Simply denoise: wavefield reconstruction via jittered undersampling

Field data example

The far-offsets of a regularly-sampled shot taken from a real marine dataset are considered. Our model consists of 255 traces separated by 6.25 m. The simulated data are obtained by three-fold undersampling this model either regularly (Figure 11(a)) or optimally-jittered (Figures 11(d)). In both cases, the nominal spatial sampling is 18.75 m. Again, the CRSI algorithm is applied (cf. equation 9). No assumption is made regarding the maximum dip in the data. Figures 11(b) and 11(e) show the CRSI results for the data plotted in Figures 11(a) and 11(d), respectively. Figures 11(c) and 11(f) show the differences scaled by a factor of four between the model and the CRSI results. The signal-to-reconstruction-errors are respectively 12.98 dB and 15.22 dB, which corroborates our observations from the synthetic data example. The performance of wavefield reconstruction by CRSI improves when the input data is optimally-jittered sampled.

rdata_subREG,rcrsi_subREG,dfrcrsi_subREG,rdata_subIRREG,rcrsi_subIRREG,dfrcrsi_subIRREG
Figure 11. Field data example. The original data (not shown) is either (a) regularly or (d) optimally-jittered three-fold undersampled along the spatial coordinate. (b) and (e) are the curvelet reconstructions with sparsity-promoting inversion given data depicted in (a) and (d), respectively. (c) and (f) are differences scaled by a factor of four between the original data and the CRSI results (b) and (e), respectively. The corresponding signal-to-reconstruction-error-ratios are 12.98 dB and 15.22 dB, which corroborates that optimally-jittered undersampling is more favorable than regular undersampling.

Simply denoise: wavefield reconstruction via jittered undersampling