Abstract
Prestack reverse time migration (RTM) is an accurate imaging method of subsurface media. The viscoacoustic prestack RTM is of practical significance because it considers the viscosity of the subsurface media. One of the steps of RTM is solving the wave equation and extrapolating the wave field forward and backward; therefore, solving accurately and efficiently the wave equation affects the imaging results and the efficiency of RTM. In this study, we use the optimal time-space domain dispersion high-order finite-difference (FD) method to solve the viscoacoustic wave equation. Dispersion analysis and numerical simulations show that the optimal time-space domain FD method is more accurate and suppresses the numerical dispersion. We use hybrid absorbing boundary conditions to handle the boundary reflection. We also use source-normalized cross-correlation imaging conditions for migration and apply Laplace filtering to remove the low-frequency noise. Numerical modeling suggests that the viscoacoustic wave equation RTM has higher imaging resolution than the acoustic wave equation RTM when the viscosity of the subsurface is considered. In addition, for the wave field extrapolation, we use the adaptive variable-length FD operator to calculate the spatial derivatives and improve the computational efficiency without compromising the accuracy of the numerical solution.
Similar content being viewed by others
References
Bickel, S. H., and Natarajan, R. R., 1985, Plane-wave Q deconvolution: Geophysics, 50(9), 1426–1439.
Carcione, J. M., Kosloff, D., and Kosloff, R., 1988, Viscoacoustic wave propagation simulation in the earth: Geophysics, 53(6), 769–777.
Cavalca, M., Fletcher, R., and Riedel, M., 2013, Q-compensation in complex media-Ray-based and wavefield extrapolation approaches: 83th Ann. Internat. Mtg, Soc. Expl. Geophys., Expanded Abstracts, 3831–3835.
Chattopadhyay, S., and Mcmechan, G. A., 2008, Imaging conditions for prestack reverse time migration: Geophysics, 73(3), S81–S89.
Chen, J. B., 2012, An average-derivative optimal scheme for frequency-domain scalar wave equation: Geophysics, 77(6), T201–T210.
Dablain, M. A., 1986, The application of high-order differencing to the scalar wave equation: Geophysics 51(1), 54–66.
Fletcher, R. P., Nichols, D., and Cavalca, M., 2012, Wave path-consistent Effective Q Estimation for Q-compensated Reverse-time Migration: 74th EAGE Annual Meeting, Expanded Abstracts, A020.
Fu, D. D., Liu, Y., Chen, Z. D., and Wang, S. Z., 1993, Acoustic wave modeling in viscoelastic media by pseudospectral method: Journal of Jianghan Petroleum Institute (in Chinese), 15(4), 32–39.
Futterman, W. I., 1962, Dispersive body waves: Journal of Geophysical Research, 67(13), 5279–5291.
Hargreaves, N. D., and Calvert, A. J., 1991, Inverse Q filtering by Fourier transform: Geophysics, 56(4), 519–527.
Kosloff, D., Pestana, R. C., and Tal-Ezer, H., 2010, Acoustic and elastic numerical wave simulations by recursive spatial derivative operators: Geophysics, 75(6), T167–T174.
Li, Q. Z., 1993, High-resolution seismic data processing: Petroleum Industry Press, China, 37–38.
Liu, H. W., Liu H., and Zou, Z., 2010, The Problems of denoise and storage in seismic RTM: Chinese Journal of Geophysics, 53(9), 2171–2180.
Liu, Y., 2013, Globally optimal finite-difference schemes based on least squares: Geophysics, 78(4), T113–T132.
Liu, Y., and Sen, M. K., 2009, A new time-space domain high-order finite-different method for the acoustic wave equation: Journal of Computational Physics, 228, 8779–8806.
Liu, Y., and Sen, M. K., 2010a, Acoustic VTI modeling with a time-space domain dispersion-relation-based finite-difference scheme: Geophysics, 75(3), A7–A13.
Liu, Y., and Sen, M. K., 2010b, A hybrid scheme for absorbing edge reflections in numerical modeling of wave propagation: Geophysics, 75(2), A1–A6.
Liu, Y., and Sen, M. K., 2011a, Finite-difference modeling with adaptive variable-length spatial operators: Geophysics, 76(4), T79–T89.
Liu, Y., and Sen, M. K., 2011b, 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.
Mittet, R., Sollie, R., and Hokstad, K., 1995, Prestack depth migration with compensation for absorption and dispersion: Geophysics, 60(5), 1485–1494.
Robertsson, J. O. A., Blanch, J. O., Symes, W. W., and Burrus, C. S., 1994, Galerkin-wavelet modeling of wave propagation: Optimal finite difference stencil design: Mathematical and Computer Modelling, 19(1), 31–38
Robinson, J. C., 1979, A technique for the continuous representation of dispersion in seismic data: Geophysics, 44(8), 1345–1351.
Robinson, J. C., 1982, Time-variable dispersion processing through the use of phased sinc functions: Geophysics, 47(7), 1106–1110.
Shan, G. J., 2009, Optimized implicit finite-difference and Fourier finite-difference migration for VTI media: Geophysics, 74(6), WCA189–WCA197.
Traynin, P., Liu, J., and Reilly, J., 2008, Amplitude and bandwidth recovery beneath gas zones using Kirchhoff prestack depth Q-migration: 78th Ann. Internat. Mtg, Soc. Expl. Geophys., Expanded Abstracts, 2412–2416.
Wang, Y. H., 2002, A stable and efficient approach of inverse Q filtering: Geophysics, 67(2), 657–663.
Wang, Y. H., and Guo, J., 2004, Seismic migration with inverse Q filtering: Geophysical Research Letters, 31, L21608.
Wang, Y. H., 2006, Inverse Q-filter for seismic resolution enhancement: Geophysics, 71(3), V51–V60.
Wang, Y. H., 2008, Inverse-Q filtered migration: Geophysics, 73(1), S1–S6.
Xie, Y., Xin, K., Sun, J., and Notfors, C., 2009, 3D prestack depth migration with compensation for frequency dependent absorption and dispersion: 79th Ann. Internat. Mtg., Soc. Explor. Geophys., Expanded Abstracts, 2919–2923.
Yan, H. Y., and Liu, Y., 2013, Visco-acoustic prestack reverse-time migration based on the time-space domain adaptive high-order finite-difference method: Geophysical Prospecting, 61(5), 941–954.
Zhang, C. H., and Ulrych, T. J., 2010, Refocusing migrated seismic images in absorptive media: Geophysics, 75(3), S103–S110.
Zhang, J. F., Wu, J. Z, and Li, X. Y., 2013, Compensation for absorption and dispersion in prestack migration: An effective Q approach: Geophysics, 78(1), S1–S14.
Zhang, J. H., and Yao, Z. X. 2012, Globally optimized finite-difference extrapolator for strongly VTI media: Geophysics, 77(4), T125–T135.
Zhang, Y., and Sun, J., 2009, Practical issues in RTM: true amplitude gathers, noise removal and harmonic-source encoding: First Break, 26(1), 29–35.
Zhang, Y., Zhang, P., and Zhang, H. Z., 2010, Compensating for visco-acoustic effects in reverse-time migration: 80th Ann. Internat. Mtg., Soc. Explor. Geophys., Expanded Abstracts, 3160–3164.
Author information
Authors and Affiliations
Corresponding author
Additional information
This research was supported by the National Nature Science Foundation of China (No. 41074100) and the Program for New Century Excellent Talents in the University of the Ministry of Education of China (No. NCET-10-0812).
Zhao Yan is a PhD student at China University of Petroleum (Beijing). He received his BE in 2008 from Yangtze University and MS in 2011 from Chengdu University of Technology. His interests include high-resolution processing of seismic data and seismic migration.
Rights and permissions
About this article
Cite this article
Zhao, Y., Liu, Y. & Ren, ZM. Viscoacoustic prestack reverse time migration based on the optimal time-space domain high-order finite-difference method. Appl. Geophys. 11, 50–62 (2014). https://doi.org/10.1007/s11770-014-0414-8
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11770-014-0414-8