Stereographic imaging condition for wave-equation migration

Abstract

Imaging under the single-scattering approximation consists of two steps: wavefield reconstruction of source and receiver wavefields from simulated and recorded data, respectively, and imaging from the extrapolated wavefields of locations where reflectors occur. Conventionally, the imaging condition indicates the presence of reflectors when propagation times of reflections in the source and receiver wavefields match. The main drawback of a conventional crosscorrelation 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 unrelated events that occur at the same time. Sources of crosstalk include seismic events corresponding to different seismic experiments, propagation paths, types of reflections (primary or multiple), or wave modes (P or S). An alternative imaging condition operates on the same extrapolated wavefields, but crosscorrelation takes place in a higher-dimension domain where seismic events are 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. Stereographic imaging attenuates wavefield crosstalk and reduces imaging artifacts compared with conventional imaging. Applications of the stereographic imaging condition include simultaneous imaging of multiple seismic experiments, multiple attenuation in the imaging condition, and attenuation of crosstalk between multiple wavefield branches or multiple wave modes.