When using seismic data to image complex structures, the reverse time migration (RTM) algorithm generally provides the best results when the velocity model is accurate. With an inexact model, moveouts appear in common image gathers (CIGs), which are either in the surface offset domain or in subsurface angle domain; thus, the stacked image is not well focused. In extended image gathers, the strongest energy of a seismic event may occur at non-zero-lag in time-shift or offset-shift gathers. Based on the operation of RTM images produced by the time-shift imaging condition, the non-zero-lag time-shift images exhibit a spatial shift; we propose an approach to correct them by a second pass of migration similar to zero-offset depth migration; the proposed approach is based on the local poststack depth migration assumption. After the proposed second-pass migration, the time-shift CIGs appear to be flat and can be stacked. The stack enhances the energy of seismic events that are defocused at zero time lag due to the inaccuracy of the model, even though the new focused events stay at the previous positions, which might deviate from the true positions of seismic reflection. With the stack, our proposed approach is also able to attenuate the long-wavelength RTM artifacts. In the case of tilted transverse isotropic migration, we propose a scheme to defocus the coherent noise, such as migration artifacts from residual multiples, by applying the original migration velocity model along the symmetry axis but with different anisotropic parameters in the second pass of migration. We demonstrate that our approach is effective to attenuate the coherent noise at subsalt area with two synthetic data sets and one real data set from the Gulf of Mexico.

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