In this section I compare my layer-stripping migration algorithm to shot-profile migration, and Kirchhoff migration using both maximum-amplitude traveltimes and band-limited Green's functions.
The shot-profile migration generated with Advance Geophysical Co.'s commercial algorithm is displayed in Figure . It produces a good structural image by recursively downward continuing source and receiver wavefields for all frequencies using explicit finite-difference extrapolators. The problem with the method is that it is expensive and it requires regular fine sampling of the recording surface. This makes it impractical for 3-D data and irregularly-sampled land data.
Figure is the result of Kirchhoff migration using maximum-amplitude traveltime and phase calculated with a paraxial ray-tracing program. Thorbjorn Rekdal did the ray tracing and Dave Nichols did the migration to produce this image (Nichols, 1994). This results in a much better image than the standard first-arrival traveltime migration of Figure , but it is not as good as my layer-stripping Kirchhoff migration. It shows that there is an advantage to maximum-amplitude ray tracing, but that the complexity of the wavefield cannot be adequately accounted for at late times. This method is generally pretty expensive and requires extensive smoothing of the slowness model to ensure stability of ray tracing.
Figure is the result of using Nichols' (1994) band-limited Green's function method to calculate traveltimes for Kirchhoff migration. The image is much better than the standard first-arrival traveltime migration of Figure , but, once again, it is not as good as my layer-stripping Kirchhoff migration. The figure shows that using traveltimes which are calculated in the seismic frequency band has a distinct advantage over first-arrival traveltimes and that the band-limited traveltimes track the high energy portions of the wavefield better, but they are still not able to capture all the events which should be summed coherently to form the best image. Nichols' method is considerably less expensive than shot-profile migration because only eight frequency components are propagated to estimate band-limited traveltimes; however, it is more expensive than finite-difference first-arrival traveltime calculation.
The target zone images of the Kirchhoff migration results are compared in Figure . The layer-stripping migration produces the best image. It is the best match to the idealized reflectivity, and it has the best overall image quality in terms of lateral continuity and structural definition.