Mul tigrid iterative algorithm in frequency domain wave equation forward modeling
Ma Zhao-gui1, Wang Shang-xu1,2
1. State Key Lab of Petroleum Resources and Prospecting,China University of Petroleum,Beijing City,102249,China;
2. Geophysical Research Institute,Research Institute of Petroleum Exploration & Development of CNPC,Beijing City,100083,China
Abstract：In solving wave equation in frequency domain,large-scale sparse matrix inverse is needed,if directly calculating the matrix inverse long time would be taken and large memory is needed,and further more it is difficult to solve 3D problem.But if utilizing the iterative algorithm which is being used nowadays,the convergence speed is very slow,or even not convergent for complicated medium model.In this paper bi-conjugate gradient stable algorithm is used to solve indefinite matrix for the outer layers,a attenuated wave equation operator in frequency domain is adopted as preconditioner for the bi-conjugate gradient stable algorithm,then multigrid algorithm is used to calculate the approximate inverse for the preconditioner for the inner layers.The method introduced in this paper raises the convergence speed for the iterative algorithm,instability problem for the iterative algorithm is also got solved,the numerical simulation results validates the effectiveness of the algorithm in this paper.
马召贵, 王尚旭, 宋建勇. 频率域波动方程正演中的多网格迭代算法[J]. 石油地球物理勘探, 2010, 45(1): 1-5.
Ma Zhao-gui, Wang Shang-xu, Song Jian-yong. Mul tigrid iterative algorithm in frequency domain wave equation forward modeling. OGP, 2010, 45(1): 1-5.
