We develop the novel theory of transmitted PS migration and show that PS transmitted arrivals in a Gulf of Mexico vertical seismic profile (VSP) data set can be migrated to accurately image a salt sheet even though the receiver array is below the transmitting boundary. We also show that migrating transmitted arrivals is effective in illuminating the base of an orebody invisible to PP reflections. In general, interfaces that bisect wavepath propagation (i.e., the source and receiver are on opposite sides of the interface and therefore invisible to PP reflections) can be imaged by migration of PS transmitted waves. These results suggest that migration of PS transmitted waves opens new opportunities in imaging nearly vertical impedance boundaries that are typically invisible to conventional reflection imaging of crosswell and VSP data.
We also present a new interferometric method, denoted as reduced-time migration, which uses the arrival-time difference between the direct P-wave and subsequent events to increase migration accuracy. Reduced-time migration removes static time shifts in the data, decreases the focusing error due to an incorrect migration velocity model, and relocates reflection or PS transmission events to be closer to their true positions. Although limited to crosswell and VSP geometries, synthetic- and field-data examples show that reduced-time migration is noticeably more accurate than conventional migration in the presence of static shifts and/or migration velocity errors. The main assumption of reduced-time migration is that the direct wave samples errors which are representative of errors in the migration aperture. Transmission wavepaths, in general, are subparallel to the direct wave and therefore the two modes encounter similar errors and, hence, reduced-time migration is effective in improving the focusing of migration energy. For the PP reflection case, the direct wave and the reflected waves often traverse different parts of the earth, therefore, reduced-time migration will remove static shifts but it is not expected to mitigate velocity errors if the errors are spatially variant. However, if there is a general and consistent bias in the velocity model, reduced-time migration is expected to deliver improved results over conventional Kirchhoff migration.