## Residual migration velocity analysis in the plane wave domain : theory and applications

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This dissertation addresses velocity depth model building using residual migration velocity analysis in the plane wave domain. The criterion used for residual migration velocity analysis is that the results of migration with the correct velocity-depth model should reveal the same geologic structure on common image gathers (CIG’s). That is, the events on the CIG are horizontally aligned since they represent the image of the same subsurface position obtained at different angles. Use of an incorrect velocity-depth model in migration causes misalignment of events in a CIG, i.e., the events on the CIG exhibit residuals. By analyzing the residuals on the CIG, we can derive the depth and the velocity corrections and thus obtain a corrected velocity depth model. I first discuss the kinematics of seismic wave propagation and explore prestack depth migration in the plane wave (τ, p) domain. Then, I derive the exact one-, two-, and three-dimensional residual migration equations in the depth-p domain after pre-stack depth migration. To perform interval velocity analysis, a suite of velocity corrections is tested to do residual migration but only one gives the best image. The combination of this velocity correction and the original migration velocity improves the velocity model. The two main advantages of the new method are that it derives interval velocities directly and is computationally very efficient because only a top down residual migration is needed instead of top-down pre-stack depth migration. Next, I apply the new method to both the synthetic and real seismic data. The synthetic data examples show that the 2D method gives a better residual migration result than the 1D method when strong dips are present but the 1D equation also works well for 2D models when the dip angles are small. After getting a new velocity depth model, one can use the new model to perform a complete residual migration which gives much better CIG’s and stacked sections than those without residual migration. Alternatively, we can also use the new model to migrate the data again and then repeat the residual velocity analysis for another iteration. The number of iterations depends on the initial model and the precision required. In the field data example, a reasonable model was obtained after only four iterations.