Time-shift imaging condition in seismic migration

Seismic imaging based on single-scattering approximation is based on analysis of the match between the source and receiver wavefields at every image loca-tion. Wavefields at depth are functions of space and time and are reconstructed from surface data either by integral methods (Kirchhoff migration) or by dif-ferential methods (reverse-time or wavefield extrapolation migration). Different methods can be used to analyze wavefield matching, of which cross-correlation is a popular option. Implementation of a simple imaging condition requires time cross-correlation of source and receiver wavefields, followed by extraction of the zero time lag. A generalized imaging condition operates by cross-correlation in both space and time, followed by image extraction at zero time lag. Images at different spatial cross-correlation lags are indicators of imaging accuracy and are also used for image angle-decomposition. In this paper, we introduce an alternative prestack imaging condition in which we preserve multiple lags of the time cross-correlation. Prestack images are de-scribed as functions of time-shifts as opposed to space-shifts between source and receiver wavefields. This imaging condition is applicable to migration by Kirchhoff, wavefield extrapolation or reverse-time techniques. The transforma-tion allows construction of common-image gathers presented as function of either time-shift or reflection angle at every location in space. Inaccurate migration velocity is revealed by angle-domain common-image gathers with non-flat events. Computational experiments using a synthetic dataset from a complex salt model demonstrate the main features of the method