A HYBRID METHOD OF MATRIX INVERSION SUITED FOR 3D IMPLICITPRESTACK DEPTH MIGRATION
适用于三维隐式叠前深度偏移中矩阵求逆的混合算法

In depth wavefield migration, in order to extend the 2-D implicit method to 3-D case, a block-like diagonal matrix has to be inverted. General speaking, the matrix inversion will consume a large amount of computation time, which heavily hinder the application of 3-D implicit scheme in waveform migration. Under the helix boundary condition, the Helmhotz matrix has Toeplitz structure with positive definite property. The inversion of matrix can be realized by spectrum LU decomposition and direct solution. This paper proposes a hybrid scheme, which combines the advantages of spectrum LU decomposition and direct solution. Based on the table of matrix element of spectrum decomposition, the Helmhotz matrix can be decomposed by recursion of the direct solution. A numerical comparison has been made with the spectrum LU decomposition and direct solution. The accuracy of Helmhotz matrix is raised 10 times than that of spectrum, and the calculation speed is faster than that of the direct solution. In this way, the method can reduce the time of matrix inversion in 3-dimensional implicit difference migration and can be used to real data processing.