On accuracy of the finite-difference and finite-element schemes with respect to P-wave to S-wave speed ratio

Geophysical Journal International

Volumn 182, Issue 1, 2010, Pages 493-510

  Moczo, Peter ^a   Kristek, Jozef ^a   Galis, Martin ^a   Pazak, Peter ^b  

^a Faculty of Natural Sciences   (Slovakia)

^b INSTITUTE OF CHEMISTRY   (Slovakia)

Author keywords

Computational seismology; Numerical approximations and analysis; Theoretical seismology

Indexed keywords

FINITE DIFFERENCE METHOD; FINITE ELEMENT METHOD; NUMERICAL MODEL; P-WAVE; S-WAVE; SEISMIC VELOCITY; WAVE PROPAGATION;

EID: 77954636473     PISSN: 0956540X     EISSN: 1365246X     Source Type: Journal    
DOI: 10.1111/j.1365-246X.2010.04639.x     Document Type: Article

References (60)

1. Alford RM, Kelly KR, Boore DM. Accuracy of finite-difference modeling of the acoustic wave equation. Geophysics 1974, 39:834-842.
2. Alterman Z, Karal FC. Propagation of elastic waves in layered media by finite-difference methods. Bull. seism. Soc. Am. 1968, 58:367-398.
3. Alterman Z, Loewenthal D. Seismic waves in a quarter and three-quarter plane. Geophys. J. R. astr. Soc. 1970, 20:101-126.
4. Alterman Z, Rotenberg A. Seismic waves in a quarter plane. Bull. seism. Soc. Am. 1969, 59:347-368.
5. Andrews DJ. A numerical study of tectonic stress release by underground explosions. Bull. seism. Soc. Am. 1973, 63:1375-1391.
6. Bamberger A, Chavent G, Lailly P. Etude de schémas numériques pour les équations de l élastodynamique linéaire. 1980, Technical Report 41, INRIA, 1980
7. Bielak J, Loukakis K, Hisada Y, Yoshimura Ch. Domain reduction method for three-dimensional earthquake modeling in localized regions. Part I: theory. Bull. seism. Soc. Am. 2003, 93:817-824.
8. Boore DM. Love waves in non-uniform waveguides: finite difference calculations. J. geophys. Res. 1970, 75:1512-1527.
9. Boore DM. Finite-difference methods for seismic wave propagation in heterogeneous materials. Methods in Computational Physics 1972, Vol. 11:1-37. Bolt BA. ed, Academic Press, New York
10. Chaljub E, Komatitsch D, Vilotte J-P, Capdeville Y, Valette B, Festa G. Spectral element analysis in seismology. Advances in Wave Propagation in Heterogeneous Earth: Advances in Geophysics 2007, Vol. 48:365-419. Wu R-S, Maupin V, eds, ed. Dmowska R., Elsevier - Academic Press, Oxford
11. Crase E, Wideman Ch, Noble M, Tarantola A. Nonlinear elastic waveform inversion of land seismic reflection data. J. geophys. Res. 1992, 97:4685-4703.
12. Day SM. Finite element analysis of seismic scattering problems. 1977, PhD thesis, University of California, San Diego
13. Day SM. Three-dimensional simulation of spontaneous rupture: the effect of non-uniform prestress. Bull. seism. Soc. Am. 1982, 72:1881-1902.
14. de la Puente J, Käser M, Dumbser M, Igel H. An arbitrary high order discontinuous Galerkin method for elastic waves on unstructured meshes IV: anisotropy. Geophys. J. Int. 2007, 169:1210-1228.
15. de la Puente J, Dumbser M, Käser M, Igel H. Discontinuous Galerkin methods for wave propagation in poroelastic media. Geophysics 2008, 73:T77-T97.
16. Dumbser M, Käser M. An arbitrary high order discontinuous Galerkin method for elastic waves on unstructured meshes II: the three-dimensional case. Geophys. J. Int. 2006, 167:319-336.
17. Dumbser M, Käser M, Toro E. An arbitrary high order discontinuous Galerkin method for elastic waves on unstructured meshes V: local time stepping and p-adaptivity. Geophys. J. Int. 2007, 171:695-717.
18. Geller RJ, Takeuchi N. A new method for computing highly accurate DSM synthetic seismograms. Geophys. J. Int. 1995, 123:449-470.
19. Geller RJ, Takeuchi N. Optimally accurate second-order time-domain finite difference scheme for the elastic equation of motion: one-dimensional case. Geophys. J. Int. 1998, 135:48-62.
20. Graves RW. Simulating seismic wave propagation in 3D elastic media using staggered-grid finite differences. Bull. seism. Soc. Am. 1996, 86:1091-1106.
21. Hughes TJR. The Finite Element Method Linear Static and Dynamic Finite Element Method Analysis 2000, Dover Publications Inc., New York
22. Igel H, Mora P, Riollet B. Anisotropic wave propagation through finite-difference grids. Geophysics 1995, 60:1203-1216.
23. Ilan A, Ungar A, Alterman ZS. An improved representation of boundary conditions in finite difference schemes for seismological problems. Geophys. J. R. astr. Soc. 1975, 43:727-745.
24. Käser M, Dumbser M. An arbitrary high order discontinuous Galerkin method for elastic waves on unstructured meshes I: the two-dimensional isotropic case with external source terms. Geophys. J. Int. 2006, 166:855-877.
25. Käser M, Dumbser M, de la Puente J, Igel H. An arbitrary high order discontinuous Galerkin method for elastic waves on unstructured meshes III: viscoelastic attenuation. Geophys. J. Int. 2007, 168:224-242.
26. Käser M, Hermann V, de la Puente J. Quantitative accuracy analysis of the discontinuous Galerkin method for seismic wave propagation. Geophysical J. Int. 2008, 173:990-999.
27. Kelly KR, Ward RW, Treitel S, Alford RM. Synthetic seismograms: a finite-difference approach. Geophysics 1976, 41:2-27.
28. Klimeš L. Accuracy of elastic finite differences in smooth media. Pageoph 1996, 148:39-76.
29. Komatitsch D, Vilotte J-P. The spectral-element method: an efficient tool to simulate the seismic response of 2D and 3D geological structures. Bull. seism. Soc. Am. 1998, 88:368-392.
30. Komatitsch D, Tromp J. Introduction to the spectral element method for three-dimensional seismic wave propagation. Geophys. J. Int. 1999, 139:806-822.
31. Komatitsch D, Martin R, Tromp J, Taylor MA, Wingate BA. Wave propagation in 2-D elastic media using a spectral element method with triangles and quadrangles. J. comput. Acoustics 2001, 9:703-718.
32. Kristek J, Moczo P. On the accuracy of the finite-difference schemes: the 1D elastic problem. Bull. seism. Soc. Am. 2006, 96:2398-2414.
33. Levander A. Fourth-order finite-difference P-SV seismograms. Geophysics 1988, 53:1425-1436.
34. Luo Y, Schuster G. Parsimonious staggered grid finite-differencing of the wave equation. Geophys. Res. Lett. 1990, 17:155-158.
35. Lysmer J. Lumped mass method for Rayleigh waves. Bull. seism. Soc. Am. 1970, 60:89-104.
36. Lysmer J, Drake LA. The propagation of Love waves across non-horizontally layered structures. Bull. seism. Soc. Am. 1971, 61:1233-1252.
37. Lysmer J, Drake LA. A finite element method for seismology. Methods in Computational Physics 1972, Vol. 11:181-216. Bolt BA, ed, Academic Press, New York
38. Ma S, Liu P. Modeling of the perfectly matched layer absorbing boundaries and intrinsic attenuation in explicit finite-element methods. Bull. seism. Soc. Am. 2006, 96:1779-1794.
39. Magnier S-A, Mora P, Tarantola A. Finite differences on minimal grids. Geophysics 1994, 59:1435-1443.
40. Marfurt KJ. Accuracy of finite-difference and finite-element modeling of the scalar and elastic wave equations. Geophysics 1984, 49:533-549.
41. Moczo P, Kristek J, Bystrický E. Stability and grid dispersion of the P-SV 4th-order staggered-grid finite-difference schemes. Studia Geophys. Geod. 2000a, 44:381-402.
42. Moczo P, Kristek J, Halada L. 3D 4th-order staggered-grid finite-difference schemes: stability and grid dispersion. Bull. seism. Soc. Am. 2000b, 90:587-603.
43. Moczo P, Kristek J, Vavryčuk V, Archuleta RJ, Halada L. 3D heterogeneous staggered-grid finite-difference modeling of seismic motion with volume harmonic and arithmetic averaging of elastic moduli and densities. Bull. seism. Soc. Am. 2002, 92:3042-3066.
44. Moczo P, Kristek J, Galis M, Pazak P, Balazovjech M. The finite-difference and finite-element modeling of seismic wave propagation and earthquake motion. Acta Phys. Slovaca 2007a, 57:177-406.
45. Moczo P, Robertsson JOA, Eisner L. The finite-difference time-domain method for modeling of seismic wave propagation. Advances in Wave Propagation in Heterogeneous Earth: Advances in Geophysics 2007b, Vol. 48:421-516. Wu R-S, Maupin V, Dmowska R. eds, in the series, Elsevier, /Academic Press, San Diego
46. Olsen KB, Archuleta RJ, Matarese JR. Magnitude 7.75 earthquake on the San Andreas fault: three-dimensional ground motion in Los Angeles. Science 1995, 270:1628-1632.
47. Pitarka A. 3D elastic finite-difference modeling of seismic motion using staggered grids with nonuniform spacing. Bull. seism. Soc. Am. 1999, 89:54-68.
48. Rodrigues D, Mora P. Analysis of a finite-difference solution to the three-dimensional elastic wave equation. 1992, 1247-1249. in the, Expanded Abstracts
49. Saenger EH, Bohlen T. Finite-difference modeling of viscoelastic and anisotropic wave propagation using the rotated staggered grid. Geophysics 2004, 69:583-591.
50. Saenger EH, Gold N, Shapiro SA. Modeling the propagation of elastic waves using a modified finite-difference grid. Wave Motion 2000, 31:77-92.
51. Seriani G, Priolo E. High-order spectral element method for acoustic wave modeling. Expanded abstracts of the Soc. Expl. Geophys. 1991, 1561-1564.
52. Seriani G, Priolo E. A spectral element method for acoustic wave simulation in heterogeneous media. Finite Elem. in Anal. and Des. 1994, 16:337-348.
53. Smith WD. The application of finite element analysis to body wave propagation problems. Geophys. J. 1975, 42:747-768.
54. Stephen RA. A comparison of finite difference and reflectivity seismograms for marine models. Geophys. J. R. astr. Soc. 1983, 72:39-57.
55. Takeuchi N, Geller RJ. Optimally accurate second order time-domain finite difference scheme for computing synthetic seismograms in 2-D and 3-D media. Phys. Earth planet. Int. 2000, 119:99-131.
56. Virieux J. SH-wave propagation in heterogeneous media: velocity-stress finite-difference method. Geophysics 1984, 49:1933-1957.
57. Virieux J. P-SV wave propagation in heterogeneous media: velocity-stress finite-difference method. Geophysics 1986, 51:889-901.
58. Yoshimura Ch, Bielak J, Hisada Y, Fernández A. Domain reduction method for three-dimensional earthquake modeling in localized regions, Part II: verification and applications. Bull. seism. Soc. Am. 2003, 93:825-840.
59. Zhang J. Quadrangle-grid velocity-stress finite-difference method for elastic-wave-propagation simulation. Geophys. J. Int. 1997, 131:127-134.
60. Zienkiewicz OC, Taylor RL. The Finite Element Method 1989, Vol. 1. 4th edn, McGraw-Hill