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

##### Abstract

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.