A graphics processing unit implementation of time-domain full-waveform inversion

Marmousi model

We use the Marmousi model for the benchmark test, as shown in the top panel of Figure 6. FWI tacitly requires a good starting model incorporated with low frequency information. 21 shots are deployed as the observations in the FWI, while 3 of them are shown in Figure 7. We use a starting model (bottom panel of Figure 6) obtained by smoothing the original model 20 times with a 5x5 window.

The FWI is carried out for 300 iterations. A 10 Hz Ricker wavelet is deployed in our modeling and inversion. We record all the updated velocity to make sure the velocity refinement is going on during the iterative procedure. The updated velocity model at iterations 1, 20, 50, 100, 180 and 300 is displayed in Figure 8. Figure 9 describes the decreasing misfit function in iterations. As can be seen from the Figures 8 and 9, the velocity model changes significantly at the early stage. Later iterations in FWI make some improvement on small details for the velocity model. More iterations will refine the model further, however, gaining less and less improvement.

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Figure 6. Top: The original Marmousi is downsampled by 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.

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Figure 7. 21 shots were deployed in the FWI. Here, shots 4, 11 and 17 are shown from left to right.

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Figure 8. The updated velocity model at iterations 1, 20, 50, 100, 180 and 300.

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Figure 9. The misfit function decreases with iteration.

A graphics processing unit implementation of time-domain full-waveform inversion