f Cray T3D MPP imlementation of solving the pentadiagonal systems in the 3D depth migration

One-pass three-dimensional (3-D) depth migration can traditionally be solved using a finite-difference method in the spatial-frequency domain (Claerbout,1985). The computation is recursive in the depth domain, but it allows parallel and independant treatment of all temporal frequency components in the frequency domain. A direct solving of the 45 degree implicit finite-difference method involves the inversion of a large pentadiagonal system. Due to the intensive floating point operations and large memory allocation, the computer implementation is considerod too difficult for a production application. Several iterative schemes have been investigated [Cole,1989]. They indicated that these iterative methods have stability problems, particularly en the low frequency components.