Stereographic imaging condition for wave-equation migration

Discussion

The imaging procedure described in this paper requires additional steps that add to the computational cost of imaging. Furthermore, there are more parameters that need to be chosen. For example, if we use local slant-stacks for local decomposition, we need to decide how many local slopes we should use, how finely we need to sample the slope parameters, how finely in space should we apply slant-stacking of the source/receiver wavefields, etc. The number of local slopes used for the imaging condition depends on wavefield sampling in space and time in order to avoid aliasing. Those challenges remain to be addressed by future research.

In all examples described in this paper, the local windows have simple rectangular shape. However, more sophisticated window types (e.g. Gaussian) are possible alternatives and might improve the quality and efficiency of the method.

We can consider tuning the stereographic imaging condition for specific applications. In current implementation, only image components with spatial coherence (e.g. reflectors) generate wavefields with spatial coherence. Diffractions, for example, do not fit this description and, thus, are removed from the image by the imaging condition. This can be seen both as a feature or as a drawback depending on the type of imaging target.

Stereographic imaging condition for wave-equation migration