改进的有限元波动方程偏移方法

Improved finite element method for wave equation migration

石油大学, 北京100083

Petroleum University, Beijins City,Intercode: 100083

本文提出的有限元法波动方程偏移方法(IPEWEM), 对波动方程深度偏移的有限元方法作了三点改进：一是从整体形成递推公式出发, 对速度场变量进行等参插值, 改变了从单元到整体的叠加构成其法的过程；二是增加了离散后的误差校正因子；三是利用矩阵的直乘分解简化了算法中的迭代矩阵, 从而得到一种深度偏移的新的递推格式。该算法保持了有限元方法的优点, 而存贮量和计算量均有大幅度下降, 精度比原来的方法要高, 成像清晰, 是一种实用的高精度深度偏移方法。

This paper proposes an improved finite element method for wave equation migration. The modification concerns following 3 aspccts: (1) instead of discretizing cells by cells, the discretization of wavc field is uniformty. (2) an error-correcting factor is introduced into the recurrence formula. (3)the recurrence formula are further simplified by direct product of matries.The proposed method preserves the advantapes of finite element methods,whereas greatly reduces the storage requirement and computational time. The precision and quality of the image rcsulted are also improved,so that the new method is of practical use.