Unsupervised deconvolution in migrated section from field data

In the sequence of the tests, we applied the deconvolution algorithms to the trace of the migrated section corresponding to the well location shown in Figure 30. The results are shown in Figure 54 and in Table 3, where the Pearson’s correlations of the outputs of the deconvolution algorithms and the reflectivity estimated from the well logs are displayed. In the tests with field data, we used a LPF whose passband has highest frequency of and stopband has lowest frequency of , where the use of LPF is indicated. As a reference, a supervised LS deconvolution filter, as described in Figure 18 in subsection 2.2, was also calculated from the migrated trace and the reflectivity estimated from the well logs. As shown in Table 3, the super-vised LS deconvolution filter produced the output with the largest correlation, which was ex-pected, as the supervised method takes into account the estimated reflectivity information in or-der to obtain the filter, in contrast to the unsupervised methods, which only use the information obtained from the seismic trace. Despite this difference, if we compare the supervised and B-ICA + LS inverse filter + LPF outputs in Figure 54, we observe that both outputs present similar fea-tures, except for the use of PEF. Also, Table 3 shows that the PEF+LPF approach presents a low correlation, in fact lower than the original trace, which indicates that this approach introduces distortion instead of improvement. The main reason for this is that the wavelet in this case is non-minimum phase. Also, the regular B-ICA also presents a low correlation, while the B-ICA + LS inverse filter + LPF approach present a slight increase of correlation if compared to the original trace.

Figure 54: 1 – Migrated trace. 2 - Reflectivity estimated from well logs. Deconvolved traces: 3 – Supervised LS deconvolution. 4 – B-ICA+LS inverse filter+LPF. 5 - PEF+LPF. 6 – B-ICA.

Table 3: Pearson correlation between the deconvolved traces and the reflectivity when the input is the migrated trace shown in Figure 54.

Minimum phase Migrated trace 53%

Supervised LS 60%

B-ICA+LS+LPF 55%

PEF+LPF 47%

B-ICA 48%

Finally, the devonvolution algorithms were tested on a subset of traces of the migrated section of Figure 30 and the results are displayed in Figure 55. We chose this set of data, as we only had access to the result of this fully processed seismic section, which was ready for seismic interpretation. It is also important to notice that we did not have access to raw data, so we could not interfere with the processing of the migrated image. As in the single trace case, a supervised LS deconvolution filter was calculated from the reflectivity estimated from the well logs and the trace corresponding to the position of the well and the same filter was applied to all traces of the subset assuming that the wavelet does not vary significantly between the traces. A similar ap-proach was used for performing deconvolution with B-ICA + LS inverse filter + LPF. The LS deconvolution filter was calculated using the migrated trace corresponding to the well position and the same filter was applied to all traces of the subset. In the PEF + LPF case, a deconvolution filter was calculated for each trace of the subset and thus each trace was deconvolved with its own filter. It is possible to observe that the PEF+LS approach distorted the image by, e.g., de-stroying the lateral continuity of some reflectors pointed by the yellow arrow in Figure 55(d) and in Figure 56(b). The B-ICA + LS inverse filter + LPF enhanced some regions of the image as in the one indicated by the yellow and green arrows in Figure 55(c), where some reflectors that were hidden or blurred in the original section become visible, as displayed in the zoomed versions in Figure 57 and Figure 58. It was also noticed that lateral continuity was not harmed by the use of the method as in the PEF+LS approach. By comparing the output of the unsupervised method to the supervised LS method, we observe that the images are comparable, but with some differ-ences, such as the reflector pointed by the yellow arrow in Figure 55(b) and Figure 59(a), which is absent in the result of the unsupervised method.

(a) (b)

(c) (d)

Figure 55: (a) Original traces. (b) Output of supervised LS deconvolution. The deconvolution filter was calculated using the reflectivity estimate from the well log and the trace corresponding to its position and was applied to all traces. (c) Deconvolution using B-ICA + LS inverse filter + LPF approach. The deconvolution filter was calculated using the trace corresponding to the well position and was applied to all traces. (d) Deconvolution using PEF + LPF. The deconvolution filter was calculated separately for each trace and then was applied to the respective trace.

(a) (b)

Figure 56: Zoomed versions of Figure 55(a) and Figure 55(d). (a) Shows the original traces, while (b) shows the result of deconvolution using PEF+LPF. The lateral continuity of some re-flectors is lost, as shown in the region pointed by the yellow arrow in (b).

(a) (b)

Figure 57: Zoomed versions of Figure 55(a) and Figure 55(c). (a) shows the original traces, while (b) shows the result of deconvolution using B-ICA+LS inverse filter+LPF approach. Some re-flectors that were hidden or weak in (a) where enhanced in (b) as pointed by the yellow arrow.

Figure 58: Zoomed versions of Figure 55(a) and Figure 55(c). (a) shows the original traces, while (b) shows the result of deconvolution using B-ICA+LS inverse filter+LPF approach. Some re-flectors that were hidden or weak in (a) where enhanced in (b) as pointed by the green arrow.

(a) (b)

Figure 59: Zoomed versions of Figure 55(b) and Figure 55(c). (a) shows the result of deconvolu-tion using the supervised LS approach, while (b) shows the result of deconvoludeconvolu-tion using B-ICA+LS inverse filter+LPF. The reflector pointed by the yellow arrow in (a) is not shown in (b).