A numerical tour of wave propagation

Numerical results

I use the Marmousi model for the benchmark test, as shown in the top panel of Figure 15. FWI tacitly requires a good starting model incorporated with low frequency information. Therefore, we use a starting model (bottom panel of Figure 15) obtained by smoothing the original model 20 times with a 5x5 window.

The FWI is carried out for 300 iterations. We record all the updated velocity to make sure the velocity refinement is going on during the iterative procedure. The updated velocity model at the iteration 1, 20, 50, 100, 180 and 300 are displyed in Figure 17. Figure 18 presents the decreasing misfit function in iterations. As can be seen from the Figures 17 and 18, the velocity model changes significantly at the early stage. Later iterations in FWI make some improvement on small details for the velocity model.

marm
Figure 15. Top: The original Marmousi is downsampled with a factor of 3 along depth and lateral direction. The shots are generated according to the subsampled Marmousi model. Bottom: The starting model of FWI for Marmousi model, which is obtained by smoothing the original model 20 times with a 5x5 window.

shotsnap
Figure 16. 21 shots were deployed in the FWI. Here, shot 4, 11 and 17 are shown from left to right

vsnap
Figure 17. The updated velocity model at the iteration 1, 20, 50, 100, 180 and 300.

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Figure 18. The misfit function decreases with the iterations.

A numerical tour of wave propagation