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Example 3: Joint inversion of simultaneous-source time-lapse data

In this example, we consider conduct a repeatability test on two different data sets from the same model (Figure1(b)). This represents a repeatability test for a time-lapse seismic monitoring case, where only amplitude differences from production-related changes are of interest. We modeled two sets of simultaneous-source data, each comprised of two sources with $ {2400}$ m separation (Figure 13). Because it is impractical to repeat both the geometry and relative shooting times between surveys, time-lapse data acquired with simultaneous sources will have high non-repeatability. Therefore, our data separation procedure serves the dual purpose of separating each simultaneous-source data into component shot records and cross-equalizing the time-lapse data sets. The individual source records for each survey are shown in Figure 14.

In this example, because we assume no change in the reservoir between surveys, the difference between the two sets of data is zero (Figures 14(e) and 14(f)). Separation results obtained by inverting the data sets separately without spatio-temporal constraints are shown in Figure 15. Note the presence of several artifacts in the difference data computed from the retrieved data sets (Figures 15(e) and 15(f)). Separation results obtained by joint-inversion with spatio-temporal regularization (equation 7) are shown in Figure 16. Note that the STCSI results are cleaner than the unconstrained results. Also, note that residual artifacts present in the unconstrained difference data sets (Figures 15(e) and 15(f)) have been attenuated in the dip-constrained results (Figures 16(e) and 16(f)). Dips estimated from the unconstrained results and used to obtain the constrained results are shown in Figure 17.

4d-or-1 4d-or-2
4d-or-1,4d-or-2
Figure 13.
Simultaneous-source data sets comprising shot-records from two sources (S1 and S2) over a segment of the model in Figure 1(b). Note that the survey parameters in (a) survey 1 are different from those of (b) survey two. If not taken into account, this discrepancy (non-repeatability) will affect the quality of the time-lapse (difference) data and the resulting estimate of reservoir property change.
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4d-1 4d-2 4d-3 4d-4 4d-1-diff 4d-2-diff
4d-1,4d-2,4d-3,4d-4,4d-1-diff,4d-2-diff
Figure 14.
Single-source data that would have been recorded for (a & b) survey 1, and (c & d) survey 2 over a segment of the model in Figure 1(a); and the difference between the two surveys (e & f). The left panel represents data from source 1, whereas the right panel represents source 2. These shot records (a - d) are the components of the two data sets shown in Figure 13. Note that because there is no production-related change between the surveys, the bottom panels are blank.
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4d-hb-1 4d-hb-3 4d-hb-2 4d-hb-4 4d-hb-1-diff 4d-hb-2-diff
4d-hb-1,4d-hb-3,4d-hb-2,4d-hb-4,4d-hb-1-diff,4d-hb-2-diff
Figure 15.
Shot gathers recovered by independent sparse inversion for (a & b) survey 1, and (c & d) survey 2; and the difference between the two surveys (e & f). The left panel represents data from source 1, whereas the right panel represents source 2. Note that the recovered data from the two surveys (top and middle panels) contain several artifacts. Also, note that due to the non-repeatability of the two surveys, the difference data (bottom panels) contain several artifacts.
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4d-reg-1 4d-reg-3 4d-reg-2 4d-reg-4 4d-reg-1-diff 4d-reg-2-diff
4d-reg-1,4d-reg-3,4d-reg-2,4d-reg-4,4d-reg-1-diff,4d-reg-2-diff
Figure 16.
Shot gathers recovered by spatio-temporal constrained sparse inversion for (a & b) survey 1, and (c & d) survey 2; and the difference between the two surveys (e & f). The left panel represents data from source 1, whereas the right panel represents source 2. Note that the residual artifacts present in the unconstrained inversion results, in both the separated and difference data (Figure 15), have been attenuated by STCSI.
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4d-dip-1 4d-dip-2
4d-dip-1,4d-dip-2
Figure 17.
Local dips (common-offset components) for (a) source 1 and (b) source 2 obtained from unconstrained inversion results (Figure 15), and used to obtain the STCSI results (Figure 16). Because there was no change between surveys, each panel was computed as the average of the local dip estimates for the two surveys.
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Next: Discussion Up: Examples Previous: Example 2: Separation of

2010-11-26