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《Chinese Journal of Geophysics》 2003-03
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LU DECOMPOSITION WITH SPECTRAL FACTORIZATION IN SEISMIC IMAGING

LUO MINGQIU 1,2 LIU HONG1 LI YOUMING1 1 Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China 2 University of California, Sonta Cruz, CA 95064, USA  
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.
【Fund】: 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 ) .
【CateGory Index】: P315
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