有限元有限差分法二维波动逆时偏移初探

提出了采用有限元有限差分实现二维波动方程的逆时偏移算法。该方法在空间上 ,联合采用有限元法和有限差分法 ;对于地表 (水平 )方向 ,使用有限元法进行离散 ,将原方程转化为一个一维 (深度和时间 )问题的方程组 ;在深度和时间方向上 ,采用有限差分法来求解。介绍了算法的基本原理 ,给出了计算实例并与使用F K(频率波数 )域相移法、频率空间域有限差分法的结果进行了比较。与采用有限元的偏移方法相比 ,本方法可以节省大量内存 ;与采用有限差分的偏移方法相比 ,可以在一定程度上提高计算精度。本算法有可能在地震勘探数据处理中发挥一定的作用

Study on revese-time migration of two-dimensional wave equation with finite difference method

A reverse-time migration method namely finite element-finite difference method (FE-FDM) for two-dimensional wave equation was proposed. The wave equation was handled by the combination of the finite element method and finite difference method in spatial domain. By the use of the semi-discretization technique of finite element method in distance-coordinate, the original problem can be written as a coupled system of partial differential equations with lower dimensions, which continuously depends on time and depth-coordinate. The finite difference method was employed to solve these partial differential equations with lower dimensions. The concept and theory of this method were introduced. Two numerical calculation examples showed the excellent performance and potential of this method.