LAUSR

Abstract Explicit depth frequency–space ( f  −  x ) prestack imaging is an attractive mechanism for seismic imaging. To date, the main focus of this method was data migration assuming an acoustic medium, but until now very little work assumed visco-acoustic media. Real seismic data usually suffer from attenuation and dispersion effects. To compensate for attenuation in a visco-acoustic medium, new operators are required. We propose using the L 1 -norm minimization technique to design visco-acoustic f  −  x extrapolators. To show the accuracy and compensation of the operators, prestack depth migration is performed on the challenging Marmousi model for both acoustic and visco-acoustic datasets. The final migrated images show that the proposed L 1 -norm extrapolation results in practically stable and improved resolution of the images.