On the separation of simultaneous-source data by inversion

Example 2: Separation of multiple sources

In this example, we consider data from the model in Figure 1(b). The simultaneous-source data comprise of data from four sources with ${800}$ m separation (Figure 8). The individual source records are shown in Figure 9. Separation results obtained by inverting the data without dip constraint are shown in Figure 10. Results obtained using the reformulated regressions in equation 6 are shown in Figure 11. Note that residual artifacts seen in the unconstrained results (Figure 10) have been attenuated. Dips estimated from the unconstrained results and used to obtain the constrained results are shown in Figure 12.

4s4-or-1
Figure 8. Simultaneous-source data comprising shot-records from four sources (S1, S2, S3 and S4) over the model in Figure 1(b).

4s4-1,4s4-2,4s4-3,4s4-4
Figure 9. Single-source data that would have been recorded by (a) source 1, (b) source 2, (c) source 3, and (d) source 4 over the model in Figure 1(b). These shot records are the components of the data shown in Figure 8.

4s4-hb-1,4s4-hb-2,4s4-hb-3,4s4-hb-4
Figure 10. Shot gathers recovered by unconstrained sparse inversion for (a) source 1, (b) source 2, (c) source 3, and (d) source 4. Note that these results contain several residual artifacts compared to the reference single-source records (Figure 9).

4s4-prc-1,4s4-prc-2,4s4-prc-3,4s4-prc-4
Figure 11. Shot gathers recovered by dip-constrained sparse inversion for (a) source 1, (b) source 2, (c) source 3, and (d) source 4. Residual artifacts present in the unconstrained example (Figure 10) have been attenuated by DCSI.

4s4-dip-1,4s4-dip-2,4s4-dip-3,4s4-dip-4
Figure 12. Local dips (common-offset components) for (a) source 1, (b) source 2, (c) source 3, and (d) source 4, obtained from the unconstrained sparse inversion (Figure 10) and used in DCSI to obtain the results in Figure 11.

On the separation of simultaneous-source data by inversion