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《Oil Geophysical Prospecting》 2010-01
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Multigrid iterative algorithm in frequency domain wave equation forward modeling

Ma Zhao-gui1,Wang Shang-xu1 and Song Jian-yong2.1.State Key Lab of Petroleum Resources and Prospecting,China University of Petroleum,Beijing City,102249,China2.Geophysical Research Institute,Research Institute of Petroleum Exploration & Development of CNPC,Beijing City,100083,China  
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.
【Fund】: 国家973项目(项目编号:2007CB209600 子课题编号:2007CB209601)资助
【CateGory Index】: O241;P631.443
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