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Investigation of Wave Phenomena in the Offshore Areas of the Arctic Region in the Process of the Seismic Survey

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Abstract

Rich with fossil minerals, offshore areas of the Arctic region attract a lot of attention from researchers, which creates the necessity to investigate the structure of the subsurface space. This work is dedicated to the simulation of one of the standard methods used, which is seismic survey. The computational domain was constructed by taking into account the main features of the offshore areas: heterogeneous ice field, water, and layered ground with an oil reservoir. The linear elasticity model was chosen as the governing system of equations and solved using the grid-characteristic method on rectangle grids. Ice was simulated using the Maxwell viscoelastic model and the Kukudzhanov elastoviscoplastic model, taking into account the temperature dependence of its Young’s modulus. The results reconstruct different wave phenomena, such as Rayleigh waves, Scholte waves, reflected from the reservoir wave front, and seismic ghost reflections, which can be used for the analysis of the structure of geological layered media.

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REFERENCES

  1. I. B. Petrov, ‘‘Problems of simulation of natural and anthropogenous processes in the Arctic zone of the Russian Federation,’’ Mat. Model. 30 (7), 103–136 (2018). https://doi.org/10.31857/S023408790000579-0

    Article  Google Scholar 

  2. R. Staroszczyk, ‘‘Formation and types of natural ice masses,’’ in Ice Mechanics for Geophysical and Civil Engineering Applications. GeoPlanet: Earth and Planetary Sciences (2018), pp. 7–19. https://doi.org/10.1007/978-3-030-03038-4_2

  3. B. Michel and R. O. Ramseier, ‘‘Classification of river and lake ice,’’ Can. Geotech. J. 8, 36–45 (1971). https://doi.org/10.1139/t71-004

    Article  Google Scholar 

  4. G. W. Timco and W. F. Weeks, ‘‘A review of the engineering properties of sea ice,’’ Cold Regions Sci. Technol. 60, 107–129 (2010). https://doi.org/10.1016/j.coldregions.2009.10.003

    Article  Google Scholar 

  5. 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 

  6. P. V. Stognii, N. I. Khokhlov, I. B. Petrov, and A. V. Favorskaya, ‘‘The comparison of two approaches to modeling the seismic waves spread in the heterogeneous 2D medium with gas cavities,’’ in Smart Modeling for Engineering Systems, Ed. by M. N. Favorskaya, A. V. Favorskaya, I. B. Petrov, and L. C. Jain, Smart Innov. Syst. Technol. 214, 101–114 (2021). https://doi.org/10.1007/978-981-33-4709-0_9

  7. 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 

  8. P. V. Stognii, D. I. Petrov, N. I. Khokhlov, and I. B. Petrov, ‘‘Simulation of seismic processes in geological exploration of Arctic shelf,’’ Russ. J. Numer. Anal. Math. Model. 32, 381–392 (2017). https://doi.org/10.1515/rnam-2017-0036

    Article  MathSciNet  Google Scholar 

  9. D. I. Petrov, I. B. Petrov, A. V. Favorskaya, N. I. Khokhlov, and I. B. Petrov, ‘‘Numerical solution of seismic exploration problems in the Arctic region by applying the grid-characteristic method,’’ Comput. Math. Math. Phys. 56, 1128–1141 (2016). https://doi.org/10.1134/S0965542516060208

    Article  MathSciNet  Google Scholar 

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

  11. I. Argatov, ‘‘Mathematical modeling of linear viscoelastic impact: Application to drop impact testing of articular cartilage,’’ Tribol. Int. 63, 213–225 (2012). https://doi.org/10.1134/S1995423912020140

    Article  Google Scholar 

  12. V. N. Kukudzhanov, Numerical Solution of Stress Non-One-Dimensional Wave Propagation Problems in Solids (VTs AN SSST, Moscow, 1976) [in Russian].

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

    Google Scholar 

  14. V. I. Golubev, E. K. Guseva, and I. B. Petrov, ‘‘Application of quasi-monotonic schemes in seismic arctic problems,’’ in Advances in Theory and Practice of Computational Mechanics, Ed. by M. N. Favorskaya, I. S. Nikitin, and N. S. Severina, Smart Innov. Syst. Technol. 27, 289–307 (2022). https://doi.org/10.1007/978-981-16-8926-0_20

  15. 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 

  16. I. B. Petrov, ‘‘Grid-characteristic methods. 55 years of developing 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 

  17. E. Pesnya, A. A. Kozhemyachenko, and A. V. Favorskaya, ‘‘Application of implicit grid-characteristic methods for modeling wave processes in linear elastic media,’’ in Intelligent Decision Technologies, Ed. by I. Czarnowski, R. J. Howlett, and L. C. Jain, Smart Innov. Syst. Technol. 238, 151–160 (2021). https://doi.org/10.1007/978-981-16-2765-1_12

  18. A. V. Favorskaya, A. V. Breus, and B. V. Galitskii, ‘‘Application of the grid-characteristic method to the seismic isolation model,’’ in Smart Modeling for Engineering Systems. GCM50 2018, Ed. by I. Petrov, A. Favorskaya, M. Favorskaya, S. Simakov, and L. Jain, Smart Innov. Syst. Technol. 133, 167–181 (2019). https://doi.org/10.1007/978-3-030-06228-6_15

  19. 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 

  20. 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 

  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. 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 

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

    MathSciNet  Google Scholar 

  24. G. Marra, C. Clivati, R. Luckett, A. Tampellini, J. Kronjger, L. Wright, A. Mura, F. Levi, S. Robinson, A. Xuereb, B. Baptie, and D. Calonico, ‘‘Ultrastable laser interferometry for earthquake detection with terrestrial and submarine cables,’’ Science (Washington, DC, U. S.) 361 (6401), 486–490 (2018). https://doi.org/10.1126/science.aat4458

    Article  Google Scholar 

  25. G. Marra, D. M. Fairweather, V. Kamalov, P. Gaynor, M. Cantono, S. Mulholland, B. Baptie, J. C. Castellanos, G. Vagenas, J.-O. Gaudron, J. Kronjäger, I. R. Hill, M. Schioppo, I. Barbeito Edreira, K. A. Burrows, C. Clivati, D. Calonico, and A. Curtis, ‘‘Optical interferometry-based array of seafloor environmental sensors using a transoceanic submarine cable,’’ Science (Washington, DC, U. S.) 376 (6595), 874–879 (2022). https://doi.org/10.1126/science.abo1939

    Article  Google Scholar 

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Funding

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

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

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Guseva, E.K., Golubev, V.I. & Petrov, I.B. Investigation of Wave Phenomena in the Offshore Areas of the Arctic Region in the Process of the Seismic Survey. Lobachevskii J Math 45, 223–230 (2024). https://doi.org/10.1134/S1995080224010189

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