Curvelet‐based migration preconditioning

Abstract

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.