The design of visco‐acoustic weighted L 1 ‐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 L 1 ‐error minimisation technique to design visco‐acoustic f – x wavefield extrapolators. The L 1 ‐error wavenumber responses provide superior extrapolator designs as compared with the previously designed equiripple L 4 ‐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 L 1 ‐error method enhances the resolution and results in practically stable images.