Stereographic imaging condition for wave-equation migrationa

Imaging under the single-scattering approximation consists of two steps: wave-field reconstruction of source and receiver wavefields from simulated and recorded data, respectively, and imaging from the extrapolated wavefields of the locations where reflectors occur. Conventionally, the imaging condition indicates the pres-ence of reflectors when propagation times of reflections in the source and receiver wavefields match. The main drawback of conventional cross-correlation imaging condition is that it ignores the local spatial coherence of reflection events and relies only on their propagation time. This leads to interference between unre-lated events that occur at the same time. Sources of cross-talk include seismic events corresponding to different seismic experiments, or different propagation paths, or different types of reflections (primary or multiple) or different wave modes (P or S). An alternative imaging condition operates on the same extrap-olated wavefields, but cross-correlation takes place in a higher-dimensional do-main where seismic events are separated based on their local space-time slope. Events are matched based on two parameters (time and local slope), thus justify-ing the name “stereographic ” for this imaging condition. Stereographic imaging attenuates wavefield cross-talk and reduces imaging artifacts compared with con-ventional imaging. Applications of the stereographic imaging condition include simultaneous imaging of multiple seismic experiments, multiple attenuation in the imaging condition, and attenuation of cross-talk between multiple wavefield branches or between multiple wave modes