Frequency-domain shot-record migration can produce higher quality images than Kirchhoff migration but typically at a greater cost. The computing cost of shot-record migration is the product of the number of shots in the survey and the expense of each individual migration. Many attempts to reduce this cost have focused on the speed of the individual migrations, trying to achieve a better trade-off between accuracy and speed.

Another approach is to reduce the number of migrations. We investigate the simultaneous migration of shot records using frequency-domain shot-record migration algorithms. The difficulty with this approach is the production of so-called crossterms between unrelated shot and receiver wavefields, which generate unwanted artifacts or noise in the final image. To reduce these artifacts and obtain an image comparable in quality to the single-shot-per-migration result, we have introduced a process called phase encoding, which shifts or disperses these crossterms. The process of phase encoding thus allows one to trade S/N ratio for the speed of migrating the entire survey.

Several encoding functions and two application strategies have been tested. The first strategy, combining multiple shots per migration and using each shot only once, reduces computation in direct relation to the number of shots combined. The second strategy, performing multiple migrations of all the shots in the survey, provides a means to reduce the crossterm noise by stacking the resulting images. The additional noise in both strategies may be tolerated if it is no stronger than the inherent seismic noise in the migrated image and if the final image is achieved with less cost.

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