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Zero-offset interferometric imaging condition

After filtering the reconstructed wavefields with pseudo WDFs, we can perform imaging with normal procedures. For the case of wavefields parametrized as a function of data coordinates, we obtain the total wavefield at image coordinates by summing over receiver coordinates $ { \mathbf{x} } $

\begin{displaymath}
W_{x} \left ( { \mathbf{y} } , { t } \right) = {\int\limits_...
...x} \left ( { \mathbf{x} } , { \mathbf{y} } , { t } \right)\;,
\end{displaymath} (6)

followed by a conventional imaging condition extracting time $ { t } =0$ from the pseudo WDF of the reconstructed wavefields:
\begin{displaymath}
R_{x} \left ( { \mathbf{y} } \right) = W_{x} \left ( { \mathbf{y} } , { t } =0 \right) \;.
\end{displaymath} (7)

The image obtained with this imaging procedure is shown in Figure 6(c). As expected, the artifacts caused by the unknown random fluctuations in the model are reduced, leaving a cleaner image of the source.

Similarly, for the case of wavefields parametrized as a function of image coordinates, we obtain the image by application of the conventional imaging condition extracting time $ { t } =0$ from the pseudo WDF of the reconstructed wavefield:

\begin{displaymath}
R_{y} \left ( { \mathbf{y} } \right) = W_{y} \left ( { \mathbf{y} } , { t } =0 \right) \;.
\end{displaymath} (8)

The image obtained with this imaging procedure is shown in Figure 6(d). As in the preceding case, the artifacts caused by the unknown random fluctuations in the model are reduced, producing a cleaner image of the source, comparable with the one in Figure 6(c).

winpcic0 winpcic1 winpcii1 winpiic1
winpcic0,winpcic1,winpcii1,winpiic1
Figure 6.
Images produced by the conventional imaging condition using the data simulated in the background model (a) and using the data simulated in the random model (b). Images produced from data simulated in the random model using the interferometric imaging condition with parametrization as a function of data coordinates (c) and as a function of image coordinates (d).
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next up previous [pdf]

Next: Multi-offset interferometric imaging condition Up: Imaging conditions Previous: Wigner distribution functions

2013-08-29