On the interface error analysis for finite difference wave simulation

Computational Geosciences

Volumn 14, Issue 4, 2010, Pages 769-778

  Lisitsa, Vadim ^a   Podgornova, Olga ^b   Tcheverda, Vladimir ^a  

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

^b SCHLUMBERGER MOSCOW RESEARCH   (Russian Federation)

Author keywords

Computational methods; Finite difference methods; Seismology; Wave equation

Indexed keywords

BULK MODULUS; ERROR ANALYSIS; FINITE DIFFERENCE METHOD; NUMERICAL METHOD; SEISMOLOGY; WAVE EQUATION; WAVE PROPAGATION; WAVE REFLECTION;

EID: 77955920029     PISSN: 14200597     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10596-010-9187-1     Document Type: Article

References (30)

1. Virieux, J.: P-SV wave propagation in heterogeneous media: velocity-stress finite-difference method. Geophysics 51(4), 889-901 (1986).
2. Madariaga, R.: Dynamics of an expanding circular fault. Bull. Seismol. Soc. Am. 66(3), 639-666 (1976).
3. Virieux, J., Madariaga, R.: Dynamic faulting studied by a finite difference method. Bull. Seismol. Soc. Am. 72(2), 345-369 (1982).
4. Saenger, E. H., Gold, N., Shapiro, S. A.: Modeling the propagation of the elastic waves using a modified finite-difference grid. Wave Motion 31, 77-92 (2000).
5. Levander, A. R.: Fourth-order finite-difference P-SV seismograms. Geophysics 53(11), 1425-1436 (1988).
6. Dablain, M. A.: The application of high-order differencing to the scalar wave equation. Geophysics 51(1), 54-66 (1986).
7. Gustafsson, B., Mossberg, E.: Time compact high order difference methods for wave propagation. SIAM J. Sci. Comput. 26(1), 259-271 (2004).
8. Gustafsson, B., Wahlund, P.: Time compact difference methods for wave propagation in discontinuous media. SIAM J. Sci. Comput. 26(1), 272-293 (2004).
9. Cohen, G., Joly, P.: Construction analysis of fourth-order finite difference schemes for the acoustic wave equation in nonhomogeneous media. SIAM J. Sci. Comput. 33(4), 1266-1302 (1996).
10. Jo, C. H., Shin, C., Suh, J. H.: An optimal 9-point, finite-difference, frequency-space, 2-D scalar wave extrapolator. Geophysics 61(2), 529-537 (1996).
11. Min, D. J., Shin, C., Kwon, B. D., Chung, S.: Improved frequency-domain elastic wave modeling using weighted-averaging difference operators. Geophysics 65(3), 884-895 (2000).
12. Zahradnik, J., Moczo P., Horn, F.: Testing four elastic finite-difference schemes for behavior at discontinuities. Bull. Seismol. Soc. Am. 83(1), 107-129 (1993).
13. Kummer, B. A. B., Dorau, F.: Hybrid modeling of elastic-wave propagation in two-dimensional laterally inhomogeneous media. Geophysics 52(6), 765-771 (1987).
14. Zhang, J.: Quadrangle-grid velocity-stress finite-difference method for elastic wave propagation simulation. Geophys. J. Int. 131(1), 127-134 (1997).
15. Saenger, E. H., Bohlen, T.: Finite-difference modeling of viscoelastic and anisotropic wave propagation using the rotated staggered grid. Geophysics 69(2), 583-591 (2004).
16. Moczo, P., Kristek, J., Vavrycuk, V., Archuleta, R. J., Halada, L.: 3D heterogeneous staggered-grid finite-differece modeling of seismic motion with volume harmonic and arithmetic averagigng of elastic moduli and densities. Bull. Seismol. Soc. Am. 92(8), 3042-3066 (2002).
17. Bansal, R., Sen, M. K.: Finite-difference modelling of S-wave splitting in anisotropic media. Geophys. Prospect. 56(3), 293-312 (2008).
18. Graves, R. W.: Simulating seismic wave propagation in 3D elastic media using staggered-grid finite difference. Bull. Seismol. Soc. Am. 86, 1091-1106 (1996).
19. Deubelbeiss, Y., Kaus, B. J. P.: Comparison of Eulerian and Lagrangian numerical techniques for the Stokes equations in the presence of strongly varying viscosity. Phys. Earth Planet. Inter. 171(1-4), 92-111 (2008).
20. Symes, W., Vdovina, T.: Interface error analysis for numerical wave propagation. Comput. Geosci. 13(3), 363-371 (2009).
21. Mitchell, A. R.: Computational Methods in Partial Differential Equations. Wiley (1969).
22. Samarskii, A. A.: Theory of Difference Schemes (in Russian). Nauka, Moscow (1983).
23. Samarskii, A. A.: The Theory of Difference Schemes, Pure and Applied Mathematics, vol. 240. CRC, Boca Raton (2001).
24. Cohen, G. (ed.): Méthodes numériques d'ordre élevé pour les ondes en régime transitoire (in French). INRIA (1994).
25. Tromp, J., Komatitsch, D., Liu, Q.: Spectral-element and adjoint methods in seismology. Commun. Comput. Phys. 3(1), 1-32 (2008).
26. Zhang, J., Verschuur, D. J.: Elastic wave propagation in heterogeneous anisotropic media using the lumped finite-element method. Geophysics 67(2), 625-638 (2002).
27. Muir, F., Dellinger, J., Etgen, J., Nichols, D.: Modeling elastic fields across irregular boundaries. Geophysics 57(9), 1189-1193 (1992).
28. Igel, H., Mora, P., Riollet, B.: Anisotropic wave propagation through finite-difference grids. Geophysics 60, 1203-1216 (1995).
29. Lisitsa, V., Vishnevsky, D.: Lebedev scheme for the numerical simulation of wave propagation in 3D anisotropic elasticity. Geophys. Prospect. (in press). doi: 10. 1111/j. 1365-2478. 2009. 00862. x.
30. Podgornova, O., Lisitsa, V., Vishnevsky, D.: Traveltime and reflection coefficients accuracy of staggered-grid finite-difference simulation of seismic waves. In: Expanded Abstracts of EAGE Annual Meeting, vol. 71, C042 (2010).