地球物理学报 ›› 2016, Vol. 59 ›› Issue (7): 2650–2662.doi: 10.6038/cjg20160728

• 应用地球物理学 • 上一篇    下一篇

基于余弦调制Chebyshev窗的弹性波高精度正演

郑婉秋1, 孟小红1, 刘建红2, 王建1   

  1. 1. 中国地质大学(北京)地球物理与信息技术学院, 北京 100083;
    2. 中国石油集团东方地球物理勘探有限责任公司物探技术研究中心, 河北 涿州 072751
  • 收稿日期:2015-11-30 修回日期:2016-06-11 出版日期:2016-07-05
  • 通讯作者: 孟小红,教授,主要从事计算与综合地球物理研究.E-mail:mxh@cugb.edu.cn E-mail:mxh@cugb.edu.cn
  • 作者简介:郑婉秋,在读硕士,主要从事复杂介质中地震波模拟及偏移成像方面的研究.E-mail:453294543@qq.com
  • 基金资助:
    国家重大科研装备研制项目(ZDYZ2012-1-02-04)和国家自然科学基金(41474106)联合资助.

High precision elastic wave equation forward modeling based on cosine modulated Chebyshev window function

ZHENG Wan-Qiu1, MENG Xiao-Hong1, LIU Jian-Hong2, WANG Jian1   

  1. 1. School of Geophysics and Information Technology, China University of Geosciences, Beijing 100083, China;
    2. BGP Research and Development Center, CNPC, Hebei Zhuozhou 072751, China
  • Received:2015-11-30 Revised:2016-06-11 Online:2016-07-05

摘要: 有限差分时间域正演是弹性波逆时偏移和全波形反演的基础,正演的计算精度也控制着偏移结果的准确性,若精度不高,则在偏移、反演后会带来假象.为了有效提高正演精度,本文结合窗函数优化方法,在窗函数截断伪谱法空间褶积序列以逼近有限差分算子的基础上,提出了一种基于Chebyshev窗的余弦调制模型,在原始Chebyshev窗的基础上引入了调制次数和调制范围,通过调节这两个参数可以人工可视化的调节截断误差,新的窗函数继承了Chebyshev窗的特点,在不明显降低截断谱范围的基础上明显降低了截断误差.本文针对不同正演阶数N,给出了一组经验调制系数,并通过数值模拟方法,对比了新方法、改进二项式窗和基于最小二乘优化方法的正演效果.结果表明,基于余弦调制的Chebyshev窗控制数值频散的能力更强,在大网格下可以得到更精确的正演结果.从经济角度分析,该方法减小了计算花费,提高了计算效率.

关键词: 有限差分, 数值频散, 窗函数, 弹性波, 余弦调制

Abstract: The finite difference forward modeling is the basis of elastic wave reverse-time migration and full waveform inversion in the time domain. The accuracy of forward modeling also controls the accuracy of seismic imaging and inversion. The migration or inversion will bring illusion if the accuracy is not high. We can get optimized explicit finite difference operators by using the window function to truncate spatial convolution counterpart of the pseudo-spectral method. Based on this, a cosine modulated Chebyshev window is designed. On the basis of the original Chebyshev window, the modulation times and modulation domain are introduced, and we can adjust truncation error visually by controlling these two parameters. As the new window function inherits the character of Chebyshev window, we observe that the spectral range using the modulated window function for truncation is significantly broader than using the conventional window function with stable error. For different forward modeling orders N, we give a set of empirical modulation factors and compare the forward modeling effect of the new method and improved binomial window by the numerical simulation method. The results demonstrate that the operators based on the cosine modulated Chebyshev window can efficiently suppress the numerical dispersion and get more accurate forward modeling results on the large grid. From economic perspective, this method reduces the computational cost and improves efficiency.

Key words: Finite difference, Numerical dispersion, Window function, Elastic wave, Cosine modulation

中图分类号: 

  • P631
Alterman Z, Karal F C Jr. 1968. Propagation of elastic waves in layered media by finite difference methods. Bull. Seism. Soc. Am., 58(1): 367-398.
Boris J P, Book D L. 1973. Flux-corrected transport. I. SHASTA, a fluid transport algorithm that works. Journal of Computational Physics, 11(1): 38-69.
Carcione J M, Kosloff D, Behle A, et al. 1992. A spectral scheme for wave propagation simulation in 3-D elastic-anisotropic media. Geophysics, 57(12): 1593-1607, doi: 10.1190/1.1443227.
Chang W F, McMechan G A. 1987. Elastic reverse time migration. Geophysics,52:1367-1375.
Cheng B J, Li X F, Long G H. 2008. Seismic waves modeling by convolutional Forsyte polynomial differentiator method. Chinese J. Geophys. (in Chinese), 51(2): 531-537.
Chu C L, Stoffa P L. 2012. Determination of finite-difference weights using scaled binomial windows. Geophysics, 77(3): W17-W26, doi: 10.1190/GEO2011-0336.1.
Dablain M A. 1986. The application of high-order differencing to the scalar wave equation. Geophysics, 51(1): 54-66, doi: 10.1190/1.1442040.
Diniz P S R, da Silva E A B, Netto S L. 2012. Digital Signal Processing System Analysis and Design. Beijing: China Machine Press.
Dong L G, Ma Z T, Cao J Z, et al. 2000. A staggered-grid high-order difference method of one-order elastic wave equation. Chinese J. Geophys. (in Chinese), 43(3): 411-419.
Fei T, Larner K. 1995. Elimination of numerical dispersion in finite-difference modeling and migration by flux-corrected transport. Geophysics, 60(6):1830-1842.
Fornberg B. 1987. The pseudospectral method: Comparisons with finite differences for the elastic wave equation. Geophysics, 52(4): 483-501, doi: 10.1190/1.1442319.
Gazdag J. 1981. Modeling of the acoustic wave equation with transform methods. Geophysics, 46(6):854-859,doi:10. 1190/1.1441223.
Igel H, Mora P, Riollet B. 1995. Anisotropic wave propagation through finite-difference grids. Geophysics, 60(4):1203-1216, doi:10.1190/1.1443849.
Kelly K R, Ward R W, Treitel S, et al. 1976. Synthetic seismograms: A finite-difference approach. Geophysics, 41(1): 2-27,doi:10.1190/1.1440605.
Kosloff D D, Baysal E. 1982. Forward modeling by a Fourier method. Geophysics, 47(10): 1402-1412, doi: 10.1190/1.1441288.
Lee C, Seo Y. 2002. A new compact spectral scheme for turbulence simulations. Journal of Computational Physics, 183(2):438-469, doi:10.1006/jcph.2002.7201.
Liu Y, Li C C, Mou Y G. 1998. Finite-difference numerical modeling of any even-order accuracy. Oil Geophysical Prospecting (in Chinese), 33(1): 1-10.
Madariaga R. 1976. Dynamics of an expanding circular fault. Bull. Seism. Soc. Am., 65: 163-188.
Saenger E H, Shapiro S. 2002. An effective velocities in fractured media: A numerical study using the rotated staggered finite-difference grid. Geophysical Prospecting, 50: 183-194.
Saenger E H,Thomas B. 2004. Finite-difference modeling of viscoelastic and anisotropic wave propagation using the rots-ted staggered grid. Geophysics, 69(2): 583-591.
Sun R, McMechan G A. 2001. Scalar reverse-time depth migration of prestack elastic seismic data. Geophysics, 66 (5): 1519-1527.
Wang Z Y, Liu H, Tang X D, et al. 2015. Optimized finite-difference operators based on Chebyshev auto-convolution combined window function. Chinese J. Geophys. (in Chinese), 58(2): 628-642, doi: 10.6038/cjg20150224.
Yang D H, Teng J W. 1997. FCT finite difference modeling of three-component seismic records in anisotropic medium. Oil Geophysical Prospecting (in Chinese), 32(2): 181-190.
Yang L, Yan H Y, Liu H. 2014. Least squares staggered-grid finite-difference for elastic wave modelling. Exploration Geophysics, 45: 255-260.
Zhang J H, Yao Z X. 2013. Optimized finite-difference operator for broadband seismic wave modeling. Geophysics, 78(1): A13-A18, doi: 10.1190/GEO2012-0277.1.
Zhou B, Greenhalgh S A. 1992. Seismic scalar wave equation modeling by a convolutional differentiator. Bull. Seism. Soc. Am., 82(1): 289-303.
附中文参考文献
程冰洁, 李小凡, 龙桂华. 2008. 基于广义正交多项式褶积微分算子的地震波场数值模拟方法. 地球物理学报, 51(2): 531-537.
董良国, 马在田, 曹景忠等. 2000. 一阶弹性波方程交错网格高阶差分解法. 地球物理学报, 43(3): 411-419.
刘洋, 李承楚, 牟永光. 1998. 任意偶数阶精度有限差分法数值模拟. 石油地球物理勘探, 33(1): 1-10.
王之洋, 刘洪, 唐祥德等. 2015. 基于Chebyshev自褶积组合窗的有限差分算子优化方法. 地球物理学报, 58(2): 628-642, doi: 10.6038/cjg20150224.
杨顶辉, 腾吉文. 1997. 各向异性介质中三分量地震记录的FCT有限差分模拟. 石油地球物理勘探, 32(2): 181-190.
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