We shall review a method of shot-profile migration  using the salt diapir model shown in Figure 8.2-1. A wave theoretical modeling scheme based on the two-way acoustic wave equation was used to generate 154 shot records. Selected shot records are shown in Figure 8.2-2. Shot spacing is 50 m and receiver spacing is 50 m. Each shot record contains 97 traces corresponding to a split-spread recording geometry with a maximum offset of 2350 m.
Figure 8.3-12a shows three shot records — one located away from the main diapiric body, one on the left flank, and one other on the right flank of the diapir. The velocity-depth model (Figure 8.3-12b), although vertically exaggerated, is the same as in Figure 8.2-1. The same shot records after shot-profile migration using the true velocity-depth model (Figure 8.3-12b) are shown in Figure 8.3-13a. Note that each shot record after migration represents partial image of the subsurface within a limited lateral extent.
Now, imagine all 154 shot records after migration placed at their corresponding shot locations along the line. Then, consider one specific receiver location. There will be traces from a number of migrated shot records that will coincide with this receiver location that are common to all. These traces consitute a common-receiver gather after shot-profile migration. Selected common-receiver gathers sorted from the migrated common-shot gathers are shown in Figure 8.3-13b. The number of traces in a common-receiver gather obviously is determined by the recording geometry.
Figure 8.2-1 (Top) An earth model in depth with a salt diapir; (middle) CMP-stacked section derived from the modeled prestack data in Figure 8.2-3; (bottom) the modeled zero-offset section. The stacked and zero-offset sections are appropriately aligned in the lateral direction with respect to the earth model above. Trace spacings in the stacked and zero-offset sections are 25 m and 50 m, respectively. No amplitude scaling has been applied to the sections. The aspect ratio of the horizontal and vertical axes in the velocity-depth model is 1.
If the velocity-depth model used in shot-profile migration corresponds to the true model, then each shot record should yield a correct image of the subsurface, albeit limited in lateral extent (Figure 8.3-13a). Then, traces from various shot records after migration at the same receiver location should represent the identical image below that receiver location. Stated differently, a common-receiver gather should contain flat events if the velocity-depth model used in shot-profile migration is correct. The final step of shot-profile migration involves the summation of the traces in each receiver gather to create the image in depth (Figure 8.3-13c). Note that the partial images with limited lateral extent from each individual shot record (Figure 8.3-13a) coincide with the complete image within the lateral extent of the line in its entirety.
Examine the common-receiver gathers in Figure 8.3-13b, closely. The receiver locations are labeled as 179, 209, and 249. Note that the events associated with the top-salt and base-salt boundaries, and the flat reflector below are positioned differently in relation to the receiver location of each gather. In case of a flat layer boundary, the event is positioned symmetrically with respect to the receiver location (179). In the case of a dipping layer boundary, such as the top-salt, the event is positioned to the right of the receiver location (209) or to the left of the receiver location (249), but always in the updip direction.
- Reshef and Kosloff, 1986, Reshef, M. and Kosloff, D., 1986, Migration of common-shot gathers: Geophysics, 51, 324–331.
- 2-D prestack depth migration
- Shot-geophone migration
- Sensitivity of image accuracy to velocity errors
- Field data examples