Curvelet-based migration preconditioning

In this paper, we introduce a preconditioner for seismic imaging–-i.e., the inversion of the linearized Born scattering operator. This preconditioner approximately corrects for the ‘‘square root’’ of the normal–-i.e., the demigration-migration operator. This approach consists of three parts, namely (i) a left preconditoner, defined by a fractional time integration designed to make the migration operator zero order, and two right preconditioners that apply (ii) a scaling in the physical domain accounting for a spherical spreading, and (iii) a curvelet-domain scaling that corrects for spatial and reflector-dip dependent amplitude errors. We show that a combination of these preconditioners lead to a significant improvement of the convergence for iterative least-squares solutions to the seismic imaging problem based on reverse-time migration operators.