Fourier methods of seismic data regularisation

Two Dimensional Plane Wave Example

Next a 2-D synthetic data example was created. A series of plane waves of different dips and frequency contents was used and can be seen in Figure 4, along with the corresponding F-K spectrum in Figure 6. One event is strongly aliased. The input data was regularised using both a standard nonuniform DFT approach and the ALFT algorithm, and the results and F-K spectra can be seen in Figure 5

2dcomp
Figure 4. Input irregular data (a), DFT regularisation result (b) and ALFT regularisation result (c).

2dcompg
Figure 5. Input irregular data (a), DFT regularisation result (b) and ALFT regularisation result (c).

allspec
Figure 6. FK Spectra of the input data (a), data with DFT regularisation (b) and data with ALFT regularisation (c).

It is apparent that the anti-leakage Fourier transform gives more uniform amplitudes and improves event alignmnet when compared to using a nonuniform DFT. Some small artifacts are still induced from multiple Fourier transformations, however these artifacts are not more pronounced than in the DFT case. The spectra show that most of the incoherent noise in the ALFT regularised image is induced from the aliased event, giving a mostly clean spectrum elsewhere. Wrongly dipping events and noise in the corresponding DFT spectrum is significantly reduced in the ALFT spectrum.

Fourier methods of seismic data regularisation