频率域波动方程正演中的多网格迭代算法  

Multigrid iterative algorithm in frequency domain wave equation forward modeling

作　　者：马召贵[1] 王尚旭[1] 宋建勇[2] 

机构地区：[1]中国石油大学油气资源与探测国家重点实验室,北京102249 [2]中国石油勘探开发研究院物探技术研究所,北京100083

出　　处：《石油地球物理勘探》2010年第1期1-5,共5页Oil Geophysical Prospecting

基　　金：国家973项目(项目编号:2007CB209600;子课题编号:2007CB209601)资助

摘　　要：频率域波动方程求解中,需要对大型的稀疏矩阵求逆。直接解法计算时间长,占用内存大,更难以求解3D问题;目前普遍采用的迭代算法又存在收敛速度慢,用于复杂介质模型甚至存在不收敛的问题。本文选择在外层利用双共轭梯度稳定算法求解不定矩阵,采用一个频率域的衰减波动方程算子作为双共轭梯度稳定算法的预条件算子,然后在内层利用多重网格算法计算该算子的近似逆。文中方法能提高整个迭代算法的收敛速度,解决迭代算法不稳定问题。数值模拟结果验证了文中算法的有效性。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.

关 键 词：多重网格算法 迭代算法 波动方程 频率域 双共轭梯度 正演 方程求解 收敛速度 

分 类 号：O241.82[理学—计算数学]