45°方程叠后深度偏移的方向导数法

Directional derivative method for 45°acoustic equation poststack depth migration

中国科学院计算中心, 北京100080

Computing Center of Chiaa Academy of Sciences, Beijing City, Internal Postcode 100080

时间偏移由于忽略了速度的横向变化而导致成像偏离正确位置。作者从45°深度偏移方程出发, 引出方向导数, 并将速度横向变化所引起的折射效应项纳入此方向导数内, 使所构造的深度偏移方法在形式上与相应的时间偏移方法一致。因此, 只需对目前生产中应用的时间偏移模块略作修改, 即增加非整数节点插值部分, 就可实现深度偏移。这样不仅节省了计算工作量, 提高了计算效率, 而且也缩短了编程的时间。数值试验结果表明, 方法是可靠有效的。

Without taking aceount of the lateral variation of velocities, time migration may cause stratigraphie images to deviate from their correct underground positions. Starting from the 45° depth migration cquation, we introduce a parameter called Mirectional derivativeu and incorporate tht refraction effect term caused by lateral velocity variation into the directional derivative so as to make the depth migration be formally consistent with the corresponding time migration. In this way,depth migration is achicvable with the current application module after a slight modification,i. e. increasing the part of non-integer nodes for interpolation. The efficiency in both computation and programming is thus improved. The results frorn numerical trial show that this method is reliable and effective.