Suppressing the low-frequency noise in reverse-time migration utilizing the non-reflecting wave equation

Zhang, L., Shi, W.G., Hou. Z.G., Ren, Y.X. and Wang, R.R., 2023. Suppressing the low-frequency noise in reverse-time migration utilizing the non-reflecting wave equation. Journal of Seismic Exploration. 32: 1-20. As a high-precision geophysical imaging method, reverse-time migration (RTM) is widely used in seismic exploration. However, the imaging quality in RTM is susceptible to low-frequency noise, which is chiefly caused by unwanted cross-correlation of reflections. In order to remove the low-frequency noise, the non-reflecting wave equation can be introduced to RTM. On this basis, we propose an improved RTM method utilizing the non-reflecting wave equation to achieve low-frequency noise suppression in prestack acoustic RTM. Specifically, the non- reflecting wave equation is only used in the process reverse- time wavefield simulation, to take advantage of its ability of weakening reflections. Accordingly, abnormal imaging points attributable to reflections can be reduced. We evaluated the denoising effect through numerical examples including a simple layered model, a concave model, and the complicated Marmousi model. The results show that low-frequency noise can be effectively suppressed by introducing the non-reflecting wave equation into RTM. This improved RTM method can achieve better imaging with less low-frequency noise compared with conventional RTM method. Moreover, the improved RTM method ensures computational efficiency without increasing storage demands.
- Araya-Polo, M., Rubio, F., De la Cruz, R., Hanzich, M., Cela, JM. and Scarpazza, D.P.,
- 3D seismic imaging through reverse-time migration on homogeneous and
- heterogeneous multi-core processors. Scientif. Program., 17: 185-198.
- Baysal, E., Kosloff, D.D. and Sherwood, J.W., 1983. Reverse time migration.
- Geophysics, 48: 1514-1524.
- Baysal, E., Kosloff, D.D. and Sherwood, J.W.C., 1984. A two-way nonreflecting wave
- equation. Geophysics, 49: 132-141.
- Bérenger, J.P., 2007. Perfectly matched layer (PML) for computational electromagnetics.
- Synth. Lect. Computat. Electromagn., 2: 1-117.
- Brougois, A., Bourget, M., Lailly, P., Poulet, M., Ricarte, P. and Versteeg, R., 1990.
- Marmousi, model and data. EAEG workshop - Practical aspects of seismic data
- inversion (cp-108).
- Chang, W.F. and McMechan, G.A.,1987. Elastic reverse-time migration. Geophysics, 52:
- 1365-1375.
- Chattopadhyay, S. and McMechan, G.A., 2008. Imaging conditions for prestack
- reverse-time migration. Geophysics, 73(3), S81-S89.
- Chen, T. and He, B.S., 2014. A normalized wavefield separation cross-correlation
- imaging condition for reverse time migration based on Poynting vector. Appl.
- Geophys., 11: 158-166.
- Chen, Y., Bai, M., Zhou, Y., Zhang, Q., Wang, Y. and Chen, H., 2019. Substituting
- smoothing with low-rank decomposition - Applications to least-squares reverse time
- migration of simultaneous source and incomplete seismic data. Geophysics, 84(4):
- $267-S283.
- Claerbout, J.F., 1971. Toward a unified theory of reflector mapping. Geophysics, 36:
- 467-481.
- Dai, W., Huang, Y. and Schuster, G.T., 2013. Least-squares reverse time migration of
- marine data with frequency-selection encoding. Geophysics, 78(4), $233-S242.
- Drossaert, F.H. and Giannopoulos, A., 2007. A nonsplit complex frequency-shifted PML
- based on recursive integration for FDTD modeling of elastic waves. Geophysics,
- 72(2): T9-T17.
- Du, X., Yang, H. and Zhang, S., 2002. Wave-transmitting problem of complex structure
- of embankment simulated by nonreflecting wave equation. J. Tsinghua Univ., Nat.
- Sci. Ed. (in Chinese), 42(8): 105-108.
- Fisher, E., McMechan, G.A., Annan, A.P. and Cosway, S.W., 1992. Examples of
- reverse-time migration of single-channel, ground-penetrating radar profiles.
- Geophysics, 57: 577-586.
- Fletcher, R.P., Du, X. and Fowler, P.J., 2009. Reverse time migration in tilted
- transversely isotropic (TTI) media. Geophysics, 74(6): WCA179-WCA 187.
- Foltinek, D., Eaton, D., Mahovsky, J., Moghaddam, P. and McGarry, R., 2009.
- Industrial-scale reverse time migration on GPU hardware. Expanded Abstr., 79th
- Ann. Internat. SEG Mtg., Houston: 2789-2793.
- Fowler, P.J., 1997. A comparative overview of prestack time migration methods.
- Expanded Abstr., 67th Ann. Internat. SEG Mtg., Dallas: 1571-1574.
- Guitton, A., 2005. Multiple attenuation in complex geology with a pattern-based
- approach. Geophysics, 70(4), V97-V 107.
- Kaelin, B. and Guitton, A., 2006. Imaging condition for reverse time migration.
- Expanded Abstr., 76th Ann. Internat. SEG Mtg., New Orleans: 2594-2598.
- Kang, W. and Cheng, J., 2012. Methods of suppressing artifacts in prestack reverse time
- migration. Progress Geophys., 3.
- Karazincir, M.H. and Gerrard, C.M., 2006. Explicit high-order reverse time pre-stack
- depth migration. Expanded Abstr., 76th Ann. Internat. SEG Mtg., New Orleans:
- 2353-2357.
- Kim, Y., Shin, C., Calandra, H. and Min, D.J., 2013. An algorithm for 3D acoustic
- time-Laplace-Fourier-domain hybrid full waveform inversion. Geophysics, 78(4):
- R151-R166.
- Lesage, A.C., Zhou, H., Araya-Polo, M., Cela, J.M. and Ortigosa, F., 2008. 3D
- reverse-time migration with hybrid finite difference-pseudospectral method.
- Expanded Abstr., 78th Ann. Internat. SEG Mtg., Las Vegas: 2257-2261.
- Levin, S.A., 1984. Principle of reverse-time migration. Geophysics, 49: 581-583.
- Liu, F., Zhang, G., Morton, S.A. and Leveille, J.P., 2007. Reverse-time migration using
- one-way wavefield imaging condition. Expanded Abstr, 77th Ann. Internat. SEG
- Mtg., San Antonio: 2170-2174.
- Liu, H., Liu, H. and Zou, Z., 2010. The problems of denoise and storage in seismic
- reverse time migration. Chin. J. Geophys., 53: 2171-2180.
- Loewenthal, D. and Mufti, I.R.,1983. Reversed time migration in spatial frequency
- domain. Geophysics, 48: 627-635.
- McMechan, G.A., 1983. Migration by extrapolation of time-dependent boundary values.
- Geophys. Prosp., 31: 413-420.
- Mehta, K., Bakulin, A., Sheiman, J., Calvert, R. and Snieder, R., 2007. Improving the
- virtual source method by wavefield separation. Geophysics, 72(4): V79-V86.
- Ren, C., Song, G. and Tian, X., 2015. The use of Poynting vector in wave-field
- decomposition imaging condition for reverse-time migration. J. Appl. Geophys., 112:
- 14-19.
- Sava, P. and Poliannikov, O., 2008. Interferometric imaging condition for wave-equation
- migration. Geophysics, 73(2): S47-S61.
- Sava, P. and Fomel, S., 2006. Time-shift imaging condition in seismic migration.
- Geophysics, 71(6): S209-S217.
- Shapiro, R., 1970. Smoothing, filtering, and boundary effects. Rev. Geophys., 8:
- 359-387.
- Suh, S.Y. and Cai, J., 2009. Reverse-time migration by fan filtering plus wavefield
- decomposition. Expanded Abstr., 79th Ann. Internat. SEG Mtg., Houston:
- 2804-2808.
- Symes, W.W., 2007. Reverse time migration with optimal checkpointing. Geophysics,
- 72(5), SM213-SM221.
- Valenciano, A.A. and Biondi, B., 2003. 2-D deconvolution imaging condition for
- shot-profile migration. Expanded Abstr., 73rd Ann. Internat. SEG Mtg., Dallas:
- 1059-1062..
- Verschuur, D.J. and Berkhout, A. J., 1997. Estimation of multiple scattering by iterative
- inversion, Part II: Practical aspects and examples. Geophysics, 62: 1596-1611.
- Wang, D., Saab, R., Yilmaz, O. and Herrmann, F.J., 2008. Bayesian wavefield separation
- by transform-domain sparsity promotion. Geophysics, 73(5): A33-A38.
- Wang, S. and Qu, Y., 1993. Mixed two-way nonreflecting wave equation migration.
- Petrol. Geophys. Explor. (in Chinese), 28: 537-542.
- Wang, Y., 2000. Reverse-time migration by a variable time-step and space-grid method.
- Expanded Abstr., 70th Ann. Internat. SEG Mtg., Calgary, AB: 798-801.
- Wang, Y., Zhou, H., Chen, H. and Chen, Y., 2018. Adaptive stabilization for
- Q-compensated reverse time migration. Geophysics, 83(1): S15-S32.
- Whitmore, N.D., 1983. Iterative depth migration by backward time propagation.
- Expanded Abstr., 53rd Ann. Internat. SEG Mtg., Las Vegas: 382-385.
- Wu, Q., Li, W., Chen, K. and Cui, J., 2000. Forward model of nonreflecting wave
- equation and its application. Petrol. Geophys. Explor. (in Chinese), 35: 147-153.
- Xu, K., Zhou, B. and McMechan, G.A., 2010. Implementation of prestack reverse time
- migration using frequency-domain extrapolation. Geophysics, 75(2): S61-S72.
- Xue, Z., Chen, Y., Fomel, S. and Sun, J., 2016. Seismic imaging of incomplete data and
- simultaneous-source data using least-squares reverse time migration with shaping
- regularization. Geophysics, 81(1): S11-S20.
- Yoon, K., Marfurt, K.J. and Starr, W., 2004. Challenges in reverse-time migration.
- Expanded Abstr., 74th Ann. Internat. SEG Mtg., Denver: 1057-1060.
- Youn, O.K. and Zhou, H.W., 2001. Depth imaging with multiples. Geophysics, 66(1):
- 246-255.
- Zhang, W. and Shen, Y., 2010. Unsplit complex frequency-shifted PML implementation
- using auxiliary differential equations for seismic wave modeling. Geophysics, 75(4):
- T141-T154.
- Zhang, Y. and Zhang, G., 2009. One-step extrapolation method for reverse time
- migration. Geophysics, 74(4): A29-A33.
- Zhu, J., Dong, M. and Li, C., 1989. The vsp’s reverse-time migration based on two-way
- nonreflecting wave equation. Petrol. Geophys. Explor. (in Chinese), 24: 256-270.
- Zhu, T. and Sun, J., 2017. Viscoelastic reverse time migration with attenuation
- compensation. Geophysics, 82(2): S61-S73.