Gazdag migration in v(z)

Gazdag modeling and migration is not a unitary operator for depth-variable velocity. As a result, we lose steep dip components of the image after migration. The least-squares imaging method can be used instead to recover the high dip components. Now the operator in equation (2) becomes the Gazdag modeling operator. Figure (a) shows the velocity function used in the experiment, and the image in the model has the same syncline reflector as Figure (a). The result of the forward Gazdag modeling is shown in Figure (b). The image obtained by the migration of this data is shown in Figure (c) and we can see that the steep dip components is weakly imaged in comparison to the original model. The image obtained by the least-squares imaging of the same data, shown in Figure (d), shows more steep dip energy.

 

Gazmiginv
Figure 6 Least-squares Gazdag imaging: (a) The velocity model for the syncline reflector shown in Figure (a), (b) Gazdag modeling, (c) The image obtained by the Gazdag migration for (b), (d) The image obtained by the least-squares Gazdag imaging for (b) (after 10 iterations).