Seismic data interpolation using nonlinear shaping regularization |

In order to test the convergence rate, we first define the measure to estimate the interpolation effect as (Chen et al., 2015):

where denotes the estimated model, and the unit of is . Figure 4 shows the convergence diagrams of normal shaping regularization and faster shaping regularization. It's obvious that the proposed faster version can get a faster convergence.

complex,complex-zero,complex-recon-o,complex-recon
Synthetic example 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 40 iterations. (d) Reconstructed section using faster shaping regularization with 20 iterations.
Figure 1. |
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complex-fk,complex-zerofk,complex-reconfk-o,complex-reconfk
FK domain demonstration corresponding to Figure 1. (a) FK domain for original synthetic data. (b) FK domain for irregularly sampled section. (c) FK domain for reconstructed section using shaping regularization after 40 iterations. (d) FK domain for reconstructed section using faster shaping regularization after 20 iterations.
Figure 2. |
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complex-error-o,complex-error,complex-errorfk,complex-errorfk-o
Error sections demonstration for synthetic example. (a) Error section using shaping regularization after 40 iterations. (b) Error section using faster shaping regularization after 20 iterations. (c) FK domain of (a). (d) FK domain of (b).
Figure 3. |
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SNRs
The SNR curves with normal and faster shaping regularization in the case of synthetic data. The solid line is for normal shaping regularization and the dashed line is for faster shaping regularization.
Figure 4. |
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Seismic data interpolation using nonlinear shaping regularization |

2015-11-24