Stererographic imaging condition for wave-equation migration

Single-scattering imaging consists of two steps: wavefield extrapolation, to reconstruct source and receiver wavefields from recorded data, and imaging, to extract from the extrapolated wavefields the locations where reflectors occur. Conventionally, the imaging condition indicates the presence of reflectors when the propagation time 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 on their propagation time. This leads to interference (cross-talk) between unrelated events that occur at the same time. Sources of cross-talk include seismic events corresponding to different seismic experiments, seismic events corresponding to different propagation paths, etc. An alternative imaging condition operates on the same extrapolated wavefields, but cross-correlation takes place in a higher-dimensional domain where seismic events are separated based on their local spacetime slope. Events are matched based on two parameters (time and local slope), thus justifying the name “stereographic” for this imaging condition. Stereographic imaging attenuates cross-talk and reduces imaging artifacts compared with conventional imaging.