A fast butterfly algorithm for generalized Radon transforms |
We now consider a 2D field seismic gather shown in Figure 15. Its Fourier transform is shown in Figure 16. Due to the comparatively wide frequency bandwidth, cannot be chosen too small (here the range of is about 306). The input sampling sizes are , , while the output sizes are chosen as , . Although this small dataset is not very suitable for showcasing the fast algorithm, our method runs in 6.62 s for , , (Figure 17), still outperforming the velocity scan which takes about 10 s (Figure 18). Note that the simplest interpolation is used in the velocity scan, any other higher order interpolation should take longer computation time.
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Figure 15. 2D field CMP gather. , . s, km. |
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Figure 16. The Fourier transform (absolute value) on time axis of the field data in Figure 15. |
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Figure 17. , . Output of the fast butterfly algorithm applied to the field data in Figure 15. , , . CPU time: 6.62 s. |
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Figure 18. , . Output of the velocity scan applied to the field data in Figure 15. CPU time: 9.91 s. |
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A fast butterfly algorithm for generalized Radon transforms |