Comparison of shot encoding functions for reverse-time migration

Reverse-time migration (RTM) represents one of the most accurate, but also one of the costliest algorithms available for imaging in complex media. The RTM computational cost can be reduced by shot encoding, i.e. by imaging simultaneously a large number of shots. This approach reduces computational cost if the number of encoded seismic experiments is smaller than the number of shots. Different encoding strategies are possible, including linear and random encoding which represent end-members of a more general family of encodings. For a fixed maximum delay (i.e., computational cost), we can trade spatial bandwidth for cross-talk noise. Linear encoding is characterized by low bandwidth and high signal-to-noise ratio, while random encoding is characterized by high bandwidth and low signal-to-noise ratio. Mixed encodings allows us to calibrate the amount of resolution desired in the migrated image, given an acceptable level of noise in the image.