Comparison with Kirchhoff migration

Figures 3 and 4 show comparisons between CAM and Kirchhoff migration results. The Kirchhoff algorithm used is derived from a preserved-amplitude approach and selects the most energetic arrival. Both CAM and Kirchhoff migration use exactly the same velocity model.

Some of the most significant differences between both approaches are well-known: in the CAM algorithm, finite frequency wave propagation is modeled avoiding the asymptotic approximations necessary for Kirchhoff. Also, for deep targets, the migration cost increases as N_z³ (number of depth samples) for Kirchhoff, whereas CAM cost only increases as N_z². However, Kirchhoff methods allow target-oriented migrations where CAM has to perform downward-continuation of the whole wavefield.

Figure 4 shows that the in-line sections around the salt body are relatively comparable in quality. Globally, CAM seems to give better results at imaging sediments bending against the salt flank on the left-hand side. The most important differences are shown by the horizontal sections (Figure 3): at a depth of 900m, CAM enhances complex high-frequency turbiditic patterns in shallow layers. At the same location, the Kirchhoff image appears at a considerably lower frequency and blurred along the in-line direction.

There are potentially 3 factors that could explain CAM's better accuracy compared to Kirchhoff migration:

• Wave propagation is handled completely differently: CAM iteratively propagates the wavefield by regular depth steps, as opposed to Green functions for Kirchhoff that are evaluated by ray tracing, wavefront construction or other methods.
• Since Green functions are not calculated for every source but rather pre-computed on a coarser grid, Kirchhoff algorithms usually include critical interpolations of traveltime maps and other attributes that may reduce accuracy for high-frequency details in the image. The only interpolations performed with CAM are the extended split-step scheme, which essentially addresses rapid velocity variations.
• Even if Kirchhoff algorithms can easily handle irregular geometries, the resulting image incorporates acquisition footprints, especially in depth slices. On the contrary, CAM requires regular geometry and acquisition problems are addressed during preprocessing through the AMO operator. Thus, the whole imaging stage is done with regularized geometry and potentially enables higher resolution in the final image.

 

kir-cam-zslice
Figure 3 Comparison between Kirchhoff (top) and CAM (bottom) imaging results: depth slice at z=900m. The Kirchhoff image has a lower frequency content, a higher noise ratio and is blurred along the in-line direction.