Angle-domain elastic reverse-time migration

Multi-component data are not usually processed with specifically designed procedures, but with procedures analogous to the ones used for single-component data. Commonly, the vertical and horizontal components of the data are taken as proxies for P and S wave modes which are imaged independently with the acoustic wave equation. This procedure works only if the vertical and horizontal component accurately represent P and S wave modes, which is not true in general. Therefore, multi-component 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 vector fields for wavefield reconstruction and imaging. The wavefields are reconstructed using the multi-component data as boundary conditions 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 cross-correlation between two wavefields leads to artifacts caused by cross-talk 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.