In the presence of strong noise, prediction filtering attenuates reflections and produces spurious events. Inversion prediction preserves the reflection amplitudes and reduces the amplitudes of the spurious events. Although I was hoping for an improvement over prediction filtering, the signal-to-noise ratio of the output of inversion prediction generally appears to be about equal to that of prediction filtering. Inversion prediction removes the response of the filter to the noise, but this effect is difficult to see in real seismic data. The main advantage of the inversion prediction technique may be to clean up the signal annihilation filter in the presence of strong noise. For real seismic data, preserving the signal amplitude and reducing the amplitudes of spurious events may be more important than eliminating the filter response. However, if the noise consists of very large spikes, eliminating the filter response becomes important. Removing the filter response with the inversion may have more effect on the calculation of an improved filter than it does on the interpretation of the section.
In the next chapter, I extend this technique to account for missing data. Allowing for missing data allows the removal of high-amplitude noise that would otherwise corrupt a least-squares inversion. Tolerating missing data also provides for prestack data, which, because of irregular acquisition, generally have not had these prediction techniques successfully applied.