Geodesic
Numerical modeling of wave processes in the rocks by grid-characteristic method
Matematičeskoe modelirovanie, Tome 30 (2018) no. 3, pp. 37-51.

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The aim of this work is to study the spatial dynamic of wave propagation in rock formations, taking into account the presence of ravines and caverns. The investigation of dynamics of seismic and acoustic waves from the explosions of different types was done. The seismograms obtained from different reception lines were considered. For the research, a series of numerical experiments using a full-wave joined simulation of acoustic and seismic wave propagation in heterogeneous mixed acoustic and linear-elastic media using grid-characteristic method to mathematically and physically correct describing the spatial dynamic wave processes and taking into account the presence of the boundary and contact surfaces, including the interfaces between the linear-elastic and acoustic environments, were performed. The analysis of the impact of the explosion type on spatial dynamic wave patterns and seismograms in the cases of horizontal and vertical lines of reception was done. The analysis of the impact of the distance between the karst cavities and the ravine on the spatial dynamic wave patterns and seismograms in the cases of horizontal and vertical lines of the reception was done. The basic types of waves that occur in the rocks, ravines and caverns from different types of explosions were investigated. The basic laws that characterize the emerging wave patterns and their impact on the seismograms were obtained.
Keywords: spatial dynamic wave processes, numerical modeling, grid-characteristic method, rock formations, seismograms. 
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A. V. Favorskaya; I. B. Petrov. Numerical modeling of wave processes in the rocks by grid-characteristic method. Matematičeskoe modelirovanie, Tome 30 (2018) no. 3, pp. 37-51. http://geodesic.mathdoc.fr/item/MM_2018_30_3_a2/

[1] Bobet A., Fakhimi A., Johnson S., Morris J., Tonon F., Yeung M. R., “Numerical models in discontinuous media: review of advances for rock mechanics applications”, Journal of Geotechnical and Geoenvironmental Engineering, 135:11 (2009), 1547–1561 | DOI

[2] Pande G., Beer G., Williams J., Numerical methods in rock mechanics, John Wiley and Sons Inc., New York, NY, USA, 1990 | MR

[3] Belytschko T., Plesha M., Dowding C. H., “A computer method for stability analysis of caverns in jointed rock”, International journal for numerical and analytical methods in geomechanics, 8:5 (1984), 473–492 | DOI

[4] Dowding C. H., Belytschko T. B., Yen H. J., “Dynamic computational analysis of openings in jointed rock”, Journal of Geotechnical Engineering, 109:12 (1983), 1551–1566 | DOI

[5] Schwer L. E., Lindberg H. E., “A finite element slideline approach for calculating tunnel response in jointed rock”, International journal for numerical and analytical methods in geomechanics, 16:7 (1992), 529–540 | DOI

[6] Dowding C. H., Belytschko T. B., Yen H. J., “A coupled finite element-rigid block method for transient analysis of rock caverns”, International Journal for Numerical and Analytical Methods in Geomechanics, 7:1 (1983), 117–127 | DOI

[7] Yang J., Liu T., Tang G., Hu T., “Modeling seismic wave propagation within complex structures”, Applied Geophysics, 6:1 (2009), 30–41 | DOI

[8] Favorskaya A. V., Petrov I. B., “Wave responses from oil reservoirs in the Arctic shelf zone”, Doklady Earth Sciences, 466:2 (2016), 214–217 | DOI | MR

[9] Favorskaya A. V., Petrov I. B., Muratov M. V., Biryukov V A., Sannikov A. V., “Grid-Characteristic Method on Unstructured Tetrahedral Grids”, Doklady Mathematics, 90:3 (2014), 781–783 | DOI | MR

[10] Favorskaya A. V., Petrov I. B., Sannikov A. V., Kvasov I. E., “Grid Characteristic Method Using High Order Interpolation on Tetrahedral Hierarchical Meshes with a Multiple Time Step”, Mathematical Models and Computer Simulations, 5:5 (2013), 409–415 | DOI

[11] Golubev V. I., Petrov I. B., Khokhlov N. I., “Numerical simulation of seismic activity by the grid-characteristic method”, Computational Mathematics and Mathematical Physics, 53:10 (2013), 1523–1533 | DOI | MR

[12] Magomedov K. M., Kholodov A. S., Setochno-harakteristicheskie chislennye metody, Nauka, M., 1988, 287 pp. | MR

[13] Ivanov V. D., Kondaurov V. I., Petrov I. B., Kholodov A. S., “Raschet dinamicheskogo deformirovaniya i razrusheniya uprugoplasticheskih tel setochno-harakteristicheskimi metodami”, Mat. model., 2:11 (1990), 10–29

[14] Favorskaya A. V., Petrov I. B., Petrov D. I., Khokhlov N. I., “Numerical modeling of wave processes in layered media in the Arctic region”, Mathematical Models and Computer Simulations, 8:4 (2016), 348–357 | DOI

[15] Friend S., Sinkholes, Pineapple Press Inc., 2002

[16] Neuendorf K. K. E., Glossary of geology, Springer Science Business Media, 2005

[17] Novatzkiy V. K., Teoriya uprugosti, Mir, M., 1975, 872 pp.

[18] LeVeque R., Finite volume methods for hyperbolic problems, Cambridge University Press, 2002 | MR

[19] Landau L. D., Lifshitz E. M., Fluid Mechanics, A Course of Theoretical Physics, 6, Pergamon Press, 1959 | MR

[20] Golubev V. I., “Metodika otobrazheniya i interpretacii rezul'tatov polnovolnovyh sejsmicheskih raschyotov”, Trudy MFTI, 6:1 (2014), 154–161