Log in

Investigation of Wave Phenomena During the Seismic Survey in the Permafrost Areas Using Two Approaches to Numerical Modeling

  • Published:
Lobachevskii Journal of Mathematics Aims and scope Submit manuscript

Abstract

In the recent years the Arctic onshore and offshore areas has become the region of interest. In the cold conditions, inhomogeneous permafrost ground with ice and methane inclusions is formed. It affects all conducted full-scale seismic measurements. The aim of this work is creation of the computational settings for reproduction of such wave processes that is able to encompass the main features of the region. Two approaches to numerical modeling are introduced and compared on the obtained wave patterns and seismograms. The first one suggests the construction of multiple curvilinear grids. For the second one, a single rectangle grid is created with different elastic parameters in each cell. Linear elasticity model is used as a governing system of equations. It was solved using the grid-characteristic method on structured grids. As a result of the analysis, the advantages and disadvantages of the approaches are distinguished. The influence of the domains on the wave profiles is studied, reproduced rich wave phenomena is defined.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Canada)

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

REFERENCES

  1. L. Li, ‘‘Special issue on numerical modeling in civil and mining geotechnical engineering,’’ Processes 10, 1571 (2022). https://doi.org/10.3390/pr10081571

    Article  Google Scholar 

  2. P. F. Antonietti, A. Ferroni, I. Mazzieri, R. Paolucci, A. Quarteroni, C. Smerzini, and M. Stupazzini, ‘‘Numerical modeling of seismic waves by discontinuous spectral element methods,’’ ESAIM: ProcS 61, 1–37 (2018). https://doi.org/10.1051/proc/201861001

  3. I. B. Petrov, ‘‘Mathematical modeling of natural and anthropogenic processes in the arctic zone,’’ Lobachevskii J. Math. 41, 552–560 (2020). https://doi.org/10.1134/S1995080220040204

    Article  MathSciNet  Google Scholar 

  4. D. A. Streletskiy, S. Clemens, J.-P. Lanckman, and N. I. Shiklomanov, ‘‘The costs of Arctic infrastructure damages due to permafrost degradation,’’ Environ. Res. Lett. 18, 015006 (2023).

  5. V. E. Romanovsky, D. S. Drozdov, N. G. Oberman, G. V. Malkova, A. L. Kholodov, S. S. Marchenko, N. G. Moskalenko, D. O. Sergeev, N. G. Ukraintseva, A. A. Abramov, D. A. Gilichinsky, and A. A. Vasiliev, ‘‘Thermal state of permafrost in Russia,’’ Permafrost Periglac. 21, 136–155 (2010).

    Article  Google Scholar 

  6. O. Anisimov and S. Zimov, ‘‘Thawing permafrost and methane emission in Siberia: Synthesis of observations, reanalysis, and predictive modeling,’’ Ambio 50, 2050–2059 (2021).

    Article  Google Scholar 

  7. A. Glikson, ‘‘The methane time bomb,’’ Energy Proc. 146, 23–29 (2018).

    Article  Google Scholar 

  8. P. M. Shearer, Introduction to Seismology (Cambridge Univ. Press, Cambridge, 2019).

    Book  Google Scholar 

  9. I. B. Petrov, ‘‘Grid-characteristic methods. 55 years of develo** and solving complex dynamic problems,’’ Math. Models Comput. Simul. 6, 6–21 (2023). https://doi.org/10.23947/2587-8999-2023-6-1-6-21

    Article  Google Scholar 

  10. A. V. Favorskaya, N. I. Khokhlov, and I. B. Petrov, ‘‘Grid-characteristic method on joint structured regular and curved grids for modeling coupled elastic and acoustic wave phenomena in objects of complex shape,’’ Lobachevskii J. Math. 41, 512–525 (2020). https://doi.org/10.1134/S1995080220040083

    Article  MathSciNet  Google Scholar 

  11. A. V. Favorskaya and V. I. Golubev, ‘‘Study the elastic waves propagation in multistory buildings, taking into account dynamic destruction,’’ in Intelligent Decision Technologies IDT 2020, Ed. by I. Petrov, A. Favorskaya, M. Favorskaya, S. Simakov, and L. Jain, Smart Innov. Syst. Technol. 193, 189–199 (2020). https://doi.org/10.1007/978-981-15-5925-9_16

  12. V. I. Golubev, A. V. Ekimenko, I. S. Nikitin, and Y. A. Golubeva, ‘‘Continuum model of layered medium for reservoir of Bazhenov formation,’’ in Processes in GeoMedia, Vol. 2 of Springer Geology, Ed. by T. Chaplina (Springer, Cham, 2021), pp. 235–245. https://doi.org/10.1007/978-3-030-53521-6_27

  13. I. S. Nikitin, V. I. Golubev, A. V. Ekimenko, and M. B. Anosova, ‘‘Simulation of seismic responses from the 3D non-linear model of the Bazhenov formation,’’ IOP Conf. Ser.: Mater. Sci. Eng. 927, 012020 (2020). https://doi.org/10.1088/1757-899X/927/1/012020

  14. I. B. Petrov and N. I. Khokhlov, ‘‘Modeling 3D seismic problems using high-performance computing systems,’’ Math. Models Comput. Simul. 6, 342–350 (2014). https://doi.org/10.1134/S2070048214040061

    Article  MathSciNet  Google Scholar 

  15. W. Nowacki, Theory of Elasticity (Wydawnictwo Naukowe, Warszawa, 1970; Mir, Moscow, 1975).

  16. V. V. Rusanov, ‘‘The calculation of the interaction of non-stationary shock waves with barriers,’’ J. Comput. Math. Phys. USSR 1, 267–279 (1961). https://doi.org/10.1016/0041-5553(62)90062-9

    Article  MathSciNet  Google Scholar 

  17. A. S. Kholodov and Ya. A. Kholodov, ‘‘Monotonicity criteria for difference schemes designed for hyperbolic equations,’’ Comput. Math. Math. Phys. 46, 1560–1588 (2006). https://doi.org/10.1134/S0965542506090089

    Article  MathSciNet  Google Scholar 

  18. E. K. Guseva, V. I. Golubev, and I. B. Petrov, ‘‘Linear, quasi-monotonic and hybrid grid-characteristic schemes for hyperbolic equations,’’ Lobachevskii J. Math. 44, 296–312 (2023). https://doi.org/10.1134/S1995080223010146

    Article  MathSciNet  Google Scholar 

  19. V. P. Berdennikov, ‘‘Study of the modulus of elasticity of ice,’’ Tr. GGI 7 (61), 13–23 (1948).

    Google Scholar 

  20. D. Nkemzi, ‘‘A new formula for the velocity of Rayleigh waves,’’ Wave Motion 26, 199–205 (1997). https://doi.org/10.1016/S0165-2125(97)00004-8

    Article  MathSciNet  Google Scholar 

  21. A. V. Favorskaya and I. B. Petrov, ‘‘Wave responses from oil reservoirs in the Arctic shelf zone,’’ Dokl. Earth Sci. 466, 214–217 (2016). https://doi.org/10.1134/S1028334X16020185

    Article  Google Scholar 

  22. A. G. Fatyanov, ‘‘A wave method of suppressing multiple waves for any complex subsurface geometry,’’ Numer. Anal. Appl. 5, 187–190 (2012). https://doi.org/10.1134/S1995423912020140

    Article  Google Scholar 

  23. J. G. Scholte, ‘‘On the Stoneley wave equation,’’ Proc. Kon. Nederl. Akad. Wetensch. 45, 20–25 (1942).

    MathSciNet  Google Scholar 

Download references

Funding

This work was carried out with the financial support of the Russian Science Foundation, project no. 21-71-10015.

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to E. K. Guseva, V. I. Golubev or I. B. Petrov.

Ethics declarations

The authors of this work declare that they have no conflicts of interest.

Additional information

Publisher’s Note.

Pleiades Publishing remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

(Submitted by A. V. Lapin)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Guseva, E.K., Golubev, V.I. & Petrov, I.B. Investigation of Wave Phenomena During the Seismic Survey in the Permafrost Areas Using Two Approaches to Numerical Modeling. Lobachevskii J Math 45, 231–238 (2024). https://doi.org/10.1134/S1995080224010190

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1995080224010190

Keywords:

Navigation