论三维等时线叠加反偏移中的有关问题

利用几何射线理论和一种考虑了积分域边缘贡献的二维稳想法，研究了三维等时线叠加反偏移中的反偏移场，反偏移加权函及反偏移孔径。结果证明，在有限孔径条件下，反偏移场的结构比已发表的结果要复杂和多。即使在最简单的条件下，反偏移场也是由反偏移信号的反偏移噪声（孔径效应）叠加而成的。而且，反偏移场的结构强烈地依赖于反偏移孔径边缘的位置。为了消除孔径效应，应采用最佳反偏移孔径和针对有限孔径的加权函数。根据定义，最佳反偏移孔径为稳相点的第一和第二Fresnel区之和。在第一Fresnel区内，有限孔径和加权函数与文献中所给出的加权函数完全一致。而在第二Fresnel区内，有限孔径加权函数为常规的加权函数与一窗函数的乘积。在反偏移孔径的边缘上，有限孔径加权函恒取零值。

ON SOME PROBLEMS IN 3-D ISOCHRONE - STACK DEMIGRATION

Using geometrical ray theory and a stationary phase method that takes the contribution from the boundary of the domain of integration into account, the author investigates the demigrated wavefield, the weight function, and the optimal demigration aperture in 3 D isochrone stack demigration. It has been shown that for a finite demigration aperture, the demigrated wavefield has a structure more complicated than that published in the literature. Even in the simplest case, the demigrated wavefield is a superposition of the demigration signal and the demigration noise (aperture effect). Also, the structure of the demigrated wavefield strongly depends on the position of the stationary point relative to the boundary of the demigration aperture. For eliminating the aperture effect, one should use the optimal migration aperture and the weight function for limited demigration aperture. By definition, an optimal demigration aperture is one consisting of the first and the second Fresnel zone of the stationary point under consideration. In the first Fresnel zone, the weight function is exactly the same as that published in the literature. In the second Fresnel zone, however, the weight function for limited demigration aperture is a product of the conventional weight function and a window function. On the boundary of the demigration aperture, the weight function for limited aperture equals to zero.