螺旋坐标系下的三维叠后深度偏移

3D post-stack depth migration in helical coordinate system.

3D偏移常用交替方向隐格式来实现 ,即将 3D平方根算子沿相互垂直的 2个方向分裂 ,这会导致明显的方位各向异性误差 (分裂误差 ) ,将算子沿多方向分裂是消除这种误差的有效手段。根据螺旋变换的思想 ,采用 4方向分裂法 ,用频率域差分法和混合法进行了三维叠后深度偏移 ,其优点是避免了不同方向求解时由于非矩形区域而带来的编程复杂性 ,明显消除了分裂误差 ,数值算例验证了该方法的正确性 ,且该方法具有较好的一般性和适用性。

The alternate direction implicit scheme is usually used in 3D migration. The scheme splits 3D square-root operator into two parts along inline and crossline directions. However, this may lead to visible azimuthal anisotropic migration errors, i.e. splitting errors. Multuway splitting is an effective method to eliminate such errors. In this paper, based on the idea of helical transformation, a new algorithm for 3D post-stack migration with four-way splitting is proposed. The algorithm is realized with ω-x finite difference method and hybrid method. The advantage of the new algorithm is its easiness to solve the extrapolation equations along difference directions while the solving area is irregular. The correctness and applicability of the method is tested with numerical examples.