The design of visco-acoustic weighted L₁-error frequency–space wavefield extrapolators

Seismic imaging is an important step for imaging the subsurface structures of the Earth. One of the attractive domains for seismic imaging is explicit frequency–space (f – x) prestack depth migration. So far, this domain focused on migrating seismic data in acoustic media, but very little work assumed visco-acoustic media. In reality, seismic exploration data amplitudes suffer from attenuation. To tackle the problem of attenuation, new operators are required, which compensates for it. We propose the weighted L₁-error minimisation technique to design visco-acoustic f – x wavefield extrapolators. The L₁-error wavenumber responses provide superior extrapolator designs as compared with the previously designed equiripple L₄-norm and L_∞-norm extrapolation wavenumber responses. To verify the new compensating designs, prestack depth migration is performed on the challenging Marmousi model dataset. A reference migrated section is obtained using non-compensating f – x extrapolators on an acoustic dataset. Then, both compensating and non-compensating extrapolators are applied to a visco-acoustic dataset, and both migrated sections are then compared. The final images show that the proposed weighted L₁-error method enhances the resolution and results in practically stable images.