Seismic data interpolation using nonlinear shaping regularization

Field example

The field data is from a marine 2-D common shot gather from a deep water Gulf of Mexico survey. The data is same as that used by Fomel (2002). In the example, we randomly remove 30% of the total traces and apply the same iterative framework as that of the previous synthetic example. The interpolation effect and FK domain spectrum are shown in Figures 5 and 6, respectively. Figures 5c and 5d, 6c and 6d both demonstrate pleasant reconstructions of the normal and faster shaping regularization, but in time-space and frequency-wavenumber domain respectively. Figures 7a and 7b show the error sections using the traditional shaping regularization after 20 iterations and the faster shaping regularization after 10 iterations, respectively. The two error sections are generally the same, indicating an equivalent interapolation performance and a faster convergence of the faster shaping regularization. Figures 7c and7d show the corresponding FK spectrum of the two error sections that are shown in Figures 7a and 7b. The convergence diagrams are shown in Figure 8, which demonstrate a faster convergence of the proposed faster version of shaping regularization. In this field data case, $\alpha$ and $\beta$ are chosen the same values as those of the previous synthetic example.

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Figure 5. Field data demonstration for seismic interpolation using shaping regularization. (a) Original synthetic data. (b) Irregularly sampled section by randomly removing 30% traces. (c) Reconstructed section using shaping regularization after 20 iterations. (d) Reconstructed section using faster shaping regularization with 10 iterations.

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Figure 6. FK domain demonstration corresponding to Figure 5. (a) FK domain for original synthetic data. (b) FK domain for irregularly sampled section. (c) FK domain for reconstructed section using shaping regularization after 20 iterations. (d) FK domain for reconstructed section using faster shaping regularization after 20 iterations.

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Figure 7. Error sections demonstration for field data example. (a) Error section using shaping regularization after 20 iterations. (b) Error section using faster shaping regularization after 10 iterations. (c) FK domain of (a). (d) FK domain of (b).

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Figure 8. The SNR curves with normal and faster shaping regularization in the case of real data. The solid line is for normal shaping regularization and the dashed line is for faster shaping regularization.

Seismic data interpolation using nonlinear shaping regularization