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Optimization of staggered grid finite-difference coefficients based on conjugate gradient method

KEJIE JIN1,2 ,  JIANPING HUANG1,2 ,  QIANG ZOU3 ,  ZIYING WANG1,2 ,  SIYOU TONG4 ,  BIN LIU5 ,  ZIDUO HU6
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1 School of Geosciences, China University of Petroleum (East China), Qingdao 266580, P.R. China.,
2 Laboratory for Marine Mineral Resources, Pilot National Laboratory for Marine Science and Technology (Qingdao), Qingdao 266071, P.R. China.,
3 Tarim Oilfield Branch, CNPC, Korla 841000, P.R. China.,
4 College of Marine Geosciences, Ocean University of China, Qingdao 266100, P.R. China.,
5 Research and Development Center Sinopec Geophysical Corp, Nanjing 210009, P.R. China.,
6 Northwest Branch, Research Institute of Petroleum Exploration & Development， PetroChina, Lanzhou 730020, P.R. China.,
JSE 2022, 31(1), 33–52;
Submitted: 15 December 2020 | Accepted: 24 October 2021 | Published: 1 February 2022
© 2022 by the Authors. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
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Abstract

The implementation of difference coefficients optimization strategy can effectively suppress numerical dispersion and improve the modeling accuracy. The conventional difference coefficients calculation method based on Taylor-series Expansion exists serious numerical dispersion. In this paper, we derive a new dispersion error function from the dispersion relation, and the optimal difference coefficients are obtained iteratively by using the conjugate gradient method, thus a staggered-grid difference coefficients optimization method based on the conjugate gradient is developed. We compare dispersion curves, snapshots and single shot records using low-velocity model, high-velocity model and Marmousi model, the results show that the new method can effectively reduce the numerical dispersion compared with the difference coefficients of the conventional Taylor-series Expansion method. The 8th-order optimized difference operators can achieve the modeling precision of 12th-order Taylor-series Expansion difference operators, which can effectively save calculation time and internal storage. The optimization method performs well for both simple model and complex model forward modeling.

Keywords
finite-difference
staggered grid
numerical dispersion
difference coefficients
conjugate gradient
References
  1. Alterman, Z.S. and Karal, F.C.J., 1968. Propagation of elastic waves in layered media byfinite-difference methods. Bull. Seismol. Soc. Am., 58: 367-398.
  2. Chu, C. and Stoffa, P.L., 2012. Determination of finite-difference weights using scaledbinomial windows. Geophysics, 77(3): W17-W26.
  3. Etgen, J.T., 2007. A tutorial on optimizing time domain finite-difference schemes:“Byond Holberg”. Technical Report, 33-43.
  4. Fei, T. and Larner, K., 1995. Elimination of numerical dispersion in finite-differencemodeling and migration by flux-corrected transport. Geophysics, 60: 1830-1842.
  5. Fornberg, B., 1987. The pseudospectral method: Comparisons with finite differences forthe elastic wave equation. Geophysics, 52: 483-501.
  6. Huang, J.P., Qu, Y.M., Li, Q.Y., Li, Z.C., Li, G.L., Bu, C.C. and Teng, H.H., 2015.
  7. Variable-coordinate forward modeling of irregular surface based on dual-variablegrid. Appl. Geophys., 12: 101-110.
  8. Igel, H., Mora, P. and Riollet, B., 1995. Anisotropic wave propagation throughfinite-difference grids. Geophysics, 60: 1203-1216.
  9. Liu, Y. and Sen, M.K., 2011. 3D acoustic wave modelling with time-space domaindispersion-relation-based finite-difference schemes and hybrid absorbing boundaryconditions. Explor. Geophys., 42: 176.
  10. Liu, Y., 2013. Globally optimal finite-difference schemes based on least-squares.Geophysics, 78(4): T113-T132.
  11. Madariaga, R., 1976. Dynamics of an expanding circular fault. Bull. Seismol. Soc. Am.,66: 639-666.
  12. Ren, Y.J., Huang, J.P., Yong, P., Liu, M.L., Cui, C. and Yang, M.W., 2018. Optimizedstaggered-grid finite-difference operators using window functions. Appl. Geophys.,15: 253-260.
  13. Ren, Z. and Liu, Y., 2015. Acoustic and elastic modeling by optimal time-space-domainstaggered-grid finite-difference schemes. Geophysics, 80(1): T17-T40.
  14. Tong, S.Y., Chen, M., Zhou, H.W., Li, L.W., Xu, X.G. and Wu, Z.Q., 2019.
  15. Reverse-time migration of converted S-waves of varying densities. J. Ocean Univ.China, 18:1093-1097.
  16. Virieux, J., 1984. SH-wave propagation in heterogeneous media: velocity-stressfinite-difference method. Explor. Geophys., 15: 265-265.
  17. Virieux, J., 1986. P-SV wave propagation in heterogeneous media; velocity-stressfinite-difference method. Geophysics, 51: 889-901.
  18. Virieux, J., Calandra, H. and Plessix, R.E., 2011. A review of the spectral,pseudo-spectral, finite-difference and finite-element modelling techniques forgeophysical imaging. Geophys. Prosp., 59: 794-813.
  19. Yang, L., Yan, H.Y. and Liu, H., 2014. Least squares staggered-grid finite-difference forelastic wave modelling. Explor. Geophys., 45: 255-260.
  20. Yang, L., Yan, H.Y. and Liu, H., 2017. Optimal staggered-grid finite-difference schemesbased on the minimax approximation method with the Remez algorithm.Geophysics, 82(1): T27-T42.
  21. Yee, K.S., 1966. Numerical solution of initial boundary value problems involving
  22. Maxwell's equations in isotropic media. IEEE Transact. Anten. Propagat., 14:302-307.
  23. Yong, P., Huang, J.P., Li, Z.C., Liao, W.Y., Qu, L.P., Li, Q.Y. and Liu, P.J., 2017.
  24. Optimized equivalent staggered-grid FD method for elastic wave modelling basedon plane wave solutions. Geophys. J. Internat., 208: 1157-1172.
  25. Zhang, J.H. and Yao, Z.X., 2013. Optimized explicit finite-difference schemes for spatialderivatives using maximum norm. J. Computat. Phys., 250: 511-526.
  26. Zhou, B. and Greenhalgh, S., 1992. Seismic scalar wave equation modeling by aconvolutional differentiator. Bull. Seismol. Soc. Am., 82: 289-303.
  27. Zhou, H. and Zhang, G., 2011. Prefactored optimized compact finite-difference schemesfor second spatial derivatives. Geophysics, 76(5): S87.
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Journal of Seismic Exploration, Print ISSN: 0963-0651, Published by AccScience Publishing
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