We apply a method to automatically estimate the background velocities using reverse-time migration. The method uses a combination of differential semblance and similarity-index (a.k.a., “semblance” or “stacking-power”) to measure the focusing error in imaging and a nonlinear optimization procedure to obtain the background velocities. A challenge in this procedure is that, for media consisting of complex and strongly refracting velocities, artifacts in the reverse-time migrated image (low-frequency noise) can cause the velocity analysis to diverge. We successfully overcome this issue by applying a simple vertical derivative filter to the image that is input to velocity analysis. The resultant velocity analysis method is tested in two 2D synthetic examples and one 2D field data example. Due to the assumptions inherent to prestack depth migration, the data that are input to velocity analysis must be singly scattered. To apply the method to multiple-rich data, we propose an image-based demultiple method. The method consists of muting events in the subsurface offset common image point gathers constructed with reverse-time migration, and remodeling the data using a kinematic demigration. A field data example shows how the image-based demultiple of the data helps to improve the velocity analysis in the presence of multiple scattering.
In reverse time migration (RTM) or full-waveform inversion (FWI), forward and reverse time propagating wavefields are crosscorrelated in time to form either the image condition in RTM or the misfit gradient in FWI. The crosscorrelation 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.
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