Numerical study of the interface errors of finite-difference simulations of seismic waves

Geophysics

Volumn 79, Issue 4, 2013, Pages T219-T232

  Vishnevsky, Dmitry ^a   Lisitsa, Vadim ^b   Tcheverda, Vladimir ^a,c   Reshetova, Galina ^c,d  

^a TROFIMUK INSTITUTE OF PETROLEUM GEOLOGY AND GEOPHYSICS   (Russian Federation)

^b NOVOSIBIRSK STATE UNIVERSITY   (Russian Federation)

^c Kazakhstan Britan Technical University   (Kazakhstan)

^d INSTITUTE OF COMPUTATIONAL MATHEMATICS AND MATHEMATICAL GEOPHYSICS   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

FINITE DIFFERENCE METHOD; SEISMIC WAVES; SEISMOLOGY; WAVE PROPAGATION;

FINITE DIFFERENCE SCHEME; FINITE DIFFERENCE SIMULATIONS; FLUID-SOLID INTERFACES; NUMERICAL DISPERSIONS; ORDER OF CONVERGENCE; SECOND ORDER CONVERGENCE; SOLID-SOLID INTERFACES; STAGGERED GRID SCHEMES;

ERRORS;

CONVERGENCE; FINITE DIFFERENCE METHOD; HOMOGENEOUS MEDIUM; NUMERICAL MODEL; SEISMIC VELOCITY; SEISMIC WAVE; WAVE PROPAGATION;

EID: 84910062815     PISSN: 00168033     EISSN: 19422156     Source Type: Journal    
DOI: 10.1190/GEO2013-0299.1     Document Type: Article

References (50)

1. Aki, K., and P. G. Richards, 1980, Quantitative seismology, theory and methods: Freeman.
2. Alford, R. M., K. R. Kelly, and D. M. Boore, 1974, Accuracy of finite-difference modeling of the acoustic wave equation: Geophysics, 39, 834-842, doi: 10.1190/1.1440470.
3. Asvadurov, S., V. Druskin, and S. Moskow, 2007, Optimal grids for anisotropic problems: Electronic Transactions on Numerical Analysis, 26, 55-81.
4. Backus, G. E., 1962, Long-wave elastic anisotropy produced by horizontal layering: Journal of Geophysical Research, 67, 4427-4440, doi: 10.1029/JZ067i011p04427.
5. Bernth, H., and C. Chapman, 2011, A comparison of the dispersion relations for anisotropic elastodynamic finite-difference grids: Geophysics, 76, no. 3, WA43-WA50, doi: 10.1190/1.3555530.
6. Brossier, R., J. Virieux, and S. Operto, 2008, Parsimonious finite volume frequency-domain method for 2-D P-SV-wave modelling: Geophysical Journal International, 175, 541-559, doi: 10.1111/j.1365-246X.2008.03839.x.
7. Cohen, G., and P. Joly, 1996, Construction analysis of fourth-order finite difference schemes for the acoustic wave equation in nonhomogeneous media: SIAM Journal on Numerical Analysis, 33, 1266-1302, doi: 10.1137/S0036142993246445.
8. Dablain, M. A., 1986, The application of high-order differencing to the scalar wave equation: Geophysics, 51, 54-66, doi: 10.1190/1.1442040.
9. Davydycheva, S., V. Druskin, and T. Habashy, 2003, An efficient finitedifference scheme for electromagnetic logging in 3D anisotropic inhomogeneous media: Geophysics, 68, 1525-1536, doi: 10.1190/1.1620626.
10. Dumbser, M., and M. Kaser, 2006, An arbitrary high-order discontinuous Galerkin method for elastic waves on unstructured meshes II. The three-dimensional isotropic case: Geophysical Journal International, 167, 319-336, doi: 10.1111/j.1365-246X.2006.03120.x.
11. Etienne, V., E. Chaljub, J. Virieux, and N. Glinsky, 2010, An hp-adaptive discontinuous Galerkin finite-element method for 3D elastic wave modelling: Geophysical Journal International, 183, 941-962, doi: 10.1111/j .1365-246X.2010.04764.x.
12. Grote, M. J., A. Schneebeli, and D. Schotzau, 2006, Discontinuous Galerkin finite element method for the wave equation: SIAM Journal on Numerical Analysis, 44, 2408-2431, doi: 10.1137/05063194X.
13. Gustafsson, B., and E. Mossberg, 2004, Time compact high order difference methods for wave propagation: SIAM Journal on Scientific Computing, 26, 259-271, doi: 10.1137/030602459.
14. Gustafsson, B., and P.Wahlund, 2004, Time compact difference methods for wave propagation in discontinuous media: SIAM Journal on Scientific Computing, 26, 272-293, doi: 10.1137/S1064827503425900.
15. Hestholm, S., and B. Ruud, 2002, 3D free-boundary conditions for coordinate- transform finite-difference seismic modelling: Geophysical Prospecting, 50, 463-474, doi: 10.1046/j.1365-2478.2002.00327.x.
16. Hestholm, S. O., and B. Ruud, 2000, 2D finite-difference viscoelastic wave modelling including surface topography: Geophysical Prospecting, 48, 341-373, doi: 10.1046/j.1365-2478.2000.00185.x.
17. Kaser, M., and M. Dumbser, 2006, An arbitrary high-order discontinuous Galerkin method for elastic waves on unstructured meshes - I. The two-dimensional isotropic case with external source terms: Geophysical Journal International, 166, 855-877, doi: 10.1111/j.1365-246X.2006.03051.x.
18. Kelly, K. R., R. W. Ward, S. Treitel, and R. M. Alford, 1976, Synthetic seismograms: A finite-difference approach: Geophysics, 41, 2-27, doi: 10.1190/1.1440605.
19. Komatitsch, D., and J.-P. Vilotte, 1998, The spectral element meth: An efficient tool to simulate the seismic response of 2D and 3D geological structures: Bulletin of the Seismological Society of America, 88, 368-392.
20. Kummer, B., A. Behle, and F. Dorau, 1987, Hybrid modeling of elasticwave propagation in two-dimensional laterally inhomogeneous media: Geophysics, 52, 765-771, doi: 10.1190/1.1442343.
21. Lebedev, V. I., 1964, Difference analogues of orthogonal decompositions of basic differential operators and some boundary value problems. I: Computational Mathematics and Mathematical Physics, 4, 449-465, doi: 10.1016/0041-5553(64)90240-X.
22. Levander, A. R., 1988, Fourth-order finite-difference P-SV seismograms: Geophysics, 53, 1425-1436, doi: 10.1190/1.1442422.
23. Lisitsa, V., and E. Lys, 2010, Reflectionless truncation of target area for axially symmetric anisotropic elasticity: Journal of Computational and Applied Mathematics, 234, 1803-1809, doi: 10.1016/j.cam.2009.08.031.
24. Lisitsa, V., O. Podgornova, and V. Tcheverda, 2010, On the interface error analysis for finite difference wave simulation: Computational Geosciences, 14, 769-778, doi: 10.1007/s10596-010-9187-1.
25. Lisitsa, V., V. Tcheverda, and D. Vishnevsky, 2012, Numerical simulation of seismic waves in models with anisotropic formations: Coupling Virieux and Lebedev finite-difference schemes: Computational Geosciences, 16, 1135-1152, doi: 10.1007/s10596-012-9308-0.
26. Lisitsa, V., and D. Vishnevskiy, 2010, Lebedev scheme for the numerical simulation of wave propagation in 3D anisotropic elasticity: Geophysical Prospecting, 58, 619-635, doi: 10.1111/j.1365-2478.2009.00862.x.
27. Min, D.-J., C. Shin, B.-D. Kwon, and S. Chung, 2000, Improved frequencydomain elastic wave modeling using weighted-averaging difference operators: Geophysics, 65, 884-895, doi: 10.1190/1.1444785.
28. Moczo, P., J. Kristek, M. Galis, E. Chaljub, and V. Etienne, 2011, 3-D finitedifference, finite-element, discontinuous-Galerkin and spectral-element schemes analysed for their accuracy with respect to P-wave to S-wave speed ratio: Geophysical Journal International, 187, 1645-1667, doi:10.1111/j.1365-246X.2011.05221.x.
29. Moczo, P., J. Kristek, M. Galis, and P. Pazak, 2010, On accuracy of the finite- difference and finite-element schemes with respect to P-wave to Swave speed ratio: Geophysical Journal International, 182, 493-510, doi:10.1111/j.1365-246X.2010.04639.x.
30. Moczo, P., J. Kristek, V. Vavrycuk, R. J. Archuleta, and L. Halada, 2002, 3D heterogeneous staggered-grid finite-difference modeling of seismic motion with volume harmonic and arithmetic averaging of elastic moduli and densities: Bulletin of the Seismological Society of America, 92, 3042-3066, doi: 10.1785/0120010167.
31. Muir, F., J. Dellinger, J. Etgen, and D. Nichols, 1992, Modeling elastic fields across irregular boundaries: Geophysics, 57, 1189-1193, doi: 10.1190/1.1443332.
32. Pissarenko, D., G. V. Reshetova, and V. A. Tcheverda, 2009, 3D finitedifference synthetic acoustic logging in cylindrical coordinates: Geophysical Prospecting, 57, 367-377, doi: 10.1111/j.1365-2478.2008.00743.x.
33. Podgornova, O., and V. Lisitsa, 2010, Accuracy analysis of finite-difference staggered-grid numerical schemes for elastic-elastic and fluid-elastic interfaces:80th Annual International Meeting, SEG, Expanded Abstracts, 3087-3091.
34. Podgornova, O., V. Lisitsa, and D. Vishnevsky, 2010, Traveltime and reflection coefficients accuracy of staggered-grid finite-difference simulation of seismic waves: 72nd Annual International Conference and Exhibition, EAGE, Extended Abstracts, C042.
35. Saenger, E. H., N. Gold, and S. A. Shapiro, 2000, Modeling the propagation of the elastic waves using a modified finite-difference grid: Wave Motion, 31, 77-92, doi: 10.1016/S0165-2125(99)00023-2.
36. Samarskii, A. A., 2001, The theory of difference schemes: CRC Press, Pure and Applied Mathematics, vol. 240.
37. Schoenberg, M., and F. Muir, 1989, A calculus for finely layered anisotropic media: Geophysics, 54, 581-589, doi: 10.1190/1.1442685.
38. Stephen, R. A., 1983, A comparison of finite difference and reflectivity seismograms for marine models: Geophysical Journal of the Royal Astronomical Society, 72, 39-57, doi: 10.1111/j.1365-246X.1983.tb02803.x.
39. Stephen, R. A., 1996, Modeling sea surface scattering by the time-domain finite difference method: Journal of the Acoustical Society of America, 100, 2070-2078, doi: 10.1121/1.417917.
40. Symes, W., and T. Vdovina, 2009, Interface error analysis for numerical wave propagation: Computational Geosciences, 13, 363-371, doi: 10.1007/s10596-008-9124-8.
41. Symes, W. W., 2007, Reverse time migration with optimal checkpointing: Geophysics, 72, no. 5, SM213-SM221, doi: 10.1190/1.2742686.
42. Tarrass, I., L. Giraud, and P. Thore, 2011, New curvilinear scheme for elastic wave propagation in presence of curved topography: Geophysical Prospecting, 59, 889-906, doi: 10.1111/j.1365-2478.2011.00972.x.
43. Tromp, J., D. Komatitsch, and Q. Liu, 2008, Spectral-element and adjoint methods in seismology: Communications in Computational Physics, 3, 1-32.
44. Virieux, J., 1986, P-SV wave propagation in heterogeneous media: Velocitystress finite-difference method: Geophysics, 51, 889-901, doi: 10.1190/1.1442147.
45. Virieux, J., H. Calandra, and R.-E. Plessix, 2011, A review of the spectral, pseudo-spectral, finite-difference and finite-element modelling techniques for geophysical imaging: Geophysical Prospecting, 59, 794-813, doi: 10.1111/j.1365-2478.2011.00967.x.
46. Virieux, J., and R. Madariaga, 1982, Dynamic faulting studied by a finite difference method: Bulletin of the Seismological Society of America, 72, 345-369.
47. Zahradnik, J., P. Moczo, and F. Horn, 1993, Testing four elastic finite-difference schemes for behavior at discontinuities: Bulletin of the Seismological Society of America, 83, 107-129.
48. Zhang, J., 1997, Quadrangle-grid velocity-stress finite-difference method for elastic-wave-propagation simulation: Geophysical Journal International, 131, 127-134, doi: 10.1111/j.1365-246X.1997.tb00599.x.
49. Zhang, J., and D. J. Verschuur, 2002, Elastic wave propagation in heterogeneous anisotropic media using the lumped finite-element method: Geophysics, 67, 625-638, doi: 10.1190/1.1468624.
50. Zhang, L., L. Wei, H. Lixin, D. Xiaogang, and Z. Hanxin, 2012, A class of hybrid DG/FV methods for conservation laws II: Two-dimensional cases: Journal of Computational Physics, 231, 1104-1120, doi: 10.1016/j.jcp .2011.03.032.