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

V. I. Golubev ; I. B. Petrov ; N. I. Khokhlov

Matematičeskoe modelirovanie, Tome 27 (2015) no. 2, pp. 139-148.

Résumé

The problem of the seismic wave's propagation in the Earth is studied. Authors proposed a method for numerical simulation of dynamic processes based on the solution of govern system of elastic equations with grid-characteristic method on structural curvilinear meshes. A set of calculations with the elastic perturbation (local extension area) in layered two-dimensional Earth model was carried out. Comparison of wave patterns and characteristics of wave responses with analytical solutions and published analogous results was done.

Détail

Keywords: global sesmic activity, computer simulation, grid-characteristic method, planet model.

Bibliographie

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

[2] A. M. Dziewonski, D. L. Anderson, “Preliminary reference Earth model”, Phys. Earth Planet. Inter., 25 (1981), 297–356 | DOI

[3] B. L. N. Kennett, E. R. Engdahl, “Traveltimes for global earthquake location and phase identification”, Geophysical Journal International, 105:2 (1991), 429–465 | DOI

[4] A. Morelli, A. M. Dziewonski, “Body-wave traveltimes and a spherically symmetric P- and S-wave velocity model”, Geophysical Journal International, 112:2 (1993), 178–184 | DOI

[5] B. L. N. Kennett, E. R. Engdahl, R. Buland, “Constraints on seismic velocities in the Earth from traveltimes”, Geophysical Journal International, 122:1 (1995), 108–124 | DOI

[6] B. Kustowski, G. Ekstrom, A. M. Dziewonski, “Anisotropic shear-wave velocity structure of the Earth's mantle: A global model”, Journal of Geophysical Research, 113 (2008), B06306 | DOI

[7] M. A. H. Heldin, P. M. Shearer, P. S. Earle, “Seismic evidence for small-scale heterogeneity through-out the Earth's mantle”, Nature, 387 (1997), 145–150 | DOI

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

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

[10] Z. S. Alterman, J. Aboudi, F. C. Karal, “Pulse propagation in a laterally heterogeneous solid elastic sphere”, Geophys. J. R. astr. Soc., 21:3 (1970), 243–260 | DOI

[11] X. Li, T. Tanimoto, “Waveforms of long-period body waves in a slightly aspherical Earth model”, Geophys. J. Int., 112:1 (1993), 92–102 | DOI

[12] M. E. Wysession, P. J. Shore, “Visualization of whole mantle propagation of seismic shear energy using normal mode summation”, Pure appl. Geophys., 142:2 (1994), 295–310 | DOI

[13] W. Friederich, 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., 122:2 (1995), 537–550 | DOI

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

[15] H. Igel, M. Weber, “SH-wave propagation in the whole mantle using high-order finite differences”, Geophys. Res. Lett., 22:6 (1995), 731–734 | DOI

[16] H. Igel, M. Weber, “P-SV wave propagation in the Earth's mantle using finite differences: application to heterogeneous lowermost mantle structure”, Geophys. Res. Lett., 23:5 (1996), 415–418 | DOI

[17] E. Chaljub, A. Tarantola, “Sensitivity of SS precursors to topography of the upper-mantle 660-km discontinuity”, Geophys. Res. Lett., 24:21 (1997), 2613–2616 | DOI

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

[19] R. J. Geller, 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., 116:2 (1994), 421–446 | DOI

[20] D. Komatitsch, 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., 88:2 (1998), 368–392

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

[22] Y. Capdeville, E. Chaljub, J. P. Vilotte, 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 (1999), 698–708

[23] H. Igel, “Wave propagation in three-dimensional spherical sections by the Chebyshev spectral method”, Geophys. J. Int., 136:3 (1999), 559–566 | DOI

[24] T. Furumura, B. L. N. Kennett, M. Furumura, “Seismic wavefield calculation for laterally heterogeneous whole earth models using the pseudospectral method”, Geophys. J. Int., 135:3 (1998), 845–860 | DOI

[25] M. Furumura, B. L. N. Kennett, T. Furumura, “Seismic wavefield calculation for laterally heterogeneous earth models. II: The influence of upper mantle heterogeneity”, Geophys. J. Int., 139:3 (1999), 623–644 | DOI

[26] Ch. Thomas, H. Igel, M. Weber, 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., 141:2 (2000), 307–320 | DOI

[27] Y. Wang, H. Takenaka, T. Furumura, “Modelling seismic wave propagation in a two-dimensional cylindrical whole-earth model using the pseudospectral method”, Geophys. J. Int., 145:3 (2001), 689–708 | DOI

[28] D. Kosloff, E. Baysal, “Forward modeling by a Fourier method”, Geophysics, 47:10 (1982), 1402–1412 | DOI

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

[30] K. M. Magomedov, A. S. Kholodov, Setochno-kharakteristicheskie chislennie metody, Nauka, M., 1988, 288 pp.

[31] I. B. Petrov, A. V. Favorskaya, A. V. Sannikov, I. E. Kvasov, “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

[32] I. E. Kvasov, S. A. Pankratov, I. B. Petrov, “Numerical simulation of seismic responses in multilayer geologic media by the grid-characteristic method”, Mathematical Models and Computer Simulations, 3:2 (2011), 196–204 | DOI

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

[34] V. I. Golubev, I. E. Kvasov, I. B. Petrov, “Influence of natural disasters on ground facilities”, Mathematical Models and Computer Simulations, 4:2 (2012), 129–134 | DOI