Skip to main content

Application of Quasi-monotonic Schemes in Seismic Arctic Problems

  • Conference paper
  • First Online:
Advances in Theory and Practice of Computational Mechanics

Abstract

Nowadays, seismic survey is the most popular method for searching of oil and gas deposits. One of the promising technologies used in Arctic region is the creation of the artificial ice island. It can be used as a platform for equipment placing. In this chapter, we enhanced the ice island mechanical model and the numerical method. To describe its dynamic behavior, the theory of linear elasticity, acoustic, Maxwell viscoelastic and Kukudzhanov elastoviscoplastic models are utilized. The grid-characteristic method on rectangular grids was used for solving the governing hyperbolic system of equations. For the construction of new higher order hybrid schemes, the grid-characteristic monotonicity criterion and quasi-monotonic schemes were used. The scheme’s behavior on continuous and discontinuous solutions was thoroughly investigated. The best hybrid scheme was finally used for the simulation of seismic survey from ice island in a two-dimensional model.

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 249.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Crawford, A.J., Mueller, D.R., Humphreys, E.R., Carrieres, T., Tran, H.: Surface ablation model evaluation on a drifting ice island in the Canadian Arctic. Cold Reg. Sci. Technol. 110, 170–182 (2015)

    Article  Google Scholar 

  2. Crawford, A., Crocker, G., Mueller, D., Desjardins, L., Saper, R., Carrieres, T.: The canadian ice island drift, deterioration and detection (CI2D3) database. J. Glaciol. 64(245), 517–521 (2018)

    Article  Google Scholar 

  3. C-CORE. Ice island study. Final report. Prepared for Minerals Management Service, US Department of the Interior. Prepared by C-CORE. Report No. R-05–014- 241 v1.0, (2005)

    Google Scholar 

  4. Petrov, I.B., Muratov, M.V., Sergeev F.I.: Elastic wave propagation modeling during exploratory drilling on artificial ice island. Appl. Math. Comput. Mech. Smart Appl. 171–183 (2021)

    Google Scholar 

  5. Muratov, M.V., Biryukov, V.A., Konov, D.S., Petrov, I.B.: Mathematical modeling of temperature changes impact on artificial ice islands. Radioelectron. Nanosyst. Inf. Technol. 13, 79–86 (2021)

    Article  Google Scholar 

  6. Favorskaya, A.V., Petrov, I.B.: Wave responses from oil reservoirs in the Arctic shelf zone. Dokl. Earth Sci. 466(2), 214–217 (2016)

    Article  Google Scholar 

  7. Stognii, P., Epifanov, V., Golubev, V., Beklemysheva, K., Miryaha, V.: The numerical modelling of dynamic processes in the ice samples using the grid-characteristic method. Proceedings of the International Conference on Port and Ocean Engineering under Arctic Conditions, POAC, 2021-June (2021)

    Google Scholar 

  8. Golubev, V.I., Shevchenko, A.V., Petrov, I.B.: Application of the Dorovsky model for taking into account the fluid saturation of geological media. J. Phys. Conf. Ser. 1715(1), № 012056 (2021)

    Google Scholar 

  9. Golubev, V.I., Vasyukov, A.V., Churyakov, M.: Modeling wave responses from thawed permafrost zones. In: Favorskaya, M.N., Favorskaya, A.V., Petrov, I.B., Jain, L.C. (eds.) Smart Modelling For Engineering Systems. SIST, vol. 214, pp. 137–148. Springer, Singapore (2021)

    Chapter  Google Scholar 

  10. Nikitin, I.S., Golubev, V.I., Golubeva, Y.A., Miryakha, V.A.: Numerical comparison of different approaches for the fractured medium simulation. In: Favorskaya, M.N., Favorskaya, A.V., Petrov, I.B., Jain, L.C. (eds.) Smart Modelling For Engineering Systems. SIST, vol. 214, pp. 87–99. Springer, Singapore (2021)

    Chapter  Google Scholar 

  11. Golubev, V., Nikitin, I., Golubeva, Y., Petrov, I.: Numerical simulation of the dynamic loading process of initially damaged media. AIP Conference Proceedings 2309, № 0033949 (2020)

    Google Scholar 

  12. Golubev, V., Nikitin, I., Ekimenko, A.: Simulation of seismic responses from fractured MARMOUSI2 model. AIP Conference Proceedings 2312, № 050006 (2020)

    Google Scholar 

  13. Argatov, I.: Mathematical modeling of linear viscoelastic impact: application to drop impact testing of articular cartilage. Tribol. Int. 63, 213–225 (2013)

    Article  Google Scholar 

  14. Kukudzhanov, V.N., Levitin, A.L.: Numerical modeling of cutting processes for elastoplastic materials in 3D-statement. Mech. Solids 43, 494–501 (2008)

    Article  Google Scholar 

  15. Zhu, J., Qiu, J.: A new fifth order finite difference WENO scheme for solving hyperbolic conservation laws. J. Comput. Phys. 318, 110–121 (2016)

    Article  MathSciNet  Google Scholar 

  16. Harari, I., Hughes, T.J.R.: Finite element methods for the Helmholtz equation in an exterior domain: model problems. Comput. Meth. Appl. Mech. Eng. 87(1), 59–96 (1991)

    Article  MathSciNet  Google Scholar 

  17. Golubev, V.I., Shevchenko, A.V., Khokhlov, N.I., Nikitin, I.S.: Numerical investigation of compact grid-characteristic schemes for acoustic problems. J. Phys. Conf. Ser. 1902(1), № 012110 (2021)

    Google Scholar 

  18. Fridrichs, K.O.: Symmetric hyperbolic linear differential equations. IBID 2, 345–392 (1954)

    Google Scholar 

  19. Harten, A.: High resolution schemes for hyperbolic conservation laws. Comput. Phys. 49(3), 357–393 (1987)

    Article  MathSciNet  Google Scholar 

  20. Shu, C.-W.: Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws. Adv. Numer. Approx. Nonlinear Hyperb. Equ. 325–432 (2006)

    Google Scholar 

  21. Kholodov, A.S., Kholodov, Y.A.: Monotonicity criteria for difference schemes designed for hyperbolic equations. Comput. Math. and Math. Phys. 46, 1560–1588 (2006)

    Article  MathSciNet  Google Scholar 

  22. Kholodov, A.S.: The construction of difference schemes of increased order of accuracy for equations of hyperbolic type. USSR Comput. Math. Math. Phys. 20(6), 234–253 (1980)

    Article  Google Scholar 

Download references

Acknowledgments

This work was supported by the Russian Science Foundation, grant number 19-11-00023.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Vasily I. Golubev .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Golubev, V.I., Guseva, E.K., Petrov, I.B. (2022). Application of Quasi-monotonic Schemes in Seismic Arctic Problems. In: Favorskaya, M.N., Nikitin, I.S., Severina, N.S. (eds) Advances in Theory and Practice of Computational Mechanics. Smart Innovation, Systems and Technologies, vol 274. Springer, Singapore. https://doi.org/10.1007/978-981-16-8926-0_20

Download citation

Publish with us

Policies and ethics