FINITE-DIFFERENCE REVERSE-TIME MIGRATION BASED ON ANISOTROPIC PURE QP WAVE EQUATION IN TTI MEDIA.

The anisotropic effects in real earth media can induce waveform distortion on seismic wave propagation. Neglecting these effects in seismic imaging processing can lead to a degradation in imaging resolution. Therefore, starting from the exact P-wave dispersion relation, we derive a pure acoustic wave equation for tilted transversely isotropic (TTI) media to accurately characterize the anisotropic effects. In contrast to the coupled pseudo-acoustic TTI wave equation, our new pure acoustic TTI wave equation generates a noise-free wavefields and remains stable for anisotropic parameters (ε < δ). The newly derived pure acoustic TTI wave equation accurately simulates the P-wave kinematic features, as demonstrated through theoretical analysis. Additionally, building on the proposed wave equation, we formulate a finite-difference operator and obtain a pure acoustic TTI wave equation that can be solved by finite-difference (FD) method. Numerical tests illustrate that the proposed FD-solvable pure acoustic TTI wave equation is highly efficient in wavefield simulation. Finally, based on the newly derived FD-solvable pure acoustic TTI wave equation, we implement TTI reverse time migration (TTI RTM). Numerical examples demonstrate the efficacy of the proposed TTI RTM scheme in correcting for anisotropic effects.
- Alkhalifah, T. (1998). Acoustic approximations for processing in transversely isotropic media. Geophysics, 63(2), 623-631. doi:10.1190/1.1444361
- Alkhalifah, T. (2000). An acoustic wave equation for anisotropic media. Geophysics, 65(4), 1239–1250. doi:10.1190/1.1444815
- Cheng, J., and Fomel, S. (2014). Fast algorithms for elastic-wave-mode separation and vector decomposition using low-rank approximation for anisotropic media. Geophysics, 79(4), C97-C110. doi:10.1190/geo2014-0032.1
- Cheng, J., Alkhalifah, T., Wu, Z., Zou, P., and Wang, C. (2016). Simulating propagation of decoupled elastic waves using low-rank approximate mixed-domain integral operators for anisotropic media. Geophysics, 81(2), T63-T77. doi:10.1190/geo2015-0184.1
- Chu, C., Macy, B. K., and Anno, P. D. (2011). Approximation of pure acoustic seismic wave propagation in TTI media. Geophysics, 76(5), WB97-WB107. doi:10.1190/geo2011-0092.1
- Chu, C., Macy, B. K., and Anno, P. D. (2013). Pure acoustic wave propagation in transversely isotropic media by the pseudo-spectral method. Geophys. Prospect., 61(3), 556-567. doi:10.1111/j.1365-2478.2012.01077.x
- Duveneck, E., Milcik, P., Bakker, P. M. and Perkins, C. (2008). “Acoustic VTI wave equations and their application for anisotropic reverse‐time migration,” in SEG Technical Program Expanded Abstracts, Las Vegas, Nevada, November 12, 2008, 2186-2190. doi:10.1190/1.3059320
- Fletcher, R. P., Du, X., and Fowler, P. J. (2009). Reverse time migration in tilted transversely isotropic (TTI) media. Geophysics, 74(6), WCA179-WCA187. doi:10.1190/1.3269902
- Fomel, S., Ying, L., and Song, X. (2013). Seismic wave extrapolation using lowrank symbol approximation. Geophys. Prospect., 61(3), 526-536. doi:10.1111/j.1365-2478.2012.01064.x
- Grechka, V., Zhang, L., and Rector III, J. W. (2004). Shear waves in acoustic anisotropic media. Geophysics, 69(2), 576-582. doi:10.1190/1.1707077
- Huang, J., Mao, Q., Mu, X., Yang, J., Ivan, M. S., Liu, Z., and Zhang, S. (2023). Least-squares reverse time migration based on an efficient pure qP-wave equation. Geophys. Prospect. doi:10.1111/1365-2478.13326
- Li, B., and Stovas, A. (2021). Decoupled approximation and separate extrapolation of P-and SV-waves in transversely isotropic media. Geophysics, 86(4), C133-C142. doi:10.1190/geo2020-0232.1
- Li, X., and Zhu, H. (2018). A finite-difference approach for solving pure quasi-P-wave equations in transversely isotropic and orthorhombic media. Geophysics, 83(4), C161-C172. doi:10.1190/geo2017-0405.1
- Liang, K., Cao, D., Sun, S., and Yin, X. (2023). Decoupled wave equation and forward modeling of qP wave in VTI media with the new acoustic approximation. Geophysics, 88(1), WA335-WA344. doi:10.1190/geo2022-0292.1
- Mao, Q., Huang, J. P., Mu, X. R., Yang, J. D., and Zhang, Y. J. (2023). Accurate simulations of pure-viscoacoustic wave propagation in tilted transversely isotropic media. Pet. Sci. doi:10.1016/j.petsci.2023.11.005
- Mu, X., Huang, J., Yong, P., Huang, J., Guo, X., Liu, D., and Hu, Z. (2020). Modeling of pure qP-and qSV-waves in tilted transversely isotropic media with the optimal quadratic approximation. Geophysics, 85(2), C71-C89. doi:10.1190/geo2018-0460.1
- Mu, X., Huang, J., Yang, J., Guo, X., and Guo, Y. (2020). Least-squares reverse time migration in TTI media using a pure qP-wave equation. Geophysics, 85(4), S199-S216. doi:10.1190/geo2019-0320.1
- Nikonenko, Y., and Charara, M. (2021). Efficient acoustic scalar wave equation modeling in VTI media. Geophysics, 86(1), T75-T90. doi:10.1190/geo2019-0846.1
- Nikonenko, Y., and Charara, M. (2023). Explicit finite-difference modeling for the acoustic scalar wave equation in tilted transverse isotropic media with optimal operators. Geophysics, 88(2), T65-T73. doi:10.1190/geo2021-0510.1
- Schleicher, J., and Costa, J. C. (2016). A separable strong-anisotropy approximation for pure qP-wave propagation in transversely isotropic media. Geophysics, 81(6), C337-C354. doi:10.1190/geo2016-0138.1
- Song, X., Fomel, S., and Ying, L. (2013). Lowrank finite-differences and lowrank Fourier finite-differences for seismic wave extrapolation in the acoustic approximation. Geophys. J. Int., 193(2), 960-969. doi:10.1093/gji/ggt017
- Stovas, A., Alkhalifah, T., and bin Waheed, U. (2020). Pure P-and S-wave equations in transversely isotropic media. Geophys. Prospect., 68(9), 2762-2769. doi:10.1111/1365-2478.13026
- Sun, J., Fomel, S., and Ying, L. (2016). Low-rank one-step wave extrapolation for reverse time migration. Geophysics, 81(1), S39-S54. doi:10.1190/geo2015-0183.1
- Thomsen, L. (1986). Weak elastic anisotropy. Geophysics, 51(10), 1954-1966. doi:10.1190/1.1442051
- Tsvankin, I. (1996). P-wave signatures and notation for transversely isotropic media: An overview. Geophysics, 61(2), 467-483. doi:10.1190/1.1443974
- Wu, Z., and Alkhalifah, T. (2014). The optimized expansion based low-rank method for wavefield extrapolation. Geophysics, 79(2), T51-T60. doi:10.1190/geo2013-0174.1
- Xu, S., and Zhou, H. (2014). Accurate simulations of pure quasi-P-waves in complex anisotropic media. Geophysics, 79(6), T341-T348. doi:10.1190/geo2014-0242.1
- Xu, S., Stovas, A., Alkhalifah, T., and Mikada, H. (2020). New acoustic approximation for transversely isotropic media with a vertical symmetry axis. Geophysics, 85(1), C1-C12. doi:10.1190/geo2019-0100.1
- Wang, W., Hua, B., McMechan, G. A., and Duquet, B. (2018). P-and S-decomposition in anisotropic media with localized low-rank approximations. Geophysics, 83(1), C13-C26. doi:10.1190/geo2017-0138.1
- Yang, J., Zhu, H., McMechan, G., and Yue, Y. (2018). Time-domain least-squares migration using the Gaussian beam summation method. Geophys. J. Int., 214(1), 548-572. doi:10.1093/gji/ggy142
- Zhan, G., Pestana, R. C., and Stoffa, P. L. (2012) Decoupled equations for reverse time migration in tilted transversely isotropic media. Geophysics, 77(2), 37–45. doi:10.1190/geo2011-0175.1
- Zhan, G., Pestana, R. C., and Stoffa, P. L. (2013). An efficient hybrid pseudospectral/finite-difference scheme for solving the TTI pure P-wave equation. J. Geophys. Eng., 10(2), 025004. doi:10.1088/1742-2132/10/2/025004
- Zhang, Z. D., Alkhalifah, T., and Wu, Z. (2019). A hybrid finite-difference/low-rank solution to anisotropy acoustic wave equations. Geophysics, 84(2), T83-T91. doi:10.1190/geo2018-0333.1
- Zhang, Y., Zhang, H., and Zhang, G. (2011) A stable TTI reverse time migration and its implementation. Geophysics, 76(3), 3–11. doi:10.1190/1.3554411
- Zhou, H., G. Zhang, and R. Bloor. (2006a). “An anisotropic acoustic wave equation for VTI media.” in 68th Annual International Conference and Exhibition, EAGE, Extended Abstracts, Vienna, June 12, 2006, H033. doi:10.3997/2214-4609.201402310.
- Zhou, H., G. Zhang, and R. Bloor. (2006b). “An anisotropic acoustic wave equation for modeling and migration in 2D TTI media.” in SEG Technical Program Expanded Abstracts, New Orleans, Louisiana, October 3, 2006, 194–198. doi:10.1190/1.2369913.
- Zhu, F., Huang, J., and Yu, H. (2018). Least-squares Fourier finite-difference pre-stack depth migration for VTI media., J. Geophys. Eng., 15(2), 421-437. doi:10.1088/1742-2140/aa9a0a
- Zhu, H. (2017). Elastic wavefield separation based on the Helmholtz decomposition. Geophysics, 82(2), S173-S183. doi:10.1190/geo2016-0419.1