geological medium

The problem of studying a depth-velocity seismic model of the geological medium

Авторы

DOI:

https://doi.org/10.56143/ujmcs.v1i1.8

Ключевые слова:

inverse kinematic problem of seismics; eikonal equation; approximation; splines.

Аннотация

A review of the algorithm for numerical solution of the inverse kinematic problem of seismics,
consisting in studying the depth-velocity model of the geological medium, is given.
The algorithm is based on the eikonal equation and the technology of smoothing multidimensional splines.

Биографии авторов

  • A.X. Begmatov, Tashkent state transport university

    Tashkent state transport university, 1 Temiryolchilar Street, Mirobod District, Tashkent, Uzbekistan.

  • Vladimir Bogdanov, Sobolev Institute of Mathematics

    Sobolev Institute of Mathematics, 4 Acad. Koptyug avenue, 630090, Novosibirsk, Russia.

  • Yuriy Volkov, Sobolev Institute of Mathematics

    Sobolev Institute of Mathematics, 4 Acad. Koptyug avenue, 630090, Novosibirsk, Russia.

Библиографические ссылки

[1] Herglotz, G.: Über das Benndorfsche Problem der Fortpflanzungsgeschwindigkeit der Erdbebenstrahlen. Physik. Zeitshrift. 8 (5), 145-147 (1907).

[2] Wiechert, E. Über Erdbebenwellen. I. Theoretisches über die Ausbreitung der Erdbebenwellen. Nachr. Ges. Wiss. Göttingen, Math.-Phys. Kl. 4, 415-529 (1907).

[3] Romanov, V. G.: Inverse problems of mathematical physics. Nauka, Moscow (1984). [Russian]

[4] Goldin, S. V.: Geometric seismics. IPGG SB RAS, Novosibirsk (2017). [Russian]

[5] Pivovarova, N. B., Pivovarov, V. G.: Methodical aspects of reconstruction of three-dimensional high-speed medium. Vestnik Otdelenia nauk oZemle RAN 1, 21 (2003).

[6] Slavina, L. B., Pivovarova, N. B.: The dynamics of seismic velocity fields during periods of increased seismic and volcanic activity in kamchatka.IFZ RAS, Moscow (2009). [Russian]

[7] Gobarenko, V., Yegorova, T., Stifenson, R.: The structure of the Kerch peninsula and north-eastern part of the Black sea crust according to the results of local seismic tomography. Geofizicheskij zhurnal 36 (2), 38-59 (2014).

[8] Anikonov, Yu. E., Pivovarova, N. B., Slavina, L. B.: Three-dimensional velocity field of the Kamchatka focal zone. In: Mathematical problems of geophysics 5 (1). Vychislitel’nyj Tsentr SO AN SSSR, Novosibirsk, 92-117 (1974). [Russian]

[9] Slavina, L. B., Pivovarova, N. B., Levina, V. I.: A study in the velocity structure of December 5, 1997, M w= 7.8 Kronotskii rupture zone,

Kamchatka. J. Volcanol. Seismol. 1 (4), 254-262 (2007).

[10] Anikonov, Yu. E., Bogdanov, V. V., Derevtsov, E. Yu., Miroshnichenko, V.L., Sapozhnikova, N. A.: Numerical solution of an inverse kinematic seismic problem with internal sources. Sib. Zh. Ind. Mat. 9 (4), 3-26 (2006).

[11] Anikonov, Yu. E., Bogdanov, V. V., Derevtsov, E. Yu., Miroshnichenko, V. L., Pivovarova, N. B., Slavina, L. B.: Some approaches to a numerical solution for the multidimensional inverse kinematic problem of seismics with inner sources. J. Inv. Ill-Posed Problems textbf17 (3), 209-238 (2009).

[12] Anikonov, Yu. E., Bogdanov, V. V., Volkov, Yu. S., Derevtsov, E. Yu.: On the determination of the velocity and elastic parameters of a medium in the focal zone from earthquake hodographs. J. Appl. Ind. Math. 15 (4), 569-585 (2021).

[13] Wendland, H.: Scattered data approximation. Cambridge, Cambridge University Press (2005).

[14] Rozhenko, A. I.: Theory and algorithms of variational spline approximation. ICM&MG SB RAS, Novosibirsk (2005). [Russian]

[15] Ignatov, M. I., Pevny, A. B.: Natural splines of many variables. Nauka, Leningrad (1991). [Russian]

[16] Schaback, R.: Native Hilbert spaces for radial basis functions I. In: New developments in approximation theory (ISNM, 132). Basel, Birkhäuser,255-282 (1999).

[17] Rozhenko, A. I.: Comparison of radial basis functions. Numer. Analysis Appl. 11 (3), 220-235 (2018).

[18] Rozhenko, A. I., Shaidorov T. S.: On spline approximation with a reproducing kernel method. Numer. Analysis Appl. 6 (4), 314-323 (2013).

[19] Bogdanov, V. V., Karsten, W. V., Miroshnichenko, V. L., Volkov, Yu. S.: Application of splines for determining the velocity characteristic of a medium from a vertical seismic survey. Central European J. Math. 11 (4), 779-786 (2013).

Опубликован

2025-05-01

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Как цитировать

The problem of studying a depth-velocity seismic modelof the geological medium: The problem of studying a depth-velocity seismic model of the geological medium. (2025). Uzbekistan Journal of Mathematics and Computer Science , 1(1), 33-40. https://doi.org/10.56143/ujmcs.v1i1.8