三维混合延拓一步法波动方程深度偏移

One-step wave equation depth migration using 3-D mixed continuation

对于二维陡倾斜地层，相位移延拓方法成像精度高、稳定性好、速度快，但难以适应速度的横向变化；频率、空间域的有限差分算法简单、稳定性好、能适应速度的纵、横向变化，但成像精度低、运算速度慢；而用快速的45°有限差分法与相位移延拓法相结合，则能使整个延拓过程既适应速度的纵、横向变化，又能够使得陡倾角地层精确归位。本文把这种混合延拓思想拓展成三维相位移加有限差分混合延拓法，并进一步提出了能适应速度纵、横向变化，构造任意复杂介质的三维一步法深度偏移。数值模拟试验结果表明，该方法具有移速度快、精度高的特点。

In the case of 2-D steep formations, phase-shift continuation method bringshigh image accuracy, good stability, fast operation I but it can hardly be adapted tolateral velocity variation. Finite difference method in frequency-space domain caus-es convenient operation, good stability and satisfactory adaptability to vertical andlateral velocity variations; however it results in poor image accuracy and slow oper-ation. Combining fast 45° finite difference method with phase-shift continuationmethod adapts whole continuation to vertical and lateral velocity variations, andachieves accurate migration of steep formations. The mixed continuation concept is extended to 3-D phase shift plus finite-dif-ference mixed continuation method, and then 3-D one-step depth migration tech-nique is put forward whlch applies to the medium where velocity varies verticallyand laterally, and where geologic structures are arbitrarily complex. Numericalmodeling result says that this technique is characterized by fast migration and highaccuracy.