A new time-space domain high-order finite-difference method for the acoustic wave equation

Journal of Computational Physics

Volumn 228, Issue 23, 2009, Pages 8779-8806

  Liu, Yang ^a,b   Sen, Mrinal K ^b  

^a CHINA UNIVERSITY OF PETROLEUM   (China)

^b UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

Acoustic wave equation; Arbitrary order accuracy; Dispersion analysis; Dispersion relation; Finite difference; Numerical modeling; Optimal finite difference stencil length; Plane wave theory; Second order spatial derivatives; Stability condition; Staggered grid finite difference; Time space domain

Indexed keywords

ACOUSTIC WAVES; ACOUSTICS; DIFFERENCE EQUATIONS; DISPERSION (WAVES); NUMERICAL METHODS; NUMERICAL MODELS; QUANTUM THEORY; STABILITY; WAVE EQUATIONS;

ACOUSTIC WAVE EQUATION; ARBITRARY ORDER; ARBITRARY-ORDER ACCURACY; DISPERSION ANALYSIS; DISPERSION RELATIONS; FINITE DIFFERENCE STENCILS; FINITE-DIFFERENCE; OPTIMAL FINITE-DIFFERENCE STENCIL LENGTH; PLANE WAVE THEORY; SECOND ORDERS; SECOND-ORDER SPATIAL DERIVATIVE; SPATIAL DERIVATIVES; STABILITY CONDITION; STAGGERED-GRID FINITE-DIFFERENCE; STAGGERED-GRIDS; TIME-SPACE DOMAINS;

FINITE DIFFERENCE METHOD;

EID: 70349733389     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2009.08.027     Document Type: Article

References (53)

1. Kelly K.R., Ward R., Treitel W.S., and Alford R.M. Synthetic seismograms: a finite-difference approach. Geophysics 41 (1976) 2-27
2. Lele S.K. Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103 (1992) 16-42
3. Robertsson J.O.A., Blanch J.O., and Symes W.W. Viscoelastic finite-difference modeling. Geophysics 59 (1994) 1444-1456
4. Bansal R., and Sen M.K. Finite-difference modelling of S-wave splitting in anisotropic media. Geophys. Prospect. 56 (2008) 293-312
5. Claerbout J.F. Imaging the Earth's Interior (1985), Blackwell Scientific Publications Inc., Palo Alto, CA
6. Larner K., and Beasley C. Cascaded migrations-improving the accuracy of finite-difference migration. Geophysics 52 (1987) 618-643
7. Li Z. Compensating finite-difference errors in 3-D migration and modeling. Geophysics 56 (1991) 1650-1660
8. Fei T., and Liner C.L. Hybrid Fourier finite difference 3D depth migration for anisotropic media. Geophysics 73 (2008) S27-S34
9. De Basabe J.D., Sen M.K., and Wheeler M.F. The interior penalty discontinuous Galerkin method for elastic wave propagation: grid dispersion. Geophys. J. Int. 175 (2008) 83-93
10. Dablain M.A. The application of high-order differencing to the scalar wave equation. Geophysics 51 (1986) 54-66
11. Fornberg B. The pseudospectral method - comparisons with finite differences for the elastic wave equation. Geophysics 52 (1987) 483-501
12. Vafidis A., Abramovici F., and Kanasewich E.R. Elastic wave propagation using fully vectorized high order finite-difference algorithms. Geophysics 57 (1992) 218-232
13. Liu C., and Liu Z. High order finite difference and multigrid methods for spatially evolving instability in a planar channel. J. Comput. Phys. 106 (1993) 92-100
14. Liu Y., Li C.C., and Mou Y.G. Finite-difference numerical modeling of any even-order accuracy. Oil Geophys. Prospect. 33 (1998) 1-10 (abstract in English)
15. Vanhille C., and Campos-Pozuelo C. A high-order finite-difference algorithm for the analysis of standing acoustic waves of finite but moderate amplitude. J. Comput. Phys. 165 (2000) 334-353
16. You D. A high-order Pade ADI method for unsteady convection-diffusion equations. J. Comput. Phys. 214 (2006) 1-11
17. Chen J.B. High-order time discretizations in seismic modeling. Geophysics 72 (2007) SM115-SM122
18. Etgen J.T., and O'Brien M.J. Computational methods for large-scale 3D acoustic finite-difference modeling: a tutorial. Geophysics 72 (2007) SM223-SM230
19. Liu Y., and Wei X.C. Finite-difference numerical modeling with even-order accuracy in two-phase anisotropic media. Appl. Geophys. 5 (2008) 107-114
20. Madariaga R. Dynamics of an expanding circular fault. Bull. Seism. Soc. Am. 66 (1976) 639-666
21. Virieux J. SH-wave propagation in heterogeneous media: velocity-stress finite-difference method. Geophysics 49 (1984) 1933-1957
22. Virieux J. P-SV wave propagation in heterogeneous media: velocity stress finite difference method. Geophysics 51 (1986) 889-901
23. Yomogida K., and Etgen J.T. 3-D wave propagation in the Los Angeles basin for the Whittier-Narrows earthquake. Bull. Seism. Soc. Am. 83 (1993) 1325-1344
24. Graves R.W. Simulating seismic wave propagation in 3D elastic media using staggered-grid finite differences. Bull. Seism. Soc. Am. 86 (1996) 1091-1106
25. Pitarka A. 3D elastic finite-difference modeling of seismic motion using staggered grids with nonuniform spacing. Bull. Seism. Soc. Am. 89 (1999) 54-68
26. Aoi S., and Fujiwara H. 3-D finite-difference method using discontinuous grids. Bull. Seism. Soc. Am. 89 (1999) 918-930
27. Mittet R. Free-surface boundary conditions for elastic staggered-grid modeling schemes. Geophysics 67 (2002) 1616-1623
28. Rojas O., Day S., Castillo J., and Dalguer L.A. Modelling of rupture propagation using high-order mimetic finite differences. Geophys. J. Int. 172 (2008) 631-650
29. Saenger E.H., Gold N., and Shapiro S.A. Modeling the propagation of elastic waves using a modified finite-difference grid. Wave Motion 31 (2000) 77-92
30. Saenger E.H., and Shapiro S.A. Effective velocities in fractured media: a numerical study using the rotated staggered finite difference grid. Geophys. Prospect. 50 (2002) 183-194
31. Saenger E.H., and Bohlen T. Finite-difference modeling of viscoelastic and anisotropic wave propagation using the rotated staggered grid. Geophysics 69 (2004) 583-591
32. Krüger O.S., Saenger E.H., and Shapiro S. Scattering and diffraction by a single crack: an accuracy analysis of the rotated staggered grid. Geophys. J. Int. 162 (2005) 25-31
33. Emerman S., Schmidt W., and Stephen R. An implicit finite-difference formulation of the elastic wave equation. Geophysics 47 (1982) 1521-1526
34. Ristow D., and Ruhl T. 3-D implicit finite-difference migration by multiway splitting. Geophysics 62 (1997) 554-567
35. Ekaterinaris J.A. Implicit, high-resolution, compact schemes for gas dynamics and aeroacoustics. J. Comput. Phys. 156 (1999) 272-299
36. Nihei T., and Ishii K. A fast solver of the shallow water equations on a sphere using a combined compact difference scheme. J. Comput. Phys. 187 (2003) 639-659
37. Sherer S.E., and Scott J.N. High-order compact finite-difference methods on general overset grids. J. Comput. Phys. 210 (2005) 459-496
38. Tian Z.F., and Dai S.Q. High-order compact exponential finite difference methods for convection-diffusion type problems. J. Comput. Phys. 220 (2007) 952-974
39. Finkelstein B., and Kastner R. Finite difference time domain dispersion reduction schemes. J. Comput. Phys. 221 (2007) 422-438
40. Finkelstein B., and Kastner R. A comprehensive new methodology for formulating FDTD schemes with controlled order of accuracy and dispersion. IEEE Trans. Antenna Propagat. 56 (2008) 3516-3525
41. Liu Y., and Sen M.K. A practical implicit finite-difference method: examples from seismic modeling. J. Geophys. Eng. 6 (2009) 231-249
42. Y. Liu, M.K. Sen, An implicit staggered-grid finite-difference method for seismic modeling, Geophys. J. Int. doi:10.1111/j.1365-246X.2009.04305.x.
43. Fornberg B. Calculation of weights in finite difference formulas. SIAM Rev. 40 (1998) 685-691
44. Holberg O. Computational aspects of the choice of operator and sampling interval for numerical differentiation in large-scale simulation of wave phenomena. Geophys. Prospect. 35 (1987) 625-655
45. Jastram C., and Behle A. Accurate finite-difference operators for modelling the elastic wave equation. Geophys. Prospect. 41 (1993) 453-458
46. Tam C.K.W., and Webb J.C. Dispersion-relation-preserving finite difference schemes for computational acoustics. J. Comput. Phys. 107 (1993) 262-281
47. Hixon R. Nonlinear comparison of high-order and optimized finite-difference schemes. Int. J. Comput. Fluid Dynam. 13 (2000) 259-277
48. Bogey C., and Bailly C. A family of low dispersive and low dissipative explicit schemes for flow and noise computations. J. Comput. Phys. 194 (2004) 194-214
49. Geller R.J., and Takeuchi N. A new method for computing highly accurate DSM synthetic seismograms. Geophys. J. Int. 123 (1995) 449-470
50. Takeuchi N., Geller R.J., and Cummins P.R. Highly accurate P-SV complete synthetic seismograms using modified DSM operators. Geophys. Res. Lett. 23 (1996) 1175-1178
51. Takeuchi N., and Geller R.J. Optimally accurate second order time-domain finite difference scheme for computing synthetic seismograms in 2-D and 3-D media. Phys. Earth Planet. Int. 119 (2000) 99-131
52. JafarGandomi A., and Takenaka H. Non-standard FDTD for elastic wave simulation: two-dimensional P-SV case. Geophys. J. Int. 178 (2009) 282-302
53. Kindelan M., Kamel A., and Sguazzero P. On the construction and efficiency of staggered numerical differentiators for the wave equation. Geophysics 55 (1990) 107-110