Poststack migration of overturning waves

The first elliptic coordinate migration example uses the zero-offset data set shown in the upper panel of Figure . The data were generated by Sava (2006) from an adapted Sigsbee model (lower panel) using exploding reflector (two-way time-domain FD) modeling from all salt body edges. Migrated multiples are present in the image below because we apply no multiple suppression prior to imaging. Note also that the time axis begins at 10 s and extends to 30 s.

 

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Figure 2 Overturning wavefield problem. Top: Exploding reflector data set generated through below model. Note that the time axis begins at 10s. Bottom: Migration velocity model.

Figure  shows the migrated image obtained by wavefield extrapolation in elliptic coordinates. The upper left panel shows the prestack migration result for a monochromatic wavefield with the elliptic coordinate system overlain. The monochromatic wavefield overturns and arrives at the dipping salt flank at normal incidence, as expected for exploding reflector modeling. Note also that the wavefield energy propagates at fairly steep angles to the extrapolation axis indicating that high-angle accuracy extrapolators are necessary for accurate imaging. The upper right panel shows the same image as the upper left, but in the elliptic coordinate system. This figure similarly depicts the monochromatic wavefield propagating at high angle to the coordinate system. The lower left and right panels show the broadband image results in Cartesian and elliptic coordinate systems, respectively. The steep salt flanks beneath the salt nose are accurately positioned, indicating that the potential for imaging overturning waves in elliptic coordinates with high-angle accuracy propagators.

 

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Figure 3 Post-stack migration of overturning waves. Upper left: Overturning monochromatic Cartesian wavefield with overlain elliptic coordinates. Top right: As in upper left panel, but for elliptic coordinates. Lower left: Broadband overturning wave image in Cartesian coordinates. Lower right: As in lower left panel, but for elliptic coordinates.