Decon in the log domain - practical considerations

Discussion and conclusion

The inversion optimizes for sparsity, since we assume that geology is sparse, but that requirement alone is not enough. We assume that in a particular marine survey, a single effective shot waveform was used to record all data, and therefore a single filter should be sufficient to deconvolve the entire dataset. The question is how much does that assumption stand up to reality. When considering increasing offsets the recorded waveform may change, and the data is likely to contain not just specular reflections but refractions as well. If there is a significant difference between effective shot waveforms within a survey, the inversion may estimate a shot waveform that produces the best average result for the input data it was given. However, this result may not be very useful for any particular trace in the data. This indicates that we should estimate the shot-waveform only from near-offset data.

The symmetry and filter length regularizations enable us to shape the desired shot waveform to our expectation: a Ricker wavelet, with some bubble reverberations trailing after it. These regularizations help in arriving at a useful result even when the shot waveform varies, such as when we use many offsets. They are easy to implement in the lag-log domain.

Instead of applying the deconvolution to a constant offset or to a multiple offset section, within which the shot waveform can change as a result of different angles of incidence, it may be preferable to apply it to data sorted by angles of incidence. For specular reflections of the same incidence angle, we can assume that the waveform is constant. Therefore, one possibility is to transform the data to the $\tau-p$ domain, and run the deconvolution on constant ray-parameter slices.

The source and receiver depths can change over the acquisition line, and therefore the effective shot waveform and its associated frequency notch may change at each shot. One way of evaluating the success of the deconvolution is in testing how it deals with the frequency notch. We would like to see the notch removed from the data, but we do not want the inversion to fill it with noise. A further avenue of research is to add the notch elimination as a parameter into the inversion.

It is important to check whether the low frequencies were filtered out in preprocessing. This will affect the result since the inversion may compensate by generating low frequencies that have nothing to do with the geology. Also, the filtering may affect the source wavelet, meaning that the Ricker we see is as much a result of preprocessing as it is of the acquisition.

Another conclusion is that success of this deconvolution method is on a dataset by dataset basis. How it functions depends on the data characteristics, and the variability of the shot waveform over traces. Considering the regularization parameters, we cannot conclude from one dataset what set of parameters will work on another.

Decon in the log domain - practical considerations