Efficient 3D elastic full-waveform inversion using wavefield reconstruction methods

In reverse time migration (RTM) or full-waveform inversion (FWI), forward and reverse time propagating wave-fields are crosscorrelated in time to form either the image condition in RTM or the misfit gradient in FWI. The cross-correlation condition requires both fields to be available at the same time instants. For large-scale 3D problems, it is not possible, in practice, to store snapshots of the wavefields during forward modeling due to extreme storage requirements. We have developed an approximate wavefield reconstruction method that uses particle velocity field recordings on the boundaries to reconstruct the forward wavefields during the computation of the reverse time wavefields. The method is computationally effective and requires less storage than similar methods. We have compared the reconstruction method to a boundary reconstruction method that uses particle velocity and stress fields at the boundaries and to the optimal checkpointing method. We have tested the methods on a 2D vertical transversely isotropic model and a large-scale 3D elastic FWI problem. Our results revealed that there are small differences in the results for the three methods.