Solving least squares Kirchhoff migration using multigrid methods

Abstract

In order to attenuate the migration artifacts and increase the special resolution of the subsurface reflectivity, conventional migration may be replaced by the least squares migration (LSM). However, this is a costly procedure. To reduce the cost, the feasibility of using the multigrid methods in solving the linear system of prestack Kirchhoff LSM equation is investigated. This study showed that the conventional method of multigrid is not viable to solve Kirchhoff LSM equation for at least two reasons. The main reason is that the Hessian matrix is not a diagonally dominant matrix. Therefore, the conventional iterative solvers of the multigrid are not effective. The performance of Conjugate Gradient (CG) multigrid is discussed. It is shown that since CG does not have a smoothing property, it should not be considered as an effective multigrid iterative solver. Using the CG as an iterative solver for the multigrid may slightly reduces the number of iterations for the same rate of convergence in the CG itself. However, it does not reduce the total computational cost.