A fast butterfly algorithm for generalized Radon transforms |
We now make two synthetic datasets using rectangular sampling , . The first one (Figure 8) has the same range as the previous example (Figure 3), while the second one (Figure 9) doubles the range of time and offset. Results of the fast algorithm are shown in Figures 10 and 11. The purpose of showing these two examples is to demonstrate that the choice of does not depend on the problem size, but rather on the range of parameters -- for the data in Figure 9, one has to increase to preserve the same accuracy (the range of is about 125 for the first dataset, and 250 for the second one).
data-2
Figure 8. 2D synthetic CMP gather. , . s, km. |
---|
data-3
Figure 9. 2D synthetic CMP gather. , . s, km. |
---|
fmod-2
Figure 10. , . Output of the fast butterfly algorithm applied to the synthetic data in Figure 8. , . CPU time: 2.46 s. Ref: CPU time of velocity scan: 21.84 s. Purple curve overlaid is the true slowness. |
---|
fmod-3
Figure 11. , . Output of the fast butterfly algorithm applied to the synthetic data in Figure 9. , . CPU time: 4.35 s. Ref: CPU time of velocity scan: 21.93 s. Purple curve overlaid is the true slowness. |
---|
A fast butterfly algorithm for generalized Radon transforms |