基于OpenMP加速的无单元逆时偏移成像  

OpenMP-accelerated element-free reverse-time migration

作　　者：周震[1] 贾晓峰[1] 

机构地区：[1]中国科学技术大学地球和空间科学学院,合肥230026

出　　处：《物探化探计算技术》2016年第6期821-831,共11页Computing Techniques For Geophysical and Geochemical Exploration

基　　金：国家自然科学基金(41374006;41274117)

摘　　要：有限元法(FEM)和有限差分法(FDM)被用于求解地震波动方程,但该两种方法,在实际运用中,计算精度和效率会出现一些不足。事实上,无单元法(EFM)已经被用于地震波模拟和偏移成像,与FDM和FEM相比,EFM具有独特的优势:不需要事先划分大量网格,仅需要研究区域中节点和边界的信息,具有局部拟合的特点。但当前EFM处理地震波模拟和成像仍存在很多问题,如求取系数矩阵耗费过多计算机内存和计算量过大的问题。这里对系数矩阵采用按行压缩(CSR)的格式存储,并采用分步计算的策略。在时间递推过程中,求解线性方程组,为了提高计算效率,基于已有的FDM数据,利用OpenMP多核加速。通过上述方法,有效地解决了内存限制和计算效率的问题。数值算例表明,这里提出的方法是精确和高效的。The wave-equation-based method was widely used in seismic modeling and imaging in the past years.Many numerical strategies such as the finite element method（FEM）and the finite difference method（FDM）are developed in solving seismic wave equations.However,both methods have some shortcomings of either accuracy or computational cost in practice.In fact,element-free method（EFM）has been applied in seismic modeling and seismic migration imaging.Compared with FEM and FDM,EFM has unique advantages：it doesn＇t need to be divided a large number of grid in advance and it satisfies local fitting because only the information of the nodes and the boundary of the study area are required in computation.However,there are many problems that EFM is applied in seismic modeling and seismic migration imaging in present,e.g.the problems of storage and computation efficiency about computing the coefficient matrix.The storage is caused by improper storage of sparse coefficient matrix.In this paper we compress the sparse matrices by the compressed sparse row（CSR）format and employ the following strategy：firstly,the value is computed at the corresponding model nodes within the influence domain of each Gauss point;secondly,the summation is performed within the influence domain of different Gauss points that contain the same model node.In the calculation of wave field time recursive,we solve the linear equations with the help of linear sparse solver＇PARDISO＇.In order to further improve the computation efficiency,we use OpenMP basing the existing FDM data.Through the above methods,we can effectively solve these problems of memory limit and computational efficiency.The final results indicate that the above methods are accurate and efficient.

关 键 词：无单元法 系数矩阵 线性方程组 OPENMP 逆时偏移 

分 类 号：P631.4[天文地球—地质矿产勘探]