| 用于波场成像的谱法LU分解 |
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| 引用本文： | 罗明秋,刘洪,李幼铭.用于波场成像的谱法LU分解[J].地球物理学报,2003,46(3):421-427. |
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| 作者姓名： | 罗明秋 刘洪 李幼铭 |
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| 作者单位： | 1.中国科学院地质与地球物理研究所, 北京 100029 2 University of California, Sonta Cruz, CA 95064, USA |
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| 基金项目： | 中国科学院知识创新工程重大项目 (KZCX1- Y0 1)，国家自然科学基金委和大庆石油管理局联合资助项目 ( 49894190 ) . |
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| 摘 要： | 地震波场模拟和偏移成像等有限差分隐格式算法中的重要环节，是实现亥姆霍兹算子表示矩阵H的快速求逆运算. 在螺旋边界条件下，H具有Toeplitz结构的正定厄密矩阵，其快速求逆可由谱法LU分解实现. 本文分析了谱法LU分解对提高计算速度的原理及特点，并着重讨论了在不同类型的介质模型中，采用谱法分解矩阵H时带来的数值误差、误差的分布及其对波场计算的影响. 研究结果表明，对均匀介质而言，矩阵H各列具有相同的非零元素分布，谱法LU分解的误差在吸收边界条件下，不影响波场模拟和成像计算；但对于非均匀介质模型，矩阵H各列具有不同的非零元素分布，谱法LU分解的误差随介质不均匀性程度的增大而增大，势必影响非均匀介质中波场计算. 在波场模拟和成像等有限差分隐格式算法中，采用谱法LU分解完成矩阵求逆时，必须考虑到并尽量减少该方法的误差对波场计算的影响.
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| 关 键 词： | 波场成像 LU分解 谱因式分解 |
| 文章编号： | 0001-5733(2003)03-0421-07 |
| 收稿时间： | 2002-2-4 |
| 修稿时间： | 2002-10-7 |
LU DECOMPOSITION WITH SPECTRAL FACTORIZATION IN SEISMIC IMAGING |
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| LUO MINGQIU.LU DECOMPOSITION WITH SPECTRAL FACTORIZATION IN SEISMIC IMAGING[J].Chinese Journal of Geophysics,2003,46(3):421-427. |
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| Authors: | LUO MINGQIU |
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| Institution: | 1.Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China 2 University of California, Sonta Cruz, CA 95064, USA |
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| Abstract: | The inversion of Helmholtz matrix, a finite-difference representation of Helmholtz operator, plays a critical role in the numerical methods of seismic modeling and 3D depth migration. The Helmholtz matrix has a Toeplitz structure with a helical boundary condition. It is easy to be inversed by an efficient LU decomposition method, a spectral factorization method (SF method). In this paper we discuss the efficiency of SF method in LU decomposition, the errors of SF method in decomposing the matrix H of several different velocity models, errors distribution and their effects on seismic imaging. The result in this paper indicates that for constant velocity model all the arrays of matrix H have same nonzero values, and the errors brought by SF method will not affect the computation of wave fields if an absorb boundary condition is used; for non-constant velocity model, each array in matrix H has different nonzero values, and the error increases with variability degree of the velocity model, which are fatal to wave fields calculation. Therefore, once a SF method is used to calculate the wave field in seismic modeling and imaging, the errors given by this method should be considered to ensure a correct wave fields, which will be discussed in another paper. |
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| Keywords: | Seismic imaging LU decomposition Spectral factorization |
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