Conclusions

We showed the theoretical justification for directly migrating passive seismic noise recordings. This method is based on the shot-profile migration procedure, but is applied to transmission data. The results from the direct migration of passive data and from the migration of simulated reflection shot gathers are identical. Depending on the objective (to have intermidiate results or not) one or the other can be used. The numerical examples showed that while with decreasing number of subsurface noise sources and shorter noise recordings drastically reduced the quality of the simulated reflection response, the migration process still delivers good results.

Lastly, correlation of each trace with every other trace produces N shot gathers each with N traces from a survey with N receivers. If correlations are performed in the frequency domain, N² traces must be inverse Fourier transformed after multiplication to produce the shot-gathers. This requirement is especially onerous when the record length is at least minutes long. Then, another Fourier transform of N² traces, though now only seconds long, must be performed to make a f-k based migration. Finally, the increased I/O associated with migrating N shots in a shot-profile migration are substantial compared with the single shot, even with many more frequencies, for direct migration utilizing an algorithm parallelized over frequency.

 

dx_100m
Figure 3 Left: Simulated reflection shot panel from 6 minutes long noise recordings with 57 regularly distributed subsurface sources with a simulated shot position at x₁=4000 m. Right: Result from direct migration of 6 minutes long noise recordings with 57 regularly distributed subsurface sources.

 

dx_500m
Figure 4 Left: Simulated reflection shot panel from 6 minutes long noise recordings with 11 regularly distributed subsurface sources with a simulated shot position at x₁=4000 m. Right: Result from direct migration of 6 minutes long noise recordings with 11 regularly distributed subsurface sources.

 

dx_1000m
Figure 5 Left: Simulated reflection shot panel from 6 minutes long noise recordings with 6 regularly distributed subsurface sources with a simulated shot position at x₁=4000 m. (b) Result from direct migration of 6 minutes long noise recordings with 6 regularly distributed subsurface sources.