LU DECOMPOSITION WITH SPECTRAL FACTORIZATION IN SEISMIC IMAGING
用于波场成像的谱法LU分解

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.