Iterative deblending of simultaneous-source seismic data using seislet-domain shaping regularization

Numerically blended synthetic data - hyperbolic events

Next, we create another synthetic example which contains hyperbolic events without dip conflicts. The unblended and blended data are shown in Figures 6a and 6b, respectively. Figure 7 shows the deblending results for the hyperbolic case. Figure 8 shows the diagrams of changing SNR for one source. In this case, the estimation error for the seislet-domain soft thresholding becomes negligible, mainly owing to the successful dip estimation when constructing the seislet transform. The strength of the $f-x$ predictive filtering also increases and its SNR diagram shows a similar behavior as the $f-k$ domain thresholding. The seislet-based shaping still outperforms the other two approaches. In this case, the percentages we use for $f-k$ domain and seislet domain thresholding are both 9 %, the filter length we use for $f-x$ predictive filtering is 4 samples.

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Figure 6. Numerically blended synthetic data (hyperbolic case). (a) Unblended data. (b) Blended data.

hyperdeblendedfft1,hyperdeblendedslet1,hyperdeblendedfxdecon1,hyperdifffft1,hyperdiffslet1,hyperdifffxdecon1,hypererrorfft1,hypererrorslet1,hypererrorfxdecon1
Figure 7. Deblending comparison for numerically blended synthetic data (hyperbolic case). (a) Deblended result using $f-k$ domain thresholding. (b) Deblended result using seislet-domain thresholding. (c) Deblended result using $f-x$ predictive filtering. (d) Blending noise corresponding to (a). (e) Blending noise corresponding to (b). (f) Blending noise corresponding to (c). (g) Estimation error corresponding to (a). (h) Estimation error corresponding to (b). (i) Estimation error corresponding to (c).

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Figure 8. Diagrams of SNR for synthetic example (hyperbolic case). The "+" line corresponds to seislet-domain thresholding. The "o" line corresponds to $f-k$ domain thresholding. The "*" line corresponds to $f-x$ predictive filtering.

Iterative deblending of simultaneous-source seismic data using seislet-domain shaping regularization