Time-shift imaging condition for converted waves

Conclusions

We develop imaging conditions for converted waves based on time-shifts between source and receiver wavefields. This method is applicable to Kirchhoff, reverse-time and wave-equation migrations and produces common-image gathers indicative of velocity errors. In wave-equation migration, time-shift imaging is more efficient than space-shift imaging, since it only involves a simple phase shift prior to the application of the usual imaging cross-correlation. Disk storage is also reduced, since the output volume depends on only one parameter (time-shift ${\tau}$) instead of three parameters (space-shift ${ \bf h}$). We show how this imaging condition can be used to construct angle-gathers from time-shift gathers. Although time-shift imaging is, in principle, capable of representing the same information as space-shift imaging, in practice the angular resolution of the angle decomposition for time-shift is much lower than the one for space-shift. This inconvenience needs to be addressed by future research.