3D field data example

This section presents an example of wave-equation migration velocity analysis applied to a 3D dataset from the Gulf of Mexico (BP3d.sini - BP3Dx.77000).

BP3d.sini shows the initial velocity model, obtained after multiple iterations of traveltime tomography. As for the preceding 2D example, the model consists of a large overhanging salt body which creates both complicated wave propagation and un-illuminated regions subsalt. Both phenomena reduce the ability of traveltime tomography to properly describe wavepaths subsalt, which leads to less accurate velocities in the complicated areas with multipathing and shadows. An example is illustrated along the inline direction in BP3d.sini, approximately at the location of the vertical line. BP3d.pini shows the image corresponding to the model in BP3d.sini.

For cost reasons, in this example I do not use the entire image. I concentrate my attention on the small anomalies located right under the salt nose as pictured in BP3d.sini. BP3d.mask indicates the portion of the image/velocity used for this analysis. I use this part of the starting (background) image to generate the wavefield corresponding to the initial (background) velocity. Then, I run normal-incidence WEMVA as discussed in wemva.

 

BP3d.sini
Figure 22 3D Gulf of Mexico example.  Initial slowness model. Compare with BP3d.smix2.

 

BP3d.pini
Figure 23 3D Gulf of Mexico example.  Initial image. Compare with BP3d.pmix2.

 

BP3d.mask
Figure 24 3D Gulf of Mexico example.  Box selected for WEMVA.

The first step in WEMVA is to generate an image perturbation. For this, I run prestack residual migration starting from the background image pictured in BP3d.pini. The velocity ratios I use are between 0.92 and 1.07. BP3d.dro shows the picked velocity ratio that optimizes angle gather flatness at every location in the 3D image. BP3d.www is the associated weight quantifying the reliability of the picks in BP3d.dro. The brighter colors indicate higher reliability than the darker ones. The subsalt picks are less reliable than those in the sedimentary region away from the salt.

 

BP3d.dro
Figure 25 3D Gulf of Mexico example.  Velocity ratio perturbation picked after residual migration.

 

BP3d.www
Figure 26 3D Gulf of Mexico example.  Data residual weight.

Based on the background image in BP3d.pini and the picks in BP3d.dro, I construct the image perturbation in BP3d.dia. As indicated earlier, this image perturbation corresponds to normal incidence, although it incorporates moveout/focusing information extracted from prestack residual migration. After 25 linear iterations of WEMVA, I obtain the slowness perturbation in BP3d.isx. I use preconditioned regularized inversion (22), where for regularization I use an isotropic Laplacian operator.

BP3d.datres shows the data residual at a fixed crossline, function of iterations. The number associated with each panel indicates the iteration number. We can observe that the data residual is decreasing in absolute magnitude and that it becomes less structured function of iterations. The plot in the lower-right panel shows the absolute magnitude of the data residual monotonically decaying function of iterations, indicating that the conjugate gradient procedure is converging.

 

BP3d.dia
Figure 27 3D Gulf of Mexico example.  Image perturbation.

 

BP3d.isx
Figure 28 3D Gulf of Mexico example.  Slowness perturbation.

 

BP3d.datres
Figure 29 3D Gulf of Mexico example.  Data residual function of iterations.

Next, I update the background slowness model by adding a smooth version of the computed perturbation to the background velocity. BP3d.wso shows the initial slowness inside the box used for WEMVA. For comparison, BP3d.wsz shows the updates slowness model in the same region. The most obvious observation we can make is that the anomalies associated with the shadow zones corresponding to the salt body are reduced, although the general trends of the slowness model remain the same. This is not a surprise, since the starting model is already a good model which does not need much updating.

 

BP3d.wso
Figure 30 3D Gulf of Mexico example.  Initial slowness model in the inversion box. Compare with BP3d.wsz.

 

BP3d.wsz
Figure 31 3D Gulf of Mexico example.  Updated slowness model in the inversion box. Compare with BP3d.wso.

BP3d.smix2 shows the slowness obtained by embedding the slowness from the inversion box in the initial slowness. This process is not ideal, since it may create velocity discontinuities that need to be smoothed-out. The model in BP3d.smix2 needed such smoothing under salt, close to the vertical salt pillar. BP3d.pmix2 shows the updated image obtained by migration with the slowness in BP3d.smix2.

 

BP3d.smix2
Figure 32 3D Gulf of Mexico example.  Updated slowness model. Compare with BP3d.sini.

 

BP3d.pmix2
Figure 33 3D Gulf of Mexico example.  Updated image. Compare with BP3d.pini.

Finally, BP3Di.70700 to BP3Dx.77000 show two inlines and two crosslines taken from the prestack image obtained by migration of the 3D prestack data with the initial and updated slowness model. From top to bottom, the panels correspond to the migrated image, a few angle gathers taken at equally spaced locations, and the semblance map computed on the angle gathers around the horizontal direction.

Since the initial and the updated velocity models are close to one-another, there are no large changes in the image. Most of the changes are marginal, and cannot be properly displayed without ``before-after'' movies. Slight increases in semblance are visible, mostly under the salt indicating better velocity and flatter gathers. Of course, since the starting model is very close to the correct one, not everything in the image improves. There are portions where the semblance actually decreases. However, the overall image quality measured by semblance increases slightly.

 

BP3Di.70700
Figure 34 3D Gulf of Mexico example.  Inline comparison of initial (left) and final (right) models. Image stack (top), angle gathers (middle) and image semblance (bottom).

 

BP3Di.77426
Figure 35 3D Gulf of Mexico example.  Inline comparison of initial (left) and final (right) models. Image stack (top), angle gathers (middle) and image semblance (bottom).

 

BP3Dx.74000
Figure 36 3D Gulf of Mexico example.  Crossline comparison of initial (left) and final (right) models. Image stack (top), angle gathers (middle) and image semblance (bottom).

 

BP3Dx.77000
Figure 37 3D Gulf of Mexico example.  Crossline comparison of initial (left) and final (right) models. Image stack (top), angle gathers (middle) and image semblance (bottom).