An novel finite difference dispersion error elimination mechanism in the Lax–Wendroff high‐order time discretization

References

1. Chen, G., Wang, Y., Wang, Z. & Zhang, S. (2020) Dispersion‐relationship‐preserving seismic modelling using the cross‐rhombus stencil with the finite‐difference coefficients solved by an over‐determined linear system. Geophysical Prospecting, 68(6), 1771–1792.
   [Google Scholar]
2. Chen, J.B. (2007) High‐order time discretizations in seismic modeling. Geophysics, 72(5), SM115–SM122.
   [Google Scholar]
3. Chen, J.B. (2011) A stability formula for Lax–Wendroff methods with fourth‐order in time and general‐order in space for the scalar wave equation. Geophysics, 76(2), T37–T42.
   [Google Scholar]
4. Chu, C. & Stoffa, P.L. (2012) Determination of finite‐difference weights using scaled binomial windows. Geophysics, 77(3), W17–W26.
   [Google Scholar]
5. Dablain, M.A. (1986) The application of high‐order differencing to the scalar wave equation. Geophysics, 51(1), 54–66.
   [Google Scholar]
6. Du, Q.Z., Li, B. & Hou, B. (2009). Numerical modeling of seismic wavefields in transversely isotropic medium with a compact staggered‐grid finite difference scheme. Applied Geophysics, 6(1), 42–49.
   [Google Scholar]
7. Etgen, J.T. (2007) A tutorial on optimizing time domain finite‐difference schemes: “Beyond Holberg”. Stanford Exploration Project Report, 129, 33–43.
   [Google Scholar]
8. Han, Y., Wu, B., Yao, G., Ma, X. & Wu, D. (2022) Eliminate time dispersion of seismic wavefield simulation with semi‐supervised deep learning. Energies, 15(20), 7701.
   [Google Scholar]
9. Jastram, C. & Behle, A. (1993) Accurate finite‐difference operators for modelling the elastic wave equation. Geophysical Prospecting, 41(4), 453–458.
   [Google Scholar]
10. Jing, H., Chen, Y., Wang, J. & Xue, W. (2019). A highly efficient time–space‐domain optimized method with Lax–Wendroff type time discretization for the scalar wave equation. Journal of Computational Physics, 393, 1–28.
    [Google Scholar]
11. Koene, E.F., Robertsson, J.O., Broggini, F. & Andersson, F. (2018) Eliminating time dispersion from seismic wave modeling. Geophysical Journal International, 213(1), 169–180.
    [Google Scholar]
12. Li, W.D., Meng, X.H., Liu, H., Wang, J., Gui, S., Xiu, C.X. & Wang, Z.Y. (2020) Optimal finite‐difference schemes for elastic wave based on improved cosine‐combined window function. Exploration Geophysics, 52(2), 221–234.
    [Google Scholar]
13. Liang, W., Wang, Y., Yang, C. & Liu, H. (2013) Acoustic wave equation modeling with new time–space domain finite difference operators. Chinese Journal of Geophysics, 56(6), 840–850.
    [Google Scholar]
14. Liang, W.Q., Wang, Y.F. & Yang, C.C. (2014) Comparison of numerical dispersion in acoustic finite‐difference algorithms. Exploration Geophysics, 46(2), 206–212.
    [Google Scholar]
15. Liang, W., Wang, Y. & Yang, C. (2015) Determining finite difference weights for the acoustic wave equation by a new dispersion‐relationship‐preserving method. Geophysical Prospecting, 63(1), 11–22.
    [Google Scholar]
16. Liang, W., Wu, X., Wang, Y. & Yang, C. (2018) A simplified staggered‐grid finite‐difference scheme and its linear solution for the first‐order acoustic wave‐equation modeling. Journal of Computational Physics, 374, 863–872.
    [Google Scholar]
17. Liang, W., Wang, Y., Cao, J. & Iturrarán‐Viveros, U. (2022) A hybrid explicit implicit staggered grid finite‐difference scheme for the first‐order acoustic wave equation modeling. Scientific Reports, 12(1), 10967.
    [Google Scholar]
18. Liu, Y. & Sen, M.K. (2009) A new time–space domain high‐order finite‐difference method for the acoustic wave equation. Journal of Computational Physics, 228(23), 8779–8806.
    [Google Scholar]
19. Liu, Y. & Sen, M.K. (2010) Acoustic VTI modeling with a time–space domain dispersion‐relation‐based finite‐difference scheme. Geophysics, 75(3), A11–A17.
    [Google Scholar]
20. Liu, Y. & Sen, M.K. (2011) Scalar wave equation modeling with time–space domain dispersion‐relation‐based staggered‐grid finite‐difference schemes. Bulletin of the Seismological Society of America, 101(1), 141–159.
    [Google Scholar]
21. Liu, Y. & Sen, M.K. (2013) Time–space domain dispersion‐relation‐based finite‐difference method with arbitrary even‐order accuracy for the 2D acoustic wave equation. Journal of Computational Physics, 232(1), 327–345.
    [Google Scholar]
22. Liu, H. & Zhang, H. (2019) Reducing computation cost by Lax–Wendroff methods with fourth‐order temporal accuracy. Geophysics, 84(3), T109–T119.
    [Google Scholar]
23. Liu, H., & Luo, Y. (2019). Comparing four numerical stencils for elastic wave simulation. In SEG Technical Program Expanded Abstracts 2019 (pp. 3745–3749). Society of Exploration Geophysicists.
    [Google Scholar]
24. Saenger, E.H. & Shapiro, S.A. (2002) Effective velocities in fractured media: a numerical study using the rotated staggered finite‐difference grid. Geophysical Prospecting, 50(2), 183–194.
    [Google Scholar]
25. Stork, C. (2013) Eliminating nearly all dispersion error from FD modeling and RTM with minimal cost increase. In: 75th EAGE conference & exhibition incorporating SPE EUROPEC 2013. Bunnik, European Association of Geoscientists & Engineers. pp. cp‐348.
26. Tan, S. & Huang, L. (2014) An efficient finite‐difference method with high‐order accuracy in both time and space domains for modelling scalar‐wave propagation. Geophysical Journal International, 197(2), 1250–1267.
    [Google Scholar]
27. Teixeira, F.L., Sarris, C., Zhang, Y., Na, D.Y., Berenger, J.P., Su, Y. & Simpson, J.J. (2023) Finite‐difference time‐domain methods. Nature Reviews Methods Primers, 3(1), 75.
    [Google Scholar]
28. Virieux, J., Calandra, H. & Plessix, R.É. (2011) A review of the spectral, pseudo‐spectral, finite‐difference and finite‐element modelling techniques for geophysical imaging. Geophysical Prospecting, 59(5), 794–813.
    [Google Scholar]
29. Wang, Y.F., Liang, W.Q., Nashed, Z., Li, X., Liang, G.H. & Yang, C.C. (2014). Seismic modeling by optimizing regularized staggered‐grid finite‐difference operators using a time–space domain dispersion relationship preserving method. Geophysics, 79(5), T277–T285.
    [Google Scholar]
30. Wang, J., Liu, Y. & Zhou, H. (2022) High temporal accuracy elastic wave simulation with new time–space domain implicit staggered‐grid finite‐difference schemes. Geophysical Prospecting, 70(8), 1346–1366.
    [Google Scholar]
31. Xu, T., Yan, H., Yu, H., & Zhang, Z. (2023). Removing Time Dispersion from Elastic WaveModeling with the pix2pix Algorithm Based on cGAN. Remote Sensing, 15(12), 3120
    [Google Scholar]
32. Yang, L., Yan, H. & Liu, H. (2016) Optimal implicit staggered‐grid finite‐difference schemes based on the sampling approximation method for seismic modelling. Geophysical Prospecting, 64(3), 595–610.
    [Google Scholar]
33. Yee, K. (1966) Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media. IEEE Transactions on Antennas and Propagation, 14(3), 302–307.
    [Google Scholar]
34. Zhang, J.H. & Yao, Z.X. (2013) Optimized explicit finite‐difference schemes for spatial derivatives using maximum norm. Journal of Computational Physics, 250, 511–526.
    [Google Scholar]
35. Zhang, L., RectorIII, J.W. & Hoversten, G.M. (2005) Finite‐difference modelling of wave propagation in acoustic tilted TI media. Geophysical Prospecting, 53(6), 843–852.
    [Google Scholar]