Velocity analysis, whether ray-based Clapp (2001) or wave-equation-based Sava and Biondi (2003), requires estimation of the curvature parameters of common image gathers (CIGs). Residual moveout and residual migration Sava (2003) are two leading methods for estimating the curvature parameters. Residual migration, the more accurate of the two methods, constrains only global velocity changes. However, residual moveout, although assuming stationary rays, estimates the curvature parameters of CIGs affected by local velocity changes.
For 2-D problems, Biondi and Symes (2003) show that the image point should be on a line that passes through the crossing point between source and receiver rays and is normal to the reflector. When the migration velocity is not the true velocity, the migrated image points move in the direction normal to the reflector at the reflection point. However, conventional residual moveout methods assume that the image point moves only vertically. For steeply dipping reflectors, the normal direction deviates from vertical, approaching horizontal for nearly vertical reflectors. Thus, the vertical moveout assumption in the conventional residual moveout methods may lead to significant errors in the estimation of the curvature parameters for velocity analysis.
In this paper, we suggest a new way to perform residual moveout, which we call dip-dependent residual moveout. The key idea is to perform phase shifts in the Fourier domain instead of image-point shifts in the space domain. In the Fourier domain, dip information can be obtained easily, so that the new method can account for dip effects and result in more accurate curvature parameters.