大倾角有限差分深度偏移

High dip finite difference depth migration.

当介质的速度在横向上存在较大的变化时,波动方程时间偏移不能使地下的构造正确成像。因此,人们开展了对深度偏移方法的研究。本文用拟微分算子方法将波动方程分裂为绕射方程和时移方程。对绕射方程进行45°单程波近似,并修改方程的系数,可使偏移角度的适应范围扩大到60°。引进辅助函数,把45°方程分解为低阶偏微分方程组,可以方便地采用差分法求解。本文提出的方法,计算量仅为15°时间偏移的1.5倍,是一种快速实用的深度偏移方法。

Wave equation time migration fails to image subsurface geological structure correctly in the case of obvious lateral seismic velocity variation. Consequently, people have begun the study of depth migration. By using pseudo differential operator, a wave equation can be split into a diffraction equation and a time shift equation. The migration range can be increased to 60° by approximating the diffraction equation to 45° one-way wave equation,with the coefficient modified. The introduction of auxiliary function makes the 45° equation change into low order partial differential equations, which can be easy solved using difference method. This method takes 1.5 times the operation of 15° equation time migration. It is a fast and practical depth migration method.