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Imaging and illumination

In order to examine this weighting operator, I began by selecting a dataset from an area with poor illumination. I chose to work with part of the Sigsbee2A dataset. This dataset has a salt body with strong shadow zones beneath its edges. The velocity model can be seen in Figure [*].

 
illumin
illumin
Figure 1
Upper left: part of the Sigsbee2A velocity model. Upper right: the flat layer reference model. Bottom: the weighting operator (${\bf W}_{\rm m}^{2}$) produced using flat layers as the reference model.
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The imaging operator I chose to use is the downward continuation migration described in Prucha et al. (1999a,b). To summarize, this migration is carried out by downward continuing the wavefield in frequency space with the Double Square Root (DSR) equation, slant stacking at each depth, and extracting the image at zero time. In 2-D, this process can be described as:
\begin{eqnarray}
P\left(\omega,x_{m},x_h;z=0\right) &
\stackrel{DSR}{\Longrighta...
 ...{Imaging}{\Longrightarrow} &
P\left(\tau=0,x_{m},{p_{h}};z\right).\end{eqnarray} (3)
(4)
(5)

The resulting image has the dimensions of depth (z), common reflection point (CRP), and offset ray parameter (ph).

The result of carrying out this migration on the synthetic dataset can be seen in Figure [*]. The stacked image (top panel) shows the shadow zones that we expect beneath the salt edges. The lower panel shows 10 different ray parameters gathers taken from between ${\rm CRP}=10 {\rm km}$ and ${\rm CRP}=12 {\rm km}$. There are definite variations along the flat events that can also be attributed to illumination problems.


next up previous print clean
Next: Weighting operator Up: Application Previous: Application
Stanford Exploration Project
7/8/2003