Isotropic angle-domain elastic reverse-time migration

Abstract

Multicomponent data usually are not processed with specifically designed procedures but with procedures analogous to those used for single-component data. In isotropic media, the vertical and horizontal components of the data commonly are taken as proxies for the P- and S-wave modes, which are imaged independently with the acoustic wave equations. This procedure works only if the vertical and horizontal components accurately represent P- and S-wave modes, which generally is not true. Therefore, multicomponent images constructed with this procedure exhibit artifacts caused by 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, which evaluates the match between wave-fields reconstructed from sources and receivers. For vector wave fields, a simple component-by-component crosscorrelation between two wavefields leads to artifacts caused by crosstalk between the unseparated wave modes. We can separate elastic wavefields after reconstruction in the subsurface and implement the imaging condition as crosscorrelation of pure wave modes instead of the Cartesian components of the displacement wavefield. This approach leads to images that are easier to interpret because 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 (crosscorrelation with zero lag in space and time) and extended to nonzero 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-variation-with-angle analysis.