Geodesic
Numerical analytic methods for calculating wave fields and restoring the velocity characteristics of inhomogeneous elastic media in the Baikal rift zone
Sibirskij žurnal industrialʹnoj matematiki, Tome 26 (2023) no. 2, pp. 188-203.

Voir la notice de l'article provenant de la source Math-Net.Ru

On the basis of a numerical method for solving direct and inverse problems, a method has been developed for tracking the dynamics of the propagation of a seismo-hydroacoustic wave field, constructing model seismograms, and estimating the velocity characteristics of the complex geophysical structure of the Baikal rift zone in the area of the village Babushkin (southeastern Baikal) - the village. Buguldeika (north-western Baikal). The choice of the profile for modeling is due to the experimental work performed here by the Institute of Physics of the Earth Russian Academy of Sciences, the Institute of Computational Mathematics and Mathematical Geophysics of the Siberian Branch of the Russian Academy of Sciences, the Institute of Geology of the Siberian Branch of the Russian Academy of Sciences in 2021. The algorithm for solving the direct problem of wave field reconstruction is based on the application of the integral Laguerre transformation in time and finite-difference approximation in spatial coordinates. The numerical model of the medium used to calculate the propagation of seismic waves was set taking into account a priori data on the velocity section of the Baikal rift zone, obtained by a number of researchers in the region according to the data of deep seismic sounding of the Earth. The results of direct numerical modeling assume the prediction of the complex structure of the wave field and are intended to facilitate its interpretation. As an approach to solving the inverse problem of restoring the velocity characteristics of an inhomogeneous media, a computational grid algorithm based on the calculation of weighted average velocities in sections of a grid superimposed on the Earth's surface is proposed and tested. By choosing the grid step, the method of approximating the discrete wave travel time curve by cubic splines, and taking into account the curvature of the head wave travel time curve in areas with a pronounced inhomogeneity of the medium structure, it is possible to determine the velocity characteristic with increased accuracy. The consistency of the reconstructed theoretical velocity model of the medium with the experimentally obtained model by the method of deep seismic sounding is shown.
Keywords: Baikal rift zone, numerical model, numerical modeling, wave field, model seismograms, grid algorithm, velocity profile, comparative analysis. 
@article{SJIM_2023_26_2_a14,
     author = {M. S. Khairetdinov and A. A. Mikhailov and V. V. Kovalevsky and D. L. Pinigina and A. A. Yakimenko},
     title = {Numerical analytic methods for calculating wave fields and restoring the velocity characteristics of inhomogeneous elastic media in the {Baikal} rift zone},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {188--203},
     publisher = {mathdoc},
     volume = {26},
     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2023_26_2_a14/}
}
TY  - JOUR
AU  - M. S. Khairetdinov
AU  - A. A. Mikhailov
AU  - V. V. Kovalevsky
AU  - D. L. Pinigina
AU  - A. A. Yakimenko
TI  - Numerical analytic methods for calculating wave fields and restoring the velocity characteristics of inhomogeneous elastic media in the Baikal rift zone
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2023
SP  - 188
EP  - 203
VL  - 26
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2023_26_2_a14/
LA  - ru
ID  - SJIM_2023_26_2_a14
ER  - 
%0 Journal Article
%A M. S. Khairetdinov
%A A. A. Mikhailov
%A V. V. Kovalevsky
%A D. L. Pinigina
%A A. A. Yakimenko
%T Numerical analytic methods for calculating wave fields and restoring the velocity characteristics of inhomogeneous elastic media in the Baikal rift zone
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2023
%P 188-203
%V 26
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2023_26_2_a14/
%G ru
%F SJIM_2023_26_2_a14
M. S. Khairetdinov; A. A. Mikhailov; V. V. Kovalevsky; D. L. Pinigina; A. A. Yakimenko. Numerical analytic methods for calculating wave fields and restoring the velocity characteristics of inhomogeneous elastic media in the Baikal rift zone. Sibirskij žurnal industrialʹnoj matematiki, Tome 26 (2023) no. 2, pp. 188-203. http://geodesic.mathdoc.fr/item/SJIM_2023_26_2_a14/

[1] V. V. Kovalevsky, A. G. Fatyanov, D. A. Karavaev, L. P. Braginskaya, A. P. Grigoryuk, V. V. Mordvinova, Ts. A. Tubanov, A. D. Bazarov, “Research and verification of the Earth's crust velocity models by mathematical simulation and active seismology methods”, Geodynamics Tectonophysics, 10:3 (2019), 569–583 | DOI

[2] M. M. Makarov, K. M. Kucher, O. E. Popov, I. A. Aslamov, N. G. Granin, “Eksperimentalnye issledovaniya rasprostraneniya tonalno-impulsnykh signalov v vode ozera Baikal”, Zhurn. priklad. i fund. issledovanii, 2018, no. 7, 54–60 | DOI

[3] A. S. Alekseev, B. M. Glinskii, V. V. Kovalevskii, M. S. Khairetdinov i dr, Aktivnaya seismologiya s moschnymi vibratsionnymi istochnikami, Filial «Geo» Izd-va SO RAN, Novosibirsk, 2004

[4] A. V. Belyashev, Ts. A. Tubanov, “Podbor skorostnykh modelei dlya lokalizatsii seismicheskikh sobytii v predelakh Baikalskoi riftovoi zony”, Geofiz. tekhnologii, 2021, no. 1, 38–51

[5] N. N. Puzyrev, M. M. Mandelbaum, S. V. Krylov, B. P. Mishenkin, G. V. Krupskaya, G. V. Petrick, “Deep seismic investigations in the Baikal rift zone”, Tectonophysics, 20:1 (1973), 85–95 | DOI

[6] S. Sun Yunshen, S. V. Krylov, Ya. Baotszyun i dr, “Glubinnoe seismicheskoe zondirovanie litosfery na mezhdunarodnom transekte Baikal-Severo-Vostochnyi Kitai”, Geologiya i geofizika, 37:2 (1996), 3–15

[7] BrinkU. S. Ten, M. H. Taylor, “Crustal structure of central Lake Baikal: Insight into intracontinental rifting”, J. Geophys. Res., 108:B3 (2003), 21–33 | DOI

[8] V. D. Suvorov, Z. R. Mishenkina, “Struktura osadochnykh otlozhenii i fundamenta pod yuzhnoi kotlovinoi ozera Baikal po dannym KMPV”, Geologiya i geofizika, 46:11 (2005), 1159–1167

[9] C. Nielsen, H. Thybo, “Lower crustal intrusions beneath the southern Baikal Rift Zone: Evidens from full-waveform modeling of wide-angle siesmic data”, Tectonophysics, 470:3-4 (2009), 298–318 | DOI

[10] V. V. Mordvinova, A. A. Artemev, “Trekhmernaya model yuga Baikalskoi riftovoi zony i sopredelnykh territorii po obmennym volnam”, Geologiya i geofizika, 51:6 (2010), 887–904

[11] F. Collino, “Perfectly matched absorbing layers for the paraxial equations”, J. Comput. Phys, 131:1 (1996), 164–180 | DOI | MR

[12] F. Collino, C. Tsogka, “Application of PML absorbing layer model to the linear elastodynamic problem in anisotropic heterogeneous media”, Geophysics, 66:1 (2001), 294–307 | DOI

[13] B. G. Mikhailenko, “Spectral Laguerre method for the approximate solution of time dependent problems”, Appl. Math. Lett, 12:4 (1999), 105–110 | DOI | MR | Zbl

[14] G. V. Konyukh, B. G. Mikhailenko, A. A. Mikhailov, “Application of the integral Laguerre transforms for forward seismic modeling”, J. Comput. Acoustics, 9:4 (2001), 1523–1541 | DOI | MR | Zbl

[15] C. C. Paige, M. A. Saunders, “LSQR: An algorithm for sparse linear equations and sparse least squares”, ACM Trans. Math. Software, 8:1 (1982), 43–71 | DOI | MR | Zbl

[16] A. R. Levander, “Fourth order velocity-stress finite-difference scheme”, Proc. 57-th SEG Annual Meeting, New Orleans, 1987, 234–245 | MR

[17] S. V. Goldin, Interpretatsiya dannykh seismicheskogo metoda otrazhennykh voln, Nedra, M., 1979

[18] O. G. Kutina, Postroenie statisticheskikh algoritmov obrabotki i interpretatsii seismicheskikh dannykh, Nedra, M., 1982

[19] Kh. Yu. Tagirov, T. G. Aslanov, Kh. D. Magomedov, “Opredelenie srednevzveshennoi skorosti seismi cheskoi volny na uchastkakh Zemli po puti ee rasprostraneniya”, Izv. Dagestan. gos. ped. un-ta. Estestvennye i tochnye nauki, 11:3 (2017), 108–114