We previously discussed that by formulating the irregular geometries problem in the least-squares sense it is possible to solve for gaps in the data using a regularization operator. The significant element of the previous section is the use of the AMO operator as the regularization term in the solution of the least-squares problem.

Recently, Rosales and Biondi 2001 developed and implemented an AMO operator for converted waves (PSAMO). This operator acts in the Fourier domain and also handles the amplitudes properly. Due to this new PSAMO operator, it is now possible to solve for the irregular geometries problem on converted wave data by following the same procedure as in the previous section.

Partial stacking requires the data to be coherent among the traces.
NMO obtains this coherency well for *PP* data. However,
for converted waves we know that the moveout is not a perfect
hyperbola, even in constant velocity media.

On conventional *PP* processing, the AMO operator is
velocity independent. However, for converted waves the
PSAMO operator depends on the ratio between the *P* and
the *S* velocities (). Therefore, we need *a priori*
velocity estimation. This fact suggests that for different
values we will have different regularization results.

Traditional *PS* processing
intends to first sort the data in the common conversion
point (CCP) domain. This process has always been
dependent on the value; therefore, the *PS* processing community performs
iterative processing (CCP binning, velocity analysis) until obtaining a satisfactory result.

The PSAMO operator that we use has the advantage of not demanding the data in the CCP domain. This operator is a cascade operation of converted wave dip moveout Rosales et al. (2001) (PSDMO) and inverse PSDMO. The input for the PSDMO operator is in the CMP domain after NMO, since this operator performs the lateral shift correction.

After performing NMO on the *PS* data and
the *PP* data, the value is Huub Den Rooijen (1991):

(8) |

In order to proceed with the *PS* data regularization, a process that
depends on the value, we need to have the
*PP* section regularized as well as the RMS velocity model.
We proceed with the following algorithm:

- 1.
- Sort the data in the CMP domain.
- 2.
- Estimate velocity model on the
*PS*section. - 3.
- Estimate the section with equation (8).
- 4.
- If it is not the first iteration, compare the previous and
the actual sections and:
- (a)
- if they are the same, finish the process.
- (b)
- if they are not, continue.

- 5.
- Apply NMO on the
*PS*section. - 6.
- Apply PSAMO regularization.
- 7.
- Apply inverse NMO.
- 8.
- Go back to step 2.

This is our main methodology to correctly regularize
*PS* data.

11/11/2002