Preconditioned iterative 3-D finite-difference migration or modeling on MPP system

In seismic data processing, the formulation of the three-dimensional one-pass 45° implicit finite-difference migration schemes requires the solution of a huge number of very large pentadiagonal complex linear systems. Most of the effort in using iterative methods to accurately solve the problem was not successful due to the bad condition numbers of the systems. We present a parallel algorithm to solve the large sparse systems iteratively, based on the preconditioned conjugate gradient (PCG) method. First, by reformation of the linear systems and choosing a special preconditioner, the PCG method is effective in solving these linear systems. By using a nonuniform distribution of linear systems among all PEs, a special global summation procedure and a heterogeneous computation technique, the parallel algorithm is quite efficient. Finally, we present some numerical results on both the CRAY-YMP and CRAY-T3D showing the efficiency and effectiveness of the algorithm