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

Exact reconstruction with saved boundaries

Since we are advocating the wavefield reconstruction method in FWI, the foremost thing is to demonstrate that the boundary saving strategy does not introduce any kind of errors or artifacts for the wavefield to be reconstructed. To attain this goal, we design a constant velocity model: velocity=2000 m/s, $nz=nx=200$ , $\Delta z=\Delta x=5$ m. A 15 Hz Ricker wavelet is taken as the source and is placed at the center of the model. We do the modeling process for 1000 steps with time interval $\Delta t=1$ ms. We record the modeled wavefield snap at 0.28 s and 0.4 s, as shown in the top panels of Figure 4. The figure shows that at time 0.4 s, the wavefield has already spread to the boundaries which absorb most of the reflection energy. In the backward steps, the reconstructed shot snaps at 0.4 s and 0.28 s are also recorded, shown in the bottom panels of Figure 4. As can be seen from the figure, the backward reconstruction starts from the boundaries (bottom left) and gradually recovers the interior wavefield (bottom right).

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Figure 4. Backward reconstruction can be realized using the saved boundaries. Note that no absorbing boundary condition is applied on the top boundary of the model in the forward modeling.

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