Angle-gather time migration

Dome model

This model contains a wide range of geologic dips across the dome as well as having a flat reflector at the base of the dome. Figure 6 shows the resulting common offset sections from traditional Kirchhoff migration. As is expected for such a simple model, the near and far offset sections are very similar and the stacked section is almost perfect. We are more interested in the result of the angle-gather migration.

Figure 7 shows the zero and large angle sections as well as the stack for angle-gather Kirchhoff migration. The zero-angle section is weak but clearly shows the correct shape and position. The large-angle section is actually only for $\gamma=25^{\circ}$. The reason for this is clear if you consider Figure 1. At greater depths, the rays associated with large reflection angles ($\gamma$) will not emerge at the surface within the model space. Therefore at angles greater than $25^{\circ }$ (the maximum useful angle), the information at later times disappears.

We expect the stacked sections for the offset method and the angle method to be identical. Although we sum over different paths for the offset-domain migration (Figure 2) and the angle-domain migration (Figure 3), the stack should sum all of the same information together for both methods. Fortunately, a comparison of the stacked sections in Figures 6 and 7 show that the results are identical as expected.

offset-dome
Figure 6. Left: Migrated offset section at zero offset. Center: Migrated offset section at far offset. Right: Stack.

angle-dome
Figure 7. Left: Migrated angle section at small angle. Center: Migrated offset section at large angle. Right: Stack.

Angle-gather time migration