Imaging complex structures with first-arrival traveltimes

LAYER-STRIPPING KIRCHHOFF MIGRATION

The layer-stripping migration method can be thought of as a hybrid algorithm that incorporates some of the advantages of shot-profile migration with the efficiency of Kirchhoff migration. This is illustrated by Figures 4 through 6.

In shot-profile migration, shots and geophones are alternately downward continued through each depth level. Figure 4 illustrates this for one line of shots or geophones. It is evident that there are many propagation paths from the surface to the image point, therefore multiple arrivals are handled. The computation is performed for all frequencies.

By contrast, first-arrival Kirchhoff migration is performed by summing data over trajectories defined by the propagation paths illustrated in Figure 5. There is only one path linking each surface position to the image point, therefore multiple arrivals are not handled. Although crossing paths are not illustrated here, they can occur.

The layer-stripping method is illustrated in Figure 6. It is a combination of Kirchhoff wave-equation datuming (Berryhill, 1979,1984) and Kirchhoff migration. The computation proceeds as follows:

1. Migrate from surface to some depth level $z_1$.
2. Downward continue to depth level $z_1$.
3. Migrate from depth level $z_1$.
4. Downward continue to depth level $z_2$.
5. Migrate from depth level $z_2$.
6. etc...

The depth step of downward continuation is much larger than the $\triangle z$ used in shot-profile migration. Since there are multiple paths from the surface to the image point, multiple arrivals are handled. Because the paths are shorter than in Figure 5, first-arrival traveltimes are more likely to be valid.

s-g Figure 4. Propagation paths from the surface to an image point for shot profile migration.

kirch Figure 5. Propagation paths from the surface to an image point for Kirchhoff downward continuation.

datum Figure 6. Propagation paths from the surface to a depth point for layer-stripping Kirchhoff downward continuation.

Imaging complex structures with first-arrival traveltimes