<?xml version="1.1" encoding="utf-8"?>
<article xsi:noNamespaceSchemaLocation="http://jats.nlm.nih.gov/publishing/1.1/xsd/JATS-journalpublishing1-mathml3.xsd" dtd-version="1.1" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"><front><journal-meta><journal-id journal-id-type="publisher-id">JSE</journal-id><journal-title-group><journal-title>Journal of Seismic Exploration</journal-title></journal-title-group><issn>0963-0651</issn><eissn/><publisher><publisher-name>AccScience Publishing</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi"/><article-categories><subj-group subj-group-type="heading"><subject>Article</subject></subj-group></article-categories><title>Optimization of staggered grid finite-difference coefficients based on conjugate gradient method</title><url>https://geophysical-press.com/journal/JSE/articles/72</url><author>JINKEJIE,HUANGJIANPING,ZOUQIANG,WANGZIYING,TONGSIYOU,LIUBIN,HUZIDUO</author><pub-date pub-type="publication-year"><year>2022</year></pub-date><volume>31</volume><issue>1</issue><history><date date-type="pub"><published-time>2022-02-01</published-time></date></history><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.</abstract><keywords>finite-difference, staggered grid, numerical dispersion, difference coefficients, conjugate gradient</keywords></article-meta></front><body/><back><ref-list><ref id="B1" content-type="article"><label>1</label><element-citation publication-type="journal"><p>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.Chu, C. and Stoffa, P.L., 2012. Determination of finite-difference weights using scaledbinomial windows. Geophysics, 77(3): W17-W26.Etgen, J.T., 2007. A tutorial on optimizing time domain finite-difference schemes:“Byond Holberg”. Technical Report, 33-43.Fei, T. and Larner, K., 1995. Elimination of numerical dispersion in finite-differencemodeling and migration by flux-corrected transport. Geophysics, 60: 1830-1842.Fornberg, B., 1987. The pseudospectral method: Comparisons with finite differences forthe elastic wave equation. Geophysics, 52: 483-501.Huang, J.P., Qu, Y.M., Li, Q.Y., Li, Z.C., Li, G.L., Bu, C.C. and Teng, H.H., 2015.Variable-coordinate forward modeling of irregular surface based on dual-variablegrid. Appl. Geophys., 12: 101-110.Igel, H., Mora, P. and Riollet, B., 1995. Anisotropic wave propagation throughfinite-difference grids. Geophysics, 60: 1203-1216.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.Liu, Y., 2013. Globally optimal finite-difference schemes based on least-squares.Geophysics, 78(4): T113-T132.Madariaga, R., 1976. Dynamics of an expanding circular fault. Bull. Seismol. Soc. Am.,66: 639-666.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.Ren, Z. and Liu, Y., 2015. Acoustic and elastic modeling by optimal time-space-domainstaggered-grid finite-difference schemes. Geophysics, 80(1): T17-T40.Tong, S.Y., Chen, M., Zhou, H.W., Li, L.W., Xu, X.G. and Wu, Z.Q., 2019.Reverse-time migration of converted S-waves of varying densities. J. Ocean Univ.China, 18:1093-1097.Virieux, J., 1984. SH-wave propagation in heterogeneous media: velocity-stressfinite-difference method. Explor. Geophys., 15: 265-265.Virieux, J., 1986. P-SV wave propagation in heterogeneous media; velocity-stressfinite-difference method. Geophysics, 51: 889-901.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.Yang, L., Yan, H.Y. and Liu, H., 2014. Least squares staggered-grid finite-difference forelastic wave modelling. Explor. Geophys., 45: 255-260.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.Yee, K.S., 1966. Numerical solution of initial boundary value problems involvingMaxwell's equations in isotropic media. IEEE Transact. Anten. Propagat., 14:302-307.Yong, P., Huang, J.P., Li, Z.C., Liao, W.Y., Qu, L.P., Li, Q.Y. and Liu, P.J., 2017.Optimized equivalent staggered-grid FD method for elastic wave modelling basedon plane wave solutions. Geophys. J. Internat., 208: 1157-1172.Zhang, J.H. and Yao, Z.X., 2013. Optimized explicit finite-difference schemes for spatialderivatives using maximum norm. J. Computat. Phys., 250: 511-526.Zhou, B. and Greenhalgh, S., 1992. Seismic scalar wave equation modeling by aconvolutional differentiator. Bull. Seismol. Soc. Am., 82: 289-303.Zhou, H. and Zhang, G., 2011. Prefactored optimized compact finite-difference schemesfor second spatial derivatives. Geophysics, 76(5): S87.</p><pub-id pub-id-type="doi"/></element-citation></ref></ref-list></back></article>
