Skip to main content
SpringerLink
Log in

Simulation of seismic processes inside the planet using the hybrid grid-characteristic method

  • Published:
Mathematical Models and Computer Simulations Aims and scope

Abstract

The problem of the propagation of seismic waves in the Earth is studied. The authors propose a method to simulate numerically dynamic processes based on the solution to determine the system of elastic body equations by a grid-characteristic method on structural curvilinear computational meshes. A set of calculations of the propagation of a perturbation (set as a local extension area) in a layered two-dimensional Earth model are carried out. Wave patterns and characteristics of wave responses are compared to analytical solutions and the published analogous results.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. H. Jeffreys and K. E. Bullen, Seismological Tables, British Association for the Advancement of Science (Burlington House, London, 1940).

    Google Scholar 

  2. A. M. Dziewonski and D. L. Anderson, “Preliminary reference Earth model,” Phys. Earth Planet. Int. 25, 297–356 (1981).

    Article  Google Scholar 

  3. B. L. N. Kennett and E. R. Engdahl, “Traveltimes for global earthquake location and phase identification,” Geophys. J. Int. 105, 429–465 (1991).

    Article  Google Scholar 

  4. A. Morelli and A. M. Dziewonski, “Body-wave traveltimes and a spherically symmetric Pand S-wave velocity model,” Geophys. J. Int. 112, 178–184 (1993).

    Article  Google Scholar 

  5. B. L. N. Kennett, E. R. Engdahl, and R. Buland, “Constraints on seismic velocities in the Earth from traveltimes,” Geophys. J. Int. 122, 108–124 (1995).

    Article  Google Scholar 

  6. B. Kustowski, G. Ekstrom, and A. M. Dziewonski, “Anisotropic shear-wave velocity structure of the Earth’s mantle: A global model,” J. Geophys. Res. 113, B06306 (2008).

    Google Scholar 

  7. M. A. H. Heldin, P. M. Shearer, and P. S. Earle, “Seismic evidence for small-scale heterogeneity throughout the Earth’s mantle,” Nature 387, 145–150 (1997).

    Article  Google Scholar 

  8. T. Lay, Q. Williams, and E. J. Garnero, “The core-mantle boundary layer and deep Earth dynamics,” Nature 392, 461–468 (1998).

    Article  Google Scholar 

  9. P. R. Cummins, N. Takeuchi, and R. J. Geller, “Computation of complete synthetic seismograms for laterally heterogeneous models using the Direct Solution Method,” Geophys. J. Int. 130, 1–16 (1997).

    Article  Google Scholar 

  10. Z. S. Alterman, J. Aboudi, and F. C. Karal, “Pulse propagation in a laterally heterogeneous solid elastic sphere,” Geophys. J. R. Astron. Soc. 21, 243–260 (1970).

    Article  MATH  Google Scholar 

  11. X. Li and T. Tanimoto, “Waveforms of long-period body waves in a slightly aspherical Earth model,” Geophys. J. Int. 112, 92–102 (1993).

    Article  Google Scholar 

  12. M. E. Wysession and P. J. Shore, “Visualization of whole mantle propagation of seismic shear energy using normal mode summation,” Pure Appl. Geophys. 142, 295–310 (1994).

    Article  Google Scholar 

  13. W. Friederich and J. Dalkolmo, “Complete synthetic seismogram for a spherically symmetric earth by a numerical computation of the Green’s function in the frequency domain,” Geophys. J. Int. 122, 537–550 (1995).

    Article  Google Scholar 

  14. K.-H. Yoon and G. A. McMechan, “Simulation of long-period 3-D elastic responses for whole earth models,” Geophys. J. Int. 120, 721–730 (1995).

    Article  Google Scholar 

  15. H. Igel and M. Weber, “SH-wave propagation in the whole mantle using high-order finite differences,” Geophys. Res. Lett. 22, 731–734 (1995).

    Article  Google Scholar 

  16. H. Igel and M. Weber, “P-SV wave propagation in the Earth’s mantle using finite differences: application to heterogeneous lowermost mantle structure,” Geophys. Res. Lett. 23, 415–418 (1996).

    Article  Google Scholar 

  17. E. Chaljub and A. Tarantola, “Sensitivity of SS precursors to topography of the upper-mantle 660-km discontinuity,” Geophys. Res. Lett. 24, 2613–2616 (1997).

    Article  Google Scholar 

  18. P. R. Cummins, N. Takeuchi, and R. J. Geller, “Computation of complete synthetic seismograms for laterally heterogeneous models using the Direct Solution Method,” Geophys. J. Int. 130, 1–16 (1997).

    Article  Google Scholar 

  19. R. J. Geller and T. Ohminato, “Computation of synthetic seismograms and their partial derivatives for heterogeneous media with arbitrary natural boundary conditions using the Direct Solution Method,” Geophys. J. Int. 116, 421–446 (1994).

    Article  Google Scholar 

  20. D. Komatitsch and J. P. Vilotte, “The spectral element method: an efficient tool to simulate the seismic response of 2D and 3D geological structures,” Bull. Seism. Soc. Am. 88, 368–392 (1998).

    Google Scholar 

  21. E. Chaljub and J. P. Vilotte, “3D wave propagation in a spherical Earth model using the spectral element method,” EOS, Trans. Am. Geophys. 79, 625–626 (1998).

    Google Scholar 

  22. Y. Capdeville, E. Chaljub, J. P. Vilotte, and J. Montagner, “A hybrid numerical method of the spectral element method and the normal modes for realistic 3D wave propagation in the Earth,” EOS, Trans. Am. Geophys. Un. 80, 698–708 (1999).

    Google Scholar 

  23. H. Igel, “Wave propagation in three-dimensional spherical sections by the Chebyshev spectral method,” Geophys. J. Int. 136, 559–566 (1999).

    Article  Google Scholar 

  24. T. Furumura, B. L. N. Kennett, and M. Furumura, “Seismic wavefield calculation for laterally heterogeneous whole earth models using the pseudospectral method,” Geophys. J. Int. 135, 8450860 (1998).

    Google Scholar 

  25. M. Furumura, B. L. N. Kennett, and T. Furumura, “Seismic wavefield calculation for laterally heterogeneous earth models-II. The influence of upper mantle heterogeneity,” Geophys. J. Int. 139, 623–644 (1999).

    Article  Google Scholar 

  26. Ch. Thomas, H. Igel, M. Weber, and F. Scherbaum, “Acoustic simulation of P-wave propagation in a heterogeneous spherical earth: numerical method and application to precursor waves to PKPdf,” Geophys. J. Int. 141, 307–320 (2000).

    Article  Google Scholar 

  27. Y. Wang, H. Takenaka, and T. Furumura, “Modelling seismic wave propagation in a two-dimensional cylindrical whole-earth model using the pseudospectral method,” Geophys. J. Int. 145, 689–708 (2001).

    Article  Google Scholar 

  28. D. Kosloff and E. Baysal, “Forward modeling by a Fourier method,” Geophysics 47, 1402–1412 (1982).

    Article  Google Scholar 

  29. E. F. Toro, M. Kaeser, M. Dumbser, and C. C. Castro, “ADER shock-capturing methods and geo-physical applications,” in Proceedings of the 25th International Symposium on Shock Waves, ISSW25, Bangalore India, 17–22 July, 2005.

    Google Scholar 

  30. K. M. Magomedov and A. S. Kholodov, Grid-Characteristic Numerical Methods (Nauka, Moscow, 1988) [in Russian].

    Google Scholar 

  31. I. B. Petrov, A. V. Favorskaya, A. V. Sannikov, and I. E. Kvasov, “Grid-characteristic method using high-order interpolation on tetrahedral hierarchical meshes with a multiple time step,” Math. Mod. Comput. Simul. 5, 409–415 (2013).

    Article  Google Scholar 

  32. I. E. Kvasov, S. A. Pankratov, and I. B. Petrov, “Numerical simulation of seismic responses in multilayer geologic media by the grid-characteristic method,” Math. Mod. Comput. Simul. 3, 196–204 (2011).

    Article  Google Scholar 

  33. 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).

    Article  MathSciNet  Google Scholar 

  34. V. I. Golubev, I. E. Kvasov, and I. B. Petrov, “Influence of natural disasters on ground facilities,” Math. Mod. Comput. Simul. 4, 129–134 (2012).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow oblast, Russia

    V. I. Golubev, I. B. Petrov & N. I. Khokhlov

Authors
  1. V. I. Golubev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. B. Petrov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. N. I. Khokhlov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. I. Golubev.

Additional information

Original Russian Text © V.I. Golubev, I.B. Petrov, N.I. Khokhlov, 2015, published in Matematicheskoe Modelirovanie, 2015, Vol. 27, No. 2, pp. 139–148.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Golubev, V.I., Petrov, I.B. & Khokhlov, N.I. Simulation of seismic processes inside the planet using the hybrid grid-characteristic method. Math Models Comput Simul 7, 439–445 (2015). https://doi.org/10.1134/S2070048215050051

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S2070048215050051

Keywords

Search

Navigation