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.
REFERENCES
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
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
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
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
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
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
L. Li, ‘‘Special issue on numerical modeling in civil and mining geotechnical engineering,’’ Processes 10, 1571 (2022). https://doi.org/10.3390/pr10081571
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
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
W. Nowacki, Theory of Elasticity (Wydawnictwo Naukowe, Warszawa, 1970; Mir, Moscow, 1975).
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
V. N. Kukudzhanov, Numerical Solution of Stress Non-One-Dimensional Wave Propagation Problems in Solids (VTs AN SSST, Moscow, 1976) [in Russian].
V. P. Berdennikov, ‘‘Study of the modulus of elasticity of ice,’’ Tr. GGI 7 (61), 13–23 (1948).
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
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
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
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
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
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
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
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
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
J. G. Scholte, ‘‘On the Stoneley wave equation,’’ Proc. Kon. Nederl. Akad. Wetensch. 45, 20–25 (1942).
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
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
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
Corresponding authors
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
About this article
Cite this article
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
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1995080224010189