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Example

The stereographic imaging condition is illustrated with an example derived from the Sigsbee 2A dataset (Paffenholz et al., 2002). Using the model in Figure 6(g), two shots are simulated by wavefield extrapolation modeling, Figures 6(a)-6(c), and a third shot is synthesized by summing the two shots together, Figure 6(e). Migration with conventional imaging condition of the three shots produces the images in Figures 6(b)-6(f). The two shots independently illuminate different parts of the model, Figures 6(b)-6(d), while the third composite shot illuminates both sides of the image, Figure 6(f). The image produced by the composite shot is populated with artifacts due to the cross-talk between the wavefields originating at the two shot locations.

Figure 6(h) shows the image obtained by imaging the composite shot, Figure 6(e), using the stereographic imaging condition. The image is free of artifacts and shows reflectors extending over the entire image, as would be expected for illumination from two shots at different locations. In this case, the stereographic imaging condition needs to take into account the local dip of the image. Since we cannot know the reflector dip prior to the application of the imaging condition, we need to loop over a range of possible dip angles and decompose the wavefields locally for all possible slope combinations. Thus, the stereographic imaging procedure matches the dip of wavefield components in local windows around every image point. Assuming that the local geologic dip is known, at least approximately, we could consider looping over a small range of local dips, thus decreasing the cost of the imaging condition. This approach was not used for the examples shown in this paper and remains to be investigated by future research.


next up previous [pdf]

Next: Discussion Up: Sava: Stereographic imaging Previous: Stereographic Imaging Condition

2013-08-29