Stereographic imaging condition for wave-equation migration

Single-scattering imaging consists of two steps: wavefield extrapolation, whose goal is to reconstruct source and receiver wavefields from recorded data, and an imaging, whose goal is 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 conditions is that they ignore the local spatial coherence of reflected events and rely purely 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 have been separated based on their local space-time slope. Events are matched based on two parameters (time and local slope), thus justifying the name “stereographic” for this imaging condition. Several numeric examples demonstrate that stereographic imaging attenuates cross-talk and reduces imaging artifacts compared with conventional imaging.