The prestack Kirchhoff migration approach is based on a model of subsurface scatterpoints that act as Huygens's secondary sources. According to Huygens principle, in the cases that scatter points lie on reflecting interface, as they are close to each other, superposition of their responses produce a coherent reflection event. Equivalent Offset Migration (EOM) is based on prestack Kirchhoff method that maps the energies of scatterpoints into an intermediate Common Scatter Point (CSP) gathers that, after successfully Normal Move Out (NMO) correction will create the migrated image. Since the data in the CSP gathers are sorted in hyperbolic paths, it serves as a useful tool for velocity analysis. In this paper, we study the behaviour of CSP gathers in areas that have strong lateral velocity variation. In this situation, we show that the traveltime response in equivalent offset domain is a tilted hyperbola that is asymmetric around vertical axis. The reason for the tilt is due to approximately a linear time shifts that depends to the dip angle and the degrees of velocity variation along the dipping interface. This effect reduces the resolution and accuracy of the velocity field picking in the semblance plots. We used three methodologies that can remedy this situation. These methods include producing two sided CSP gathers and analysing left and right sided gathers separately, estimating the tilt value using a least square fitting approach, and defining a Linear Time Shifted Hyperbolic Radon (LTSHR) transform.
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