Plane-wave migration in tilted coordinates

An exploding-reflector dataset with overturned waves

Our first example is a synthetic dataset designed to test imaging of overturned waves (Sava, 2006). Figure 3 shows the model with typical overturned rays. The exploding reflector data are modeled from the boundary of the salt and recorded at the surface. The data are modeled using the time-domain two-way wave equation. Figure 8 shows the exploding reflector data received at the surface. The overturned events are recorded from $x=-20$ to $5$ km at $t=10$ to $25$s.

To verify the extrapolation of overturned waves in tilted coordinates, we mute the non-overturned events that are received at the surface earlier than 10s. We migrate the dataset using a tilted coordinate system with a tilting angle of $70^\circ$, as shown in Figure 4. As demonstrated in the previous section, the waves illuminating the overhanging salt flanks do not overturn in the tilted coordinate system (Figure 4). For comparison, we also migrate the dataset using reverse-time migration. Figure 9 compares the images from these two methods. Figure 9a is the migrated image obtained by plane-wave migration in tilted coordinates, and Figure 9b is the image obtained by reverse-time migration. The image from reverse-time migration has lower frequency; otherwise they are comparable. The comparison shows that most of the overturned energy is imaged by the migration in tilted coordinates, and all the overhanging salt flanks are imaged correctly.

Plane-wave migration in tilted coordinates