Hubral观测的解析证明

ON THE PROOF HUBRAL' S OBSERVATION

同济大学

对共中心点叠加剖面进行常规地震偏移是复杂地区地震资料处理的一个重要步骤,它使地下界面的成像更为清晰。但它只适用于均匀介质或水平层状介质,当地下界面存在倾角时,其下面的反射点的绕射曲线虽仍近似为一双曲线,但其最小点已偏离反射点的水平位置,因此经过偏移后,像点与反射点的水平位置就有较大的误差。1977年Hubral提出绕射曲线的最小点位于成像射线出射地面的位置,即沿成像射线的旅行时为最小,这就是Hubral观测。这是Larner著名的成像射线深度偏移的理论基础,同时也是非均匀介质地震勘探的一个基础理论问题。本文利用解析的方法在二维单倾斜界面的条件下证明了这一结论。同时还对常规偏移的横向误差及纵向误差作了定量的讨论。

One of very important methods in seismic data processing for gologically complex areas is seismic migration which makes a clear picture of the subsurfaces. But it applies only to homogeneous media or layered earth. When a diffractor is under a dipping interface there is a considerable deviation between the image point and the diffractor. The reason is that diffractor is not vertically under the apex of its diffraction curve, and conventional migratotions (Kirchhoff, finite difference and F-K methods) only collapse seismic energies along the diffraction curve to the apex. Hubral^[1] suggested in 1977 without proof that the apex is just under the emergent point of the image ray,along which the travelling time is minimum. This conclution is named after Hubral's Guess or Hubial's Observation (lamer et al^[3], 1981). This is the foundation of Larner's well-known depth migration for migrated time section, as swell as the fundamental problem of exploration in inhomogeneous media. This paper proves the conclution under the condition of 2 -D with single dipping interface by an analytic method. It also discribes the relationship between the deviation of the image point off the diffractor and the velocity ratio with all kinds of angles.