Time-shift imaging condition in seismic migration

Abstract

Seismic imaging based on single-scattering approximation is in the analysis of the match between the source and receiver 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 wavefield extrapolation migration). Different methods can be used to analyze wavefield matching, of which crosscorrelation is a 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 image-angle 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 between source and receiver wavefields. This imaging condition is applicable to migration by Kirchhoff, wavefield extrapolation, or reverse-time techniques. The transformation allows construction of common-image gathers presented as functions of either time shift or reflection angle at every location in space. Inaccurate migration velocity is revealed by angle-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.