Time-shift imaging condition in seismic migration

Seismic imaging based on single-scattering approximationisintheanalysisofthematchbetweenthesourceandreceiver wavefields at every image location. Wavefields at depth are functions of space and time and are reconstructed from surface data either by integral methods Kirchhoff migration or by differential methods reverse-time or wavefieldextrapolationmigration.Differentmethodscanbeused toanalyzewavefieldmatching,ofwhichcrosscorrelationisa popular option. Implementation of a simple imaging condition requires time crosscorrelation of source and receiver wavefields, followed by extraction of the zero time lag. A generalized imaging condition operates by crosscorrelation in both space and time, followed by image extraction at zero time lag. Images at different spatial crosscorrelation lags are indicators of imaging accuracy and are also used for imageangle decomposition. In this paper, we introduce an alternative prestack imaging condition in which we preserve multiple lags of the time crosscorrelation. Prestack images are described as functions of time shifts as opposed to space shifts betweensourceandreceiverwavefields.Thisimagingcondition is applicable to migration by Kirchhoff, wavefield extrapolation, or reverse-time techniques. The transformation allows construction of common-image gathers presented as functionsofeithertimeshiftorreflectionangleateverylocationinspace.Inaccuratemigrationvelocityisrevealedbyangle-domain common-image gathers with nonflat events. Computational experiments using a synthetic data set from a complex salt model demonstrate the main features of the method.