New curvilinear scheme for elastic wave propagation in presence of curved topography

Geophysical Prospecting

Volumn 59, Issue 5, 2011, Pages 889-906

  Tarrass, Issam ^a   Giraud, Luc ^b   Thore, Pierre ^c  

^a CSTJF   (France)

^b CERFACS   (France)

^c NONE   (United Kingdom)

Author keywords

Computing aspects; Modelling; Topography

Indexed keywords

COMPUTING ASPECTS; DISCRETE SCHEME; DISPERSION ANALYSIS; FREE SURFACES; MATERIAL HETEROGENEITY; MODELLING; NUMERICAL ACCURACY; NUMERICAL NOISE; RUNGE-KUTTA;

OPTIMIZATION; RUNGE KUTTA METHODS; WAVE PROPAGATION;

TOPOGRAPHY;

ELASTIC WAVE; NUMERICAL METHOD; NUMERICAL MODEL; OPTIMIZATION; WAVE MODELING; WAVE PROPAGATION;

EID: 80051885834     PISSN: 00168025     EISSN: 13652478     Source Type: Journal    
DOI: 10.1111/j.1365-2478.2011.00972.x     Document Type: Article

References (55)

1. Alford R.M., Kelly K.R. and Boore D.M. 1974. Accuracy of finite difference modeling of the acoustic wave equation. Geophysics 39, 834-842.
2. Appelö D. and Petersson N.A. 2009. A stable finite difference method for the elastic wave equation on complex geometries with free surfaces. Communications in Computational Physics 5, 84-107.
3. Berland J., Bogey C., Marsden O. and Bailly C. 2007. High-order, low dispersive and low dissipative explicit schemes for multiple-scale and boundary problems. Journal of Computational Physics 224, 637-662.
4. Bogey C. and Bailly C. 2004. A family of low dispersive and low dissipative explicit schemes for flow and noise computations. Journal of Computational Physics 194, 194-214.
5. Bohlen T. and Saenger E.H. 2006. Accuracy of heterogeneous staggered-grid finite-difference modeling of rayleigh waves. Geophysics 71, T109-T115.
6. Boyd J.P. 2006. A proof that the discrete singular convolution (DSC)/Lagrange-distributed approximating function (LDAF) method is inferior to high order finite differences. Journal of Computational Physics 214, 538-549.
7. Brossier R., Virieux J. and Operto S. 2008. Parsimonious finite-volume frequency-domain method for 2-D P-SV-wave modelling. Geophysical Journal International 175, 541-559.
8. Chen J.B. 2006. Modeling the scalar wave equation with Nyström methods. Geophysics 71, T151-T158.
9. Cohen G. and Joly P. 1990. Fourth order schemes for the heterogeneous acoustics equation. Computer Methods in Applied Mechanics and Engineering 80, 397-407.
10. th SEG meeting, San Francisco, California, USA, Expanded Abstracts, 987-991.
11. Dablain M.A. 1986. The application of high-order differencing to the scalar wave equation. Geophysics 51, 54-66.
12. Falk R.S. and Richter G.R. 1999. Explicit finite element methods for symmetric hyperbolic equations. SIAM Journal on Numerical Analysis 36, 935-952.
13. Fornberg B. 1988a. Generation of finite difference formulas on arbitrarily spaced grids. Mathematics of Computation 51, 699.
14. Fornberg B. 1988b. The pseudospectral method: Accurate representation of interfaces in elastic wave calculations. Geophysics 53, 625-637.
15. Ganzha V.G. and Vorozhtsov E.V. 2001. Stability investigation of Runge-Kutta schemes with artificial dissipator on curvilinear grids for the Euler equations. Mathematics and Computers in Simulation 58, 1-35.
16. Garvin W. 1956. Exact transient solution of the buried line source problem. Proceedings of the Royal Society of London Series A 234, 528-541.
17. Gutowski P., Hron F., Wagner D. and Treitel S. 1984. S*. Bulletin of the Seismological Society of America 74, 61-78.
18. Haras Z. and Ta'asan S. 1994. Finite difference schemes for long-time integration. Journal of Computational Physics 114, 265-279.
19. Hestholm S. 1999. Three-dimensional finite difference viscoelastic wave modelling including surface topography. Geophysical Journal International 139, 852-878.
20. Hestholm S. 2003. Elastic wave modeling with free surfaces: Stability of long simulations. Geophysics 68, 314-321.
21. Hestholm S. and Ruud B. 1994. 2D finite-difference elastic wave modelling including surface topography. Geophysical Prospecting 42, 371-390.
22. Hestholm S. and Ruud B. 1998. 3-D finite-difference elastic wave modeling including surface topography. Geophysics 63, 613-622.
23. Hestholm S.O. and Ruud B. 2000. 2D finite-difference viscoelastic wave modelling including surface topography. Geophysical Prospecting 48, 341-373.
24. Holberg O. 1987. Computational aspects of the choice of operator and sampling interval for numerical simulation of wave phenomena. Geophyscal Prospecting 35, 629-655.
25. Hu F.Q., Hussaini M.Y. and Manthey J.L. 1996. Low-dissipation and low-dispersion Runge-Kutta schemes for computational acoustics. Journal of Computational Physics 124, 177-191.
26. Hustedt B., Operto S. and Virieux J. 2004. Mixed-grid and staggered-grid finite-difference methods for frequency-domain acoustic wave modelling. Geophysical Journal International 157, 1269-1296.
27. Kamel A., Sguazzero P. and Kindelan M. 1995. Cost-effective staggered schemes for the numerical simulation of wave propagation. International Journal on Numerical Methods in Engineering 38, 755-773.
28. Käser M. and Iske A. 2005. ADER schemes on adaptive triangular meshes for scalar conservation laws. Journal of Computational Physics 205, 486-508.
29. Kindelan M., Kamel A. and Sguazzero P. 1990. On the construction and efficiency of staggered numerical differentiators for the wave equation. Geophysics 55, 107-110.
30. Komatitsch D., Coutel F. and Mora P. 1996. Tensorial formulation of the wave equation for modelling curved interfaces. Geophysical Journal International 127, 156-168.
31. Komatitsch D. and Tromp J. 1999. Introduction to the spectral element method for three-dimensional seismic wave propagation. Geophysical Journal International 139, 806-822.
32. Komatitsch D. and Vilotte J.P. 1998. 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 88, 368-392.
33. Kristek J., Moczo P. and Archuleta R.J. 2002. Efficient methods to simulate planar free surface in the 3D 4th-order staggered-grid finite-difference schemes. Studia Geophysica et Geodetica 46, 355-381.
34. LeVeque R. 2002. Finite Volume Methods for Hyperbolic Problems. Cambridge University Press.
35. Levy D. and Tadmor E. 1998. From semidiscrete to fully discrete: Stability of Runge-Kutta schemes by the energy method. SIAM Review 40, 40-73.
36. Lombard B., Piraux J., Gelis C. and Virieux J. 2008. Free and smooth boundaries in 2-D finite-difference schemes for transient elastic waves. Geophysical Journal International 172, 252.
37. Magnier S., Mora P. and Tarantola A. 1994. Finite differences on minimal grids. Geophysics 59, 1435-1443.
38. Mittet R. 2002. Free-surface boundary conditions for elastic staggered-grid modeling schemes. Geophysics 67, 1616-1623.
39. Monk P. and Richter G. 2005. A discontinuous Galerkin method for linear symmetric hyperbolic systems in inhomogeneous media. SIAM Journal on Scientific Computing 22, 443-477.
40. Robertsson J.O.A. 1996. A numerical free-surface condition for elastic/viscoelastic finite-difference modeling in the presence of topography. Geophysics 61, 1921-1934.
41. Rodrigues D. 1993. Large scale modeling of seismic wave propagation. PhD thesis, Ecole Centrale des Arts et Manufactures.
42. Ruud B. and Hestholm S. 2001. 2D surface topography boundary conditions in seismic wave modelling. Geophysical Prospecting 49, 445-460.
43. Strikwerda J.C. 2004. Finite Difference Schemes and Partial Differential Equations, 2 edn. SIAM.
44. Tal-Ezer H. 1986. Spectral methods in time for hyperbolic equations. SIAM Journal on Numerical Analysis 23, 11-26.
45. Tam C., Webb J. and Dong Z. 1993. A study of the short wave components in computational acoustics. Journal on Computational Acoustics 1, 1-30.
46. Tam C.K. and Webb J.C. 1993. Dispersion-Relation-Preserving finite difference schemes for computational acoustics. Journal of Computational Physics 107, 262-281.
47. Tessmer E., Kosloff D. and Behle A. 1992. Elastic wave propagation simulation in the presence of surface topography. Geophysical Journal International 108, 621-632.
48. Titarev V.A. and Toro E.F. 2005. ADER schemes for three-dimensional non-linear hyperbolic systems. Journal of Computational Physics 204, 715-736.
49. th International Conference on Nonlinear Hyperbolic Problems, Expanded Abstracts.
50. Vichnevetsky R. and Bowles J. 1982. Fourier Analysis of Numerical Approximations of Hyperbolic Equations. SIAM.
51. Vichnevetsky R. and Schutter F.D. 1975. A frequency analysis of finite difference and finite-element methods for initial value problems. AICA, Dept. of Computer Science, Rutgers University.
52. Virieux J. 1986. P-SV wave propagation in heterogeneous media: Velocity-stress finite-difference method. Geophysics 51, 889-901.
53. Wells V. and Renaut R. 1997. Computing aerodynamically generated noise. Annual Review of Fluid Mechanics 29, 161-199.
54. Zhang W. and Chen X. 2006. Traction image method for irregular free surface boundaries in finite difference seismic wave simulation. Geophysical Journal International 167, 337-353.
55. Zingg D.W., Lomax H. and Jurgens H. 1996. High-accuracy finite-difference schemes for linear wave propagation. SIAM Journal on Scientific Computing 17, 328-346.