Abstract
The aim of this work is to study the spatial dynamic of wave propagation in rock formations, taking into account ravines and caverns. The dynamics of the seismic and acoustic waves generated by explosions of different types is investigated using seismograms measured by several reception lines. The research uses the numerical experiments using the full-wave joint simulation of acoustic and seismic wave propagation in heterogeneous mixed acoustic and linear-elastic media. The grid-characteristic method is used to obtain the mathematically and physically correct description of spatial dynamic wave processes taking the boundary and contact surfaces, including the interfaces between the linearelastic and the acoustic environments, into consideration. The influence of the type of explosion on the spatial dynamic wave patterns and seismograms is analyzed for the cases of horizontal and vertical reception lines. The dependences of spatial dynamic wave patterns and seismograms recorded by the horizontal and vertical reception lines on the distance of the karst caverns from the ravine are studied. The basic types of waves that different types of explosions generate in the rock formations, ravines, and caverns are investigated. The basic laws that characterize the emerging wave patterns and their influence on seismograms are found.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. Bobet, A. Fakhimi, S. Johnson, J. Morris, F. Tonon, and M. R. Yeung, “Numerical models in discontinuous media: review of advances for rock mechanics applications,” J. Geotech. Geoenviron. Eng. 135, 1547–1561 (2009).
G. Pande, G. Beer, and J. Williams, Numerical Methods in Rock Mechanics (Wiley, New York, 1990).
T. Belytschko, M. Plesha, and C. H. Dowding, “A computer method for stability analysis of caverns in jointed rock,” Int. J. Numer. Anal. Methods Geomech. 8, 473–492 (1984).
C. H. Dowding, T. B. Belytschko, and H. J. Yen, “Dynamic computational analysis of openings in jointed rock,” J. Geotech. Eng. 109, 1551–1566 (1983).
L. E. Schwer and H. E. Lindberg, “A finite element slideline approach for calculating tunnel response in jointed rock,” Int. J. Numer. Anal. Methods Geomech. 16, 529–540 (1992).
C. H. Dowding, T. B. Belytschko, and H. J. Yen, “A coupled finite element-rigid block method for transient analysis of rock caverns,” Int. J. Numer. Anal. Methods Geomech. 7, 117–127 (1983).
J. Yang, T. Liu, G. Tang, and T. Hu, “Modeling seismic wave propagation within complex structures,” Appl. Geophys. 6, 30–41 (2009).
A. V. Favorskaya and I. B. Petrov, “Wave responses from oil reservoirs in the Arctic shelf zone,” Dokl. Earth Sci. 466, 214–217 (2016).
A. V. Favorskaya, I. B. Petrov, M. V. Muratov, V. A. Biryukov, and A. V. Sannikov, “Grid-characteristic method on unstructured tetrahedral grids,” Dokl. Math. 90, 781–783 (2014).
A. V. Favorskaya, I. B. Petrov, A. V. Sannikov, and I. E. Kvasov, “Grid characteristic method using high order interpolation on tetrahedral hierarchical meshes with a multiple time step,” Math. Models Comput. Simul. 5, 409–415 (2013).
V. I. Golubev, I. B. Petrov, and N. I. Khokhlov, “Numerical simulation of seismic activity by the grid-characteristic method,” Comput. Math. Math. Phys. 53, 1523–1533 (2013).
K. M. Magomedov and A. S. Kholodov, Grid-Characteristic Numerical Methods (Nauka, Moscow, 1988) [in Russian].
V. D. Ivanov, V. I. Kondaurov, I. B. Petrov, and A. S. Kholodov, “Calculation of dynamic deformation and distructure of elastic-plastic body by grid-characteristic methods,” Mat. Model. 2 (11), 10–29 (1990).
A. V. Favorskaya, I. B. Petrov, D. I. Petrov, and N. I. Khokhlov, “Numerical modeling of wave processes in layered media in the Arctic region,” Math. Models Comput. Simul. 8, 348–357 (2016).
S. Friend, Sinkholes (Pineapple, Sarasota, FL, 2002).
K. K. E. Neuendorf, Glossary of Geology (Springer, New York, 2005).
W. Nowacki, Teoria Sprezystosci (PWN, Warsawa, 1970)
R. LeVeque, Finite Volume Methods for Hyperbolic Problems (Cambridge Univ. Press, Cambridge, 2002).
L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 6: Fluid Mechanics (Nauka, Moscow, 1986; Pergamon, New York, 1987).
V. I. Golubev, “Technique of visualization and interpretation of full-wave seismic modeling results,” Tr. MFTI 6 (1), 154–161 (2014).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A.V. Favorskaya, I.B. Petrov, 2018, published in Matematicheskoe Modelirovanie, 2018, Vol. 30, No. 3, pp. 37–51.
Rights and permissions
About this article
Cite this article
Favorskaya, A.V., Petrov, I.B. Numerical Modeling of Wave Processes in Rocks by the Grid-Characteristic Method. Math Models Comput Simul 10, 639–647 (2018). https://doi.org/10.1134/S207004821805006X
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S207004821805006X