Prestack reverse-time migration with a time-space domain adaptive high-order staggered-grid finite-difference method
Hongyong Yan 1 2 4 Yang Liu 2 Hao Zhang 3
+ Author Affiliations
- Author Affiliations
1 Key Laboratory of Petroleum Resources Research, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, 100029, China.
2 State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing, 102249, China.
3 CGGVeritas Services (Singapore) Pte Ltd, 9 Serangoon North Avenue 5, 554531, Singapore.
4 Corresponding author. Email: yanhongyong@163.com
Exploration Geophysics 44(2) 77-86 https://doi.org/10.1071/EG12047
Submitted: 27 July 2012 Accepted: 22 January 2013 Published: 6 March 2013
Abstract
With advanced computational power, prestack reverse-time migration (RTM) is being used increasingly in seismic imaging. The accuracy and efficiency of RTM strongly depends on the algorithms used for numerical solutions of wave equations. Hence, how to solve the wave equation accurately and rapidly is very important in the process of RTM. In this paper, in order to improve the accuracy of the numerical solution, we use a time-space domain staggered-grid finite-difference (SFD) method to solve the acoustic wave equation, and develop a new acoustic prestack RTM scheme based on this time-space domain high-order SFD. Synthetic and real data tests demonstrate that the RTM scheme improves the imaging quality significantly compared with the conventional SFD RTM. Meanwhile, in the process of wavefield extrapolation, we apply adaptive variable-length spatial operators to compute spatial derivatives to decrease computational costs effectively with little reduction of the accuracy of the numerical solutions.
Key words: acoustic wave equation, adaptive variable-length, reverse-time migration, staggered-grid finite-difference, time-space domain.
References
Alford, R. M., Kelly, K. R., and Boore, D. M., 1974, Accuracy of finite-difference modeling of the acoustic wave equation: Geophysics, 39, 834–842| Accuracy of finite-difference modeling of the acoustic wave equation:Crossref | GoogleScholarGoogle Scholar |
Baysal, E., Kosloff, D. D., and Sherwood, J. W. C., 1983, Reverse time migration: Geophysics, 48, 1514–1524
| Reverse time migration:Crossref | GoogleScholarGoogle Scholar |
Bérenger, J. P., 1994, A perfectly matched layer for the absorption of electromagnetic waves: Journal of Computational Physics, 114, 185–200
| A perfectly matched layer for the absorption of electromagnetic waves:Crossref | GoogleScholarGoogle Scholar |
Chang, W. F., and McMechan, G. A., 1987, Elastic reverse-time migration: Geophysics, 52, 1365–1375
| Elastic reverse-time migration:Crossref | GoogleScholarGoogle Scholar |
Chang, W. F., and McMechan, G. A., 1990, 3D acoustic prestack reverse-time migration: Geophysical Prospecting, 38, 737–755
| 3D acoustic prestack reverse-time migration:Crossref | GoogleScholarGoogle Scholar |
Chang, W. F., and McMechan, G. A., 1994, 3D elastic prestack reverse-time depth migration: Geophysics, 59, 597–609
| 3D elastic prestack reverse-time depth migration:Crossref | GoogleScholarGoogle Scholar |
Chattopadhyay, S., and McMechan, G. A., 2008, Imaging conditions for prestack reverse time migration: Geophysics, 73, S81–S89
| Imaging conditions for prestack reverse time migration:Crossref | GoogleScholarGoogle Scholar |
Chen, J. B., 2007, High-order time discretizations in seismic modelling: Geophysics, 72, SM115–SM122
| High-order time discretizations in seismic modelling:Crossref | GoogleScholarGoogle Scholar |
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, T37–T42
| A stability formula for Lax-Wendroff methods with fourth-order in time and general-order in space for the scalar wave equation:Crossref | GoogleScholarGoogle Scholar |
da Silva Neto, F., Costa, J., Schleicher, J., and Novais, A., 2011, 2.5D reverse time migration: Geophysics, 76, S143–S149
| 2.5D reverse time migration:Crossref | GoogleScholarGoogle Scholar |
Dablain, M. A., 1986, The application of higher differencing to the scalar wave equation: Geophysics, 51, 54–66
| The application of higher differencing to the scalar wave equation:Crossref | GoogleScholarGoogle Scholar |
Dong, L. G., Ma, Z. T., Cao, J. Z., Wang, H. Z., Gao, J. H., Lei, B., and Xu, S. Y., 2000, A staggered-grid high-order difference method of one-order elastic wave equation: Chinese Journal of Geophysics, 43, 411–419
Dong, Z., and McMechan, G. A., 1993, 3D prestack migration in anisotropic media: Geophysics, 58, 79–90
| 3D prestack migration in anisotropic media:Crossref | GoogleScholarGoogle Scholar |
Du, Q., and Qin, T., 2009, Multicomponent prestack reverse-time migration of elastic waves in transverse isotropic medium: Chinese Journal of Geophysics, 52, 801–807
Du, Q., Zhu, Y., and Ba, J., 2012, Polarity reversal correction for elastic reverse time migration: Geophysics, 77, S31–S41
| Polarity reversal correction for elastic reverse time migration:Crossref | GoogleScholarGoogle Scholar |
Duveneck, E., and Bakker, P. M., 2011, Stable P-wave modeling for reverse-time migration in tilted TI media: Geophysics, 76, S65–S75
| Stable P-wave modeling for reverse-time migration in tilted TI media:Crossref | GoogleScholarGoogle Scholar |
Etgen, J. T., and O’Brien, M. J., 2007, Computational methods for large-scale 3D acoustic finite-difference modeling: a tutorial: Geophysics, 72, SM223–SM230
| Computational methods for large-scale 3D acoustic finite-difference modeling: a tutorial:Crossref | GoogleScholarGoogle Scholar |
Finkelstein, B., and Kastner, R., 2007, Finite difference time domain dispersion reduction schemes: Journal of Computational Physics, 221, 422–438
| Finite difference time domain dispersion reduction schemes:Crossref | GoogleScholarGoogle Scholar |
Fletcher, R. P., Du, X., and Fowler, P. J., 2009, Reverse time migration in tilted transversely isotropic (TTI) media: Geophysics, 74, WCA179–WCA187
| Reverse time migration in tilted transversely isotropic (TTI) media:Crossref | GoogleScholarGoogle Scholar |
Igel, H., Riollet, B., and Mora, P., 1992, Accuracy of staggered 3-D finite-difference grids for anisotropic wave propagation: 62nd Annual International Meeting, SEG, Expanded Abstracts, 1244–1246.
Karazincir, M. H., and Gerrard, C. M., 2006, Explicit high-order reverse time pre-stack depth migration: 76th Annual International Meeting, SEG, Expanded Abstracts, 2353–2367.
Kelly, K. R., Ward, R., Treitel, W. S., and Alford, R. M., 1976, Synthetic seismograms: a finite-difference approach: Geophysics, 41, 2–27
| Synthetic seismograms: a finite-difference approach:Crossref | GoogleScholarGoogle Scholar |
Komatitsch, D., and Vilotte, J., 1998, The spectral element method: an efficient tool to simulate the seismic response of 2D and 3D geological structures: Bulletin of the Seismological Society of America, 88, 368–392
Kosloff, D., and Baysal, E., 1982, Forward modeling by a Fourier method: Geophysics, 47, 1402–1412
| Forward modeling by a Fourier method:Crossref | GoogleScholarGoogle Scholar |
Levander, A. R., 1988, Fourth-order finite-difference P-SV seismograms: Geophysics, 53, 1425–1436
| Fourth-order finite-difference P-SV seismograms:Crossref | GoogleScholarGoogle Scholar |
Liu, Y., and Sen, M. K., 2009, A new time-space domain high-order finite-difference method for the acoustic wave equation: Journal of Computational Physics, 228, 8779–8806
| A new time-space domain high-order finite-difference method for the acoustic wave equation:Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BD1MXht1GnsLvL&md5=04f48c3d999e8dbd8863f275cef73c15CAS |
Liu, Y., and Sen, M. K., 2010, Acoustic VTI modeling with a time-space domain dispersion-relation-based finite-difference scheme: Geophysics, 75, A11–A17
| Acoustic VTI modeling with a time-space domain dispersion-relation-based finite-difference scheme:Crossref | GoogleScholarGoogle Scholar |
Liu, Y., and Sen, M. K., 2011a, 3D acoustic wave modelling with time-space domain dispersion-relation-based finite-difference schemes and hybrid absorbing boundary conditions: Exploration Geophysics, 42, 176–189
| 3D acoustic wave modelling with time-space domain dispersion-relation-based finite-difference schemes and hybrid absorbing boundary conditions:Crossref | GoogleScholarGoogle Scholar |
Liu, Y., and Sen, M. K., 2011b, Finite-difference modeling with adaptive variable-length spatial operators: Geophysics, 76, T79–T89
| Finite-difference modeling with adaptive variable-length spatial operators:Crossref | GoogleScholarGoogle Scholar |
Liu, Y., and Sen, M. K., 2011c, Scalar wave equation modeling with time-space domain dispersion-relation-based staggered-grid finite-difference schemes: Bulletin of the Seismological Society of America, 101, 141–159
| Scalar wave equation modeling with time-space domain dispersion-relation-based staggered-grid finite-difference schemes:Crossref | GoogleScholarGoogle Scholar |
Liu, Y., and Wei, X., 2005, A stability criterion of elastic wave modeling by Fourier method: Journal of Geophysics and Engineering, 2, 153–157
| A stability criterion of elastic wave modeling by Fourier method:Crossref | GoogleScholarGoogle Scholar |
Liu, Y., Li, C., and Mou, Y., 1998, Finite-difference numerical modeling of any even-order accuracy: Oil Geophysical Prospecting, 33, 1–10
| 1:STN:280:DyaK1c7lt1altA%3D%3D&md5=cba2746d1f9aa2f2e533d98c6a94fc6dCAS |
Loewenthal, D., Wang, C. J., and Juhlin, C., 1991, High order finite difference modeling and reverse time migration: Exploration Geophysics, 22, 533–545
| High order finite difference modeling and reverse time migration:Crossref | GoogleScholarGoogle Scholar |
McMechan, G. A., 1983, Migration by extrapolation of time dependent boundary values: Geophysical Prospecting, 31, 413–420
| Migration by extrapolation of time dependent boundary values:Crossref | GoogleScholarGoogle Scholar |
Mufti, I. R., 1990, Large-scale three-dimensional seismic models and their interpretive significance: Geophysics, 55, 1166–1182
| Large-scale three-dimensional seismic models and their interpretive significance:Crossref | GoogleScholarGoogle Scholar |
Paffenholz, J., Stefani, J., McLain, B., and Bishop, K., 2002, Sigsbee 2A synthetic subsalt dataset: image quality as function of migration algorithm and velocity model error: 64th EAGE Conference, Extended Abstracts, B019.
Rivière, B., and Wheeler, M., 2003, Discontinuous finite element methods for acoustic and elastic wave problems: , 329, 271–282
| Discontinuous finite element methods for acoustic and elastic wave problems:Crossref | GoogleScholarGoogle Scholar |
Tessmer, E., 2011, Using the rapid expansion method for accurate time-stepping in modeling and reverse-time migration: Geophysics, 76, S177–S185
| Using the rapid expansion method for accurate time-stepping in modeling and reverse-time migration:Crossref | GoogleScholarGoogle Scholar |
Virieux, J., 1984, SH-wave propagation in heterogeneous media: velocity stress finite-difference method: Geophysics, 49, 1933–1942
| SH-wave propagation in heterogeneous media: velocity stress finite-difference method:Crossref | GoogleScholarGoogle Scholar |
Virieux, J., 1986, P-SV wave propagation in heterogeneous media: velocity stress finite difference method: Geophysics, 51, 889–901
| P-SV wave propagation in heterogeneous media: velocity stress finite difference method:Crossref | GoogleScholarGoogle Scholar |
Whitmore, D., 1983, Iterative depth migration by backward time propagation: 53rd Annual International Meeting, SEG, Expanded Abstracts, 382–385.
Wu, W. J., Lines, L. R., and Lu, H. X., 1996, Analysis of higher-order, finite-difference schemes in 3-D reverse-time migration: Geophysics, 61, 845–856
| Analysis of higher-order, finite-difference schemes in 3-D reverse-time migration:Crossref | GoogleScholarGoogle Scholar |
Yan, H. Y., 2012, Study on numerical modeling of seismic wavefields in viscoelastic media and pre-stack reverse-time migration: Ph.D. dissertation, China University of Petroleum (Beijing).
Yan, H. Y., and Liu, Y., 2012, Rotated staggered grid high-order finite-difference numerical modeling for wave propagation in viscoelastic TTI media: Chinese Journal of Geophysics, 55, 1354–1365
Zhang, Y., and Sun, J., 2009, Practical issues of reverse time migration: true amplitude gathers, noise removal and harmonic-source encoding: First Break, 26, 19–25
Zhang, Y., Zhang, H., and Zhang, G., 2011, A stable TTI reverse time migration and its implementation: Geophysics, 76, WA3–WA11
| A stable TTI reverse time migration and its implementation:Crossref | GoogleScholarGoogle Scholar |