The spectral element method for elastic wave equations - Application to 2-D and 3-D seismic problems

International Journal for Numerical Methods in Engineering

Volumn 45, Issue 9, 1999, Pages 1139-1164

  Komatitsch, Dimitri ^a   Vilotte, Jean Pierre ^a   Vai, Rossana ^b   Castillo Covarrubias, JOSÉ M ^b   Sánchez Sesma, Francisco J ^b  

^a INSTITUT DE PHYSIQUE DU GLOBE DE PARIS   (France)

^b UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO   (Mexico)

Author keywords

Elastodynamics; Explicit spectral element method; Seismology

Indexed keywords

EARTHQUAKE ENGINEERING; ELASTIC WAVE; SEISMIC DESIGN; WAVE PROPAGATION;

EID: 0033618332     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0207(19990730)45:9<1139::AID-NME617>3.0.CO;2-T     Document Type: Article

References (61)

1. Virieux J. P-SV wave propagation in heterogeneous media: velocity-stress finite-difference method. Geophysics 1986; 51:889-901.
2. Levander AR. Fourth-order finite-difference P-SV seismograms. Geophysics 1988; 53:1425-1436.
3. Dablain MA. The application of high-order differencing to the scalar wave equation. Geophysics 1986; 51(1):54-66.
4. Bayliss A, Jordan KE, Lemesurier BJ, Turkel E. A fourth-order accurate finite-difference scheme for the computation of elastic waves. Bulletin of the Seismological Society of America 1986; 76:1115-1132.
5. Jih RS, McLaughlin KL, Der ZA. Free-boundary conditions of arbitrary polygonal topography in a two-dimensional explicit elastic finite-difference scheme. Geophysics 1988; 53:1045-1055.
6. Ohminato T, Chouet BA. A free-surface boundary condition for including 3D topography in the finite difference method. Bulletin of the Seismological Society of America 1997; 87:494-515.
7. Frankel A. Three-dimensional simulations of ground motions in the San Bernardino valley, California, for hypothetical earthquakes on the San Andreas fault. Bulletin of the Seismological Society of America 1993; 83;1020-1041.
8. Olsen KB, Archuleta RJ. 3-D simulation of earthquakes on the Los Angeles fault system. Bulletin of the Seismological Society of America 1996; 86(3):575-596.
9. Lysmer J, Drake LA. A finite element method for seismology. In Methods in Computational Physics, vol. 11. Academic Press: New York, 1972.
10. Marfurt KJ. Accuracy of finite-difference and finite-element modeling of the scalar wave equations. Geophysics 1984; 49:533-549.
11. Hulbert GM, Hughes TJR. Space-time finite element methods for second-order hyperbolic equations. Computer Methods in Applied Mechanics and Engineering 1990; 84:327-348.
12. Richter GR. An explicit finite element method for the wave equation. Applied Numerical Mathematics 1994; 16:65-80.
13. Thompson LL, Pinsky P. A space-time finite element method for structural acoustics in infinite domains. Part 1: Formulation, stability and convergence. Computer Methods in Applied Mechanics and Engineering 1996; 132:195-227.
14. Manolis G, Beskos DE. Boundary Element Methods in Elastodynamics. Unwin Hyman: London, 1988.
15. Bonnet M. Équations intégrales et éléments de frontière. CNRS Éditions: Eyrolles, Paris, 1995.
16. Sánchez-Sesma FJ, Rosenblueth E. Ground motion at canyons of arbitrary shape under incident SH waves. Earthquake Engineering and Structural Dynamics 1979; 7:441-450.
17. Sánchez-Sesma FJ, Ramos-Martinez J, Campillo M. An indirect boundary element method applied to simulate the seismic response of alluvial valleys for incident P, SV and Rayleigh waves. Earthquake Engineering and Structural Dynamics 1993; 22:279-295.
18. Aki K, Larner KL, Surface motion of a layered medium having an irregular interface, due to incident plane SH waves. Journal of Geophysical Research 1970; 75:933-954.
19. Bouchon M. Discrete wavenumber representation of elastic wave fields in three space dimensions. Journal of Geophysical Research 1979; 84:3609-3614.
20. Géli L, Bard PY, Julien B. The effect of topography on earthquake ground motion: a review and new results. Bulletin of the Seismological Society of America 1988; 78:42-63.
21. Bouchon M, Aki K. Discrete wavenumber representation of seismic-source wave fields. Bulletin of the Seismological Society of America 1977; 67:259-277.
22. Kawase H, Aki K. A study on the response of a soft sedimentary basin for incident S, P and Rayleigh waves, with special reference to the long duration observed in Mexico City. Bulletin of the Seismological Society of America 1989; 79:1361-1382.
23. Gazdag J. Modeling of the acoustic wave equation with transform methods. Geophysics 1981; 46:854-859.
24. Kosloff D, Baysal E. Forward modeling by the Fourier method. Geophysics 1982; 47:1402-1412.
25. Fornberg B. The pseudospectral method: accurate representation of interfaces in elastic wave calculations. Geophysics 1988; 53:625-637.
26. Kosloff D, Kessler D, Filho AQ, Tessmer E, Behle A, Strahilevitz R. Solution of the equations of dynamics elasticity by a Chebyshev spectral method. Geophysics 1990; 55:748-754.
27. Carcione JM, Wang PJ. A Chebyshev collocation method for the wave equation in generalized coordinates. Computers and Fluid Dynamics Journal 1993; 2:269-290.
28. Carcione JM. Domain decomposition for wave propagation problems. Journal of Scientific Computing 1991; 6(4): 453-472.
29. Patera AT. A spectral element method for fluid dynamics: laminar flow in a channel expansion. Journal of Computational Physics 1984; 54:468-488.
30. Maday Y, Patera AT. Spectral element methods for the incompressible Navier-Stokes equations. In State of the Art Survey in Computational Mechanics, Noor AK, Oden JT (eds). 1989:71-143.
31. Babuška I, Szabó BA, Katz IN. The p version of the finite element method. SIAM Journal on Numerical Analysis 1981; 18:512-545.
32. Priolo E, Carcione JM, Seriani G, Numerical simulation of interface waves by high-order spectral modeling techniques. Journal of the Acoustical Society of America 1994; 95(2):681-693.
33. Faccioli E, Maggio F, Quarteroni A, Tagliani A. Spectral-domain decomposition methods for the solution of acoustic and elastic wave equations. Geophysics 1996; 61(4):1160-1174.
34. Faccioli E, Maggio F, Paolucci R, Quarteroni A. 2D and 3D elastic wave propagation by a pseudo-spectral domain decomposition method. Journal of Seismology 1997; 1:237-251.
35. Orszag SA. Spectral methods for problems in complex geometries. Journal of Computational Physics 1980; 37:70-92.
36. Fischer P. Analysis and application of a parallel spectral element method for the solution of the Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering 1990; 80:483-491.
37. Kawase H. Time-domain response of a semi-circular canyon for incident SV, P and Rayleigh waves calculated by the discrete wavenumber boundary element method. Bulletin of the Seismological Society of America 1988; 78:1415-1437.
38. Sánchez-Sesma FJ, Campillo M. Diffraction of P, SV and Rayleigh waves by topographic features: a boundary integral formulation. Bulletin of the Seismological Society of America 1991; 81:2234-2253.
39. Vai R, Castillo-Covarrubias JM, Sánchez-Sesma FJ, Komatitsch D, Vilotte JP. Elastic wave propagation in an irregularly layered medium. Soil Dynamics and Earthquake Engineering 1999; 18:11-18.
40. Madariaga R. Earthquake source theory: a reviéw. In Earthquakes, Observation Theory and Interpretation, Kanamori H, Boschi E. (eds). North-Holland: Amsterdam, 1983, The Enrico Fermi Summer School of Physics, 55th course.
41. Givoli D. Non-reflecting boundary conditions: review article. Journal of Computational Physics 1991; 94:1-29.
42. Givoli D, Keller JB. Non-reflecting boundary conditions for elastic waves. Wave motion 1990; 12:261-279.
43. Thompson LL, Pinsky P. A space-time finite element method for structural acoustics in infinite domains. Part 2: Exact time-dependent non-reflecting boundary conditions. Computer Methods in Applied Mechanics and Engineering 1996; 132:229-258.
44. Thompson LL. Design and analysis of space-time and Galerkin-least-squares finite element methods for fluid structure interactions in exterior domains. Ph. D. Thesis, Stanford University, California, 1994.
45. Clayton R, Engquist B. Absorbing boundary conditions for acoustic and elastic wave equations. Bulletin of the Seismological Society of America 1977; 67:1529-1540.
46. Stacey R. Improved transparent boundary formulations for the elastic wave equation. Bulletin of the Seismological Society of America 1988; 78(6):2089-2097.
47. Maday Y, Rønquist EM. Optimal error analysis of spectral methods with emphasis on non-constant coefficients and deformed geometries. Computer Methods in Applied Mechanics and Engineering 1990; 80:91-115.
48. Tordjman N. Éléments finis d'ordre élevé avec condensation de masse pour l'équation des ondes. Ph.D. Thesis, Université Paris IX Dauphine, Paris, 1995.
49. Simo JC, Tarnow N, Wong KK. Exact energy-momentum conserving algorithms and symplectic schemes for nonlinear dynamics. Computer Methods in Applied Mechanics and Engineering 1992; 100:63-116.
50. Tarnow N, Simo JC. How to render second order accurate time-stepping algorithms fourth order accurate while retaining the stability and conservation properties. Computer Methods in Applied Mechanics and Engineering 1994; 115: 233-252.
51. Hughes TJR. The Finite Element Method, Linear Static and Dynamic Finite Element Analysis. Prentice-Hall International: Englewood Cliffs, NJ, 1987.
52. Komatitsch D. Méthodes spectrales et éléments spectraux pour l'équation de l'élastodynamique 2D et 3D en milieu hétérogène, Ph. D. Thesis, Institut de Physique du Globe de Paris, Paris, 1997.
53. Komatitsch D, Vilotte JP. The spectral element method: an efficient tool to simulate the seismic response of 2D and 3D geological structures. Bulletin of the Seismological Society of America 1998; 88:368-392.
54. Moczo P, Bystrický E, Kristek J, Carcione JM, Bouchon M. Hybrid modeling of P-SV seismic motion at inhomogeneous viscoelastic topographic structures. Bulletin of the Seismological Society of America 1997; 87:1305-1323.
55. Trifunac MD. Scattering of plane SH waves by a semi-cylindrical canyon. Earthquake Engineering and Structural Dynamics 1973; 1:267-281.
56. Wong HL. Effect of surface topography on the diffraction of P, SV and Rayleigh waves. Bulletin of the Seismological Society of America 1982; 72:1167-1183.
57. Pedersen HA, Sánchez-Sesma FJ, Campillo M. Three-dimensional scattering by two-dimensional topographies. Bulletin of the Seismological Society of America 1994; 84:1169-1183.
58. Bouchon M, Schultz CA, Töksoz MN. Effect of three-dimensional topography on seismic motion. Journal of Geophysical Research 1996; 101:5835-5846.
59. Bouchon M, Barker JS. Seismic response of a hill: the example of Tarzana, California. Bulletin of the Seismological Society of America 1996; 86(1A):66-72.
60. Bonamassa O, Vidale JE. Directional site resonances observed from aftershocks of the 18th October 1989 Loma Prieta earthquake. Bulletin of the Seismological Society of America 1991; 81:1945-1957.
61. Spudich P, Hellweg M, Lee WHK. Directional topographic site response at Tarzana observed in aftershocks of the 1994 Northridge, California, earthquake: implications for mainshock motions. Bulletin of the Seismological Society of America 1996; 86(1B):S193-S208.