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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.
**OverProb
**

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.

**XM
**

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.

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Stanford Exploration Project

5/6/2007