On the separation of simultaneous-source data by inversion

Discussion

Any reliable separation method for simultaneous-source data sets must be applicable to any kind of seismic data, must be independent of the number of seismic sources, and must retain important amplitude information. In the first example, we showed that our inversion formulation (DCSI) can be used to separate data from complex (sub-salt) geological environments. The separation results in Figure 4 show that $l_{2}$ inversion is inadequate for data separation. Significant improvement is obtained in the quality of these results by using a hybrid instead of the $l_{2}$ norm (Figure 5). In addition, the separation results can be further improved by dip-constrained inversion (Figure 6) to produce results of comparable quality to the original single-source data (Figure 3). In the second example, we showed that with our approach, we can separate any number of seismic sources. Whereas the unconstrained results (Figure 10) contain several residual artifacts, the dip-constrained results (Figure 11) are comparable to the reference single-source data (Figure 9). In the last example, we showed that this method can be applied to amplitude-sensitive studies such as time-lapse seismic reservoir monitoring. This repeatability test, shows that our method can be used to regularize and cross-equalize time-lapse simultaneous-source data sets. By incorporating both spatial and temporal constraints into the inversion, we are able to attenuate differences caused by non-repeatable acquisition parameters during the separation problem. The residual artifacts present in separately inverted data sets (Figure 15) are removed by our STCSI formulation (Figure 16).

On the separation of simultaneous-source data by inversion