\section{Introduction}A key challenge for imaging in complex areas is accuratedetermination of a velocity model in the area under investigation. Migration velocity analysis is based on the principle thatimage accuracy indicators are optimized whendata are correctly imaged. A common procedure for velocity analysis is to examine thealignment of images created with multi-offset data.An optimal choice of image analysis can be done in the angle domain which is free of some complicatedartifacts present in surface offset gathers in complex areas\cite[]{GEO69-02-05620575}.\parMigration velocity analysis after migration by wavefieldextrapolation requires image decompositionin scattering angles relativeto reflector normals. Several methods have been proposed for such decompositions\cite[]{GEO55-09-12231234,SEG-1999-08240827,SEG-2000-08300833,GEO67-03-08830889,XieWu.adcig,GEO68-03-10651074,SEG-2003-08890892,Fomel.seg.3dadcig,GEO69-05-12831298}.These procedures require decomposition of extrapolated wavefields in variables that arerelated to the reflection angle.A key component of such image decompositions is the imaging condition.A careful implementation of the imaging condition preservesall information necessary to decompose images in theirangle-dependent components. The challenge is efficient and reliable construction of theseangle-dependent images for velocity or amplitude analysis.In migration with wavefield extrapolation, a prestack imaging conditionbased on spatial shifts of the source and receiver wavefields allowsfor angle-decomposition\cite[]{GEO67-03-08830889,SavaFomel.pag}.Such formed angle-gathers describe reflectivity as afunction of reflection angles and are powerful tools for migrationvelocity analysis (MVA) or amplitude versus angle analysis (AVA).However, due to the large expense of space-time cross-correlations, especially in three dimensions, this imaging methodology is not used routinely in data processing.This paper presents a different form of imaging condition.The key idea of this new method is to usetime-shifts instead of space-shifts between wavefields computed from sources and receivers.Similarly to the space-shift imaging condition, an image is built byspace-time cross-correlations of subsurface wavefields,and multiple lags of the time cross-correlation are preserved in the image.Time-shifts have physical meaning that can be related directlyto reflection geometry, similarly to the procedure used forspace-shifts. Furthermore, time-shift imaging is cheaper to apply than space-shift imaging, and thus it might alleviate some of the difficultiesposed by costly cross-correlations in 3D space-shift imaging condition.The idea of a time-shift imaging condition is related to the idea ofdepth focusing analysis \cite[]{SEG-1986-S7.6,GEO57-12-16081622,GEO58-08-11481156,SEG-1995-0465,SEG-1996-0463}.The main novelty of our approach is that we employ time-shifting to construct angle-domain gathers for prestack depth imaging.The time-shift imaging concept is applicable to Kirchhoff migration, migration by wavefield extrapolation, or reverse-time migration.We present a theoretical analysis of this new imaging condition,followed by a physical interpretation leading to angle-decomposition.Finally, we illustrate the method with images of the complex Sigsbee 2Adataset \cite[]{SEG-2002-21222125}.