Migration in the angle domain creates seismic images for different reflection angles. We present a method for computing angle-domain common-image gathers from seismic images obtained by depth migration using wavefield continuation. Our method operates on prestack migrated images and produces the output as a function of the reflection angle, not as a function of offset ray parameter as in other alternative approaches. The method amounts to a radial-trace transform in the Fourier domain and is equivalent to a slant stack in the space domain. We obtain the angle gathers using a stretch technique that enables us to impose smoothness through regularization. Several examples show that our method is accurate, fast, robust, and easy to implement. The main anticipated applications of our method are in the areas of migration-velocity analysis and amplitude-versus-angle analysis.

Seismic imaging based on single-scattering approximation is based on 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 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 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 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.

Prestack depth migration of shot profiles by downward continuation is a practical imaging algorithm that is especially cost‐effective for sparse‐shot wide‐azimuth geometries. The interpretation of offset as the displacement between the downward‐propagating (shot) wavefield and upward‐propagating (receiver) wavefield enables us to extract offset‐domain common image‐point (CIP) gathers during shot‐profile migration. The offset‐domain gathers can then be transformed to the angle domain with a radial‐trace mapping originally introduced for shot‐geophone migration. The computational implications of this procedure include both the additional cost of multioffset imaging and an implicit transformation from shot‐geophone to midpoint‐offset coordinates. Although this algorithm provides a mechanism for imaging angle‐dependent reflectivity via shot‐profile migration, for sparse‐shot geometries the fundamental problem of shot‐aliasing may severely impact the quality of CIP gathers.

Multicomponent data are not usually processed with specifically designed procedures, but with procedures analogous to the ones used for single-component data. In isotropic media, the vertical and horizontal components of the data are commonly taken as proxies for the P-and S-wave modes which are imaged independently with acoustic wave equations. This procedure works only if the vertical and horizontal component accurately represent P-and S-wave modes, which is not true in general. Therefore, multicomponent images constructed with this procedure exhibit artifacts caused by the incorrect wave mode separation at the surface. An alternative procedure for elastic imaging uses the full vector fields for wavefield reconstruction and imaging. The wavefields are reconstructed using the multicomponent data as a boundary condition for a numerical solution to the elastic wave equation. The key component for wavefield migration is the imaging condition that evaluates the match between wavefields reconstructed from sources and receivers. For vector wavefields, a simple component-by-component crosscorrelation between two wavefields leads to artifacts caused by crosstalk between the unseparated wave modes. An alternative method is to separate elastic wavefields after reconstruction in the subsurface and implement the imaging condition as cross-correlation of pure wave modes instead of the Cartesian components of the displacement wavefield. This approach leads to images that are easier to interpret, since they describe reflectivity of specified wave modes at interfaces of physical properties. As for imaging with acoustic wavefields, the elastic imaging condition can be formulated conventionally (cross-correlation with zero lag in space and time), as well as extended to non-zero space and time lags. The elastic images produced by an extended imaging condition can be used for angle decomposition of primary (PP or SS) and converted (PS or SP) reflectivity. Angle gathers constructed with this procedure have applications for migration velocity analysis and amplitude versus angle analysis.